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Table of Content06 Counterparty Credit Risk, Collateral and Funding

Damiano Brigo, Massimo Morini & Andrea PallaviciniChapter 1 - Introduction

18 Upstream Petroleum Fiscal and Valuation Modeling in Excel

Ken Kasriel & David Wood Chapter 5 - Abandonment

32 Fixed Income Relative Value AnalysisDoug Huggins & Christian Schaller Chapter 1 - Relative Value

48 The Principles of BankingMoorad Choudhry Chapter 16 - Bank Strategy I: Formulating Strategy and Direction

68 An Introduction to Value-at-Risk5th EditionMoorad Choudhry Chapter 1 - An Introduction to Risk

80 Credit Securitisations and DerivativesDaniel Rösch & Harald Scheule Chapter 1 - Credit Securitizations and Derivatives

88 Mastering IlliquidityThomas Meyer, Peter Cornelius, Christian Diller & Didier Guennoc Chapter 1 - Introduction

102 A Workout in Computational FinanceAndreas Binder & Michael Aichinger Chapter 2 - Binomial Trees

114 Introduction to Private Equity2nd EditionCyril Demaria Chapter 1 - Private Equity as an Economic Driver: A Historical Perspective

136 The Economics of Commodity MarketsJulien Chevallier & Florian Ielpo Chapter 1 - Individual Dynamics: From Trends to Risks

Some of these chapters are from advance uncorrected first proofs and are subject to change.All information and references must be checked against final bound books.

Remember, simply quote promotion code PRMIA when ordering direct through www.wiley.com to receive 40% off!

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Counterparty Credit Risk, Collateral and FundingWith Pricing Cases For All Asset ClassesDamiano Brigo, Massimo Morini & Andrea Pallavicini978-0-470-74846-6 • Hardback • 464 pages • March 2013 Buy Now!

JWBK573-c01 JWBK573-Brigo Printer: Yet to Come February 13, 2013 8:55 Trim: 244mm × 168mm

1

Introduction

This chapter is based on the summary given in Brigo (2011b) [34].In this introductory chapter we present a dialogue that clarifies the main issues dealt with

in the book. This chapter is also a stand-alone informal guide to problems in counterparty riskvaluation and measurement, with references for readers who may wish to pursue further thedifferent aspects of this type of credit risk. Later chapters in the book will provide in-depthstudies of all aspects of counterparty risk.

1.1 A DIALOGUE ON CVA

Although research on counterparty risk pricing started way back in the nineties, with us joiningthe effort back in 2002, the different aspects of counterparty credit risk exploded after the startof the global financial crisis in 2007. In less than four years we have seen the emergence ofa number of features that the market operators are struggling to account for with consistency.Further, the several possible definitions and methodologies for counterparty risk may createconfusion. This dialogue is meant to provide an informal guide to the different aspects ofcounterparty risk. It is in the form of questions and answers between a CVA expert and anewly hired colleague, and provides detailed references for investigating the different areassketched here in more detail.

1.2 RISK MEASUREMENT: CREDIT VaR

Q: [Junior colleague, he is looking a little worried] I am new in this area of counterparty risk,and I am struggling to understand the different measures and metrics. Could you start byexplaining generally what counterparty risk is?

A: [Senior colleague, she is looking at the junior colleague reassuringly.] The risk taken on byan entity entering an Over-The-Counter (OTC) contract with one (or more) counterpartyhaving a relevant default probability. As such, the counterparty might not respect itspayment obligations.

Q: What kind of counterparty risk practices are present in the market?A: Several, but most can be divided into two broad areas. Counterparty risk measurement for

capital requirements, following Basel II, or counterparty risk from a pricing point of view,when updating the price of instruments to account for possible default of the counterparty.However, the distinction is now fading with the advent of Basel III.

Q: [Shifts nervously] Let us disentangle this a little, I am getting confused.A: Fine. Where do we start from?Q: Let us start from Counterparty Risk Measurement for Capital Requirements. What is that?A: It is a risk that one bank faces in order to be able to lend money or invest towards a

counterparty with relevant default risk. The bank needs to cover for that risk by settingcapital aside, and this can be done after the risk has been measured.

Q: You are saying that we aim at measuring that risk?

http://eu.wiley.com/WileyCDA/WileyTitle/productCd-047074846X.html

7


1

Introduction

This chapter is based on the summary given in Brigo (2011b) [34].In this introductory chapter we present a dialogue that clarifies the main issues dealt with

in the book. This chapter is also a stand-alone informal guide to problems in counterparty riskvaluation and measurement, with references for readers who may wish to pursue further thedifferent aspects of this type of credit risk. Later chapters in the book will provide in-depthstudies of all aspects of counterparty risk.

1.1 A DIALOGUE ON CVA

Although research on counterparty risk pricing started way back in the nineties, with us joiningthe effort back in 2002, the different aspects of counterparty credit risk exploded after the startof the global financial crisis in 2007. In less than four years we have seen the emergence ofa number of features that the market operators are struggling to account for with consistency.Further, the several possible definitions and methodologies for counterparty risk may createconfusion. This dialogue is meant to provide an informal guide to the different aspects ofcounterparty risk. It is in the form of questions and answers between a CVA expert and anewly hired colleague, and provides detailed references for investigating the different areassketched here in more detail.

1.2 RISK MEASUREMENT: CREDIT VaR

Q: [Junior colleague, he is looking a little worried] I am new in this area of counterparty risk,and I am struggling to understand the different measures and metrics. Could you start byexplaining generally what counterparty risk is?

A: [Senior colleague, she is looking at the junior colleague reassuringly.] The risk taken on byan entity entering an Over-The-Counter (OTC) contract with one (or more) counterpartyhaving a relevant default probability. As such, the counterparty might not respect itspayment obligations.

Q: What kind of counterparty risk practices are present in the market?A: Several, but most can be divided into two broad areas. Counterparty risk measurement for

capital requirements, following Basel II, or counterparty risk from a pricing point of view,when updating the price of instruments to account for possible default of the counterparty.However, the distinction is now fading with the advent of Basel III.

Q: [Shifts nervously] Let us disentangle this a little, I am getting confused.A: Fine. Where do we start from?Q: Let us start from Counterparty Risk Measurement for Capital Requirements. What is that?A: It is a risk that one bank faces in order to be able to lend money or invest towards a

counterparty with relevant default risk. The bank needs to cover for that risk by settingcapital aside, and this can be done after the risk has been measured.

Q: You are saying that we aim at measuring that risk?


4 Counterparty Credit Risk, Collateral and Funding

A: Indeed, and this measurement will help the bank decide how much capital the bank shouldset aside (capital requirement) in order to be able to face losses coming from possibledefaults of counterparties the bank is dealing with.

Q: Could you make an example of such a measure?A: A popular measure is Value at Risk (VaR). It is basically a percentile on the loss distribution

associated with the position held by the bank, over a given time horizon. More precisely,it is a percentile (say the 99.9th percentile) of the initial value of the position minus thefinal value at the risk horizon, across scenarios.

Q: Which horizon is usually taken?A: When applied to default risk the horizon is usually one year and this is called “Credit VaR

(CrVaR)”. If this is taken at the 99.9-th percentile, then you have a loss that is exceededonly in 1 case out of 1,000. The Credit VaR is either the difference of the percentile fromthe mean, or the percentile itself. There is more than one possible definition.

Q: Is this a good definition of credit risk?A: [Frowning] Well what does “good” really mean? It is not a universally good measure. It

has often been criticized, especially in the context of pure market risk without default,for lack of sub-additivity. In other terms, it does not always acknowledge the benefits ofdiversification, in that in some paradoxical situations the risk of a total portfolio can belarger than the sum of the risks in a single position. A better measure from that point ofview would be expected shortfall, known also as tail VaR, conditional VaR, etc.

Q: And what is that?A: This is loosely defined as the expected value of the losses beyond the VaR point. But this

need not concern us too much at present.Q: Fine. How is Credit VaR typically calculated?A: Credit VaR is calculated through a simulation of the basic financial variables underlying

the portfolio under the historical probability measure, commonly referred to as P , up tothe risk horizon. The simulation also includes the default of the counterparties. At the riskhorizon, the portfolio is priced in every simulated scenario of the basic financial variables,including defaults, obtaining a number of scenarios for the portfolio value at the riskhorizon.

Q: So if the risk horizon is one year, we obtain a number of scenarios for what will be thevalue of the portfolio in one year, based on the evolution of the underlying market variablesand on the possible default of the counterparties.

A: Precisely. A distribution of the losses of the portfolio is built based on these scenarios ofportfolio values. When we say “priced” we mean to say is that the discounted future cashflows of the portfolio, after the risk horizon, are averaged conditional on each scenarioat the risk horizon but under another probability measure, the Pricing measure, or Risk-neutral measure, or Equivalent Martingale measure if you want to go technical, commonlyreferred as Q.

Q: Not so clear . . . [Looks confused]A: [Sighing] All right, suppose your portfolio has a call option on equity, traded with a

corporate client, with a final maturity of two years. Suppose for simplicity there is nointerest rate risk, so discounting is deterministic. To get the Credit VaR, roughly, yousimulate the underlying equity under the P measure up to one year, and obtain a numberof scenarios for the underlying equity in one year. Also, you need to simulate the defaultscenarios up to one year, to know in each scenariowhether the counterparties have defaultedor not. This default simulation up to one year is under the measure P as well. And you

8



A: Indeed, and this measurement will help the bank decide how much capital the bank shouldset aside (capital requirement) in order to be able to face losses coming from possibledefaults of counterparties the bank is dealing with.

Q: Could you make an example of such a measure?A: A popular measure is Value at Risk (VaR). It is basically a percentile on the loss distribution

associated with the position held by the bank, over a given time horizon. More precisely,it is a percentile (say the 99.9th percentile) of the initial value of the position minus thefinal value at the risk horizon, across scenarios.

Q: Which horizon is usually taken?A: When applied to default risk the horizon is usually one year and this is called “Credit VaR

(CrVaR)”. If this is taken at the 99.9-th percentile, then you have a loss that is exceededonly in 1 case out of 1,000. The Credit VaR is either the difference of the percentile fromthe mean, or the percentile itself. There is more than one possible definition.

Q: Is this a good definition of credit risk?A: [Frowning] Well what does “good” really mean? It is not a universally good measure. It

has often been criticized, especially in the context of pure market risk without default,for lack of sub-additivity. In other terms, it does not always acknowledge the benefits ofdiversification, in that in some paradoxical situations the risk of a total portfolio can belarger than the sum of the risks in a single position. A better measure from that point ofview would be expected shortfall, known also as tail VaR, conditional VaR, etc.

Q: And what is that?A: This is loosely defined as the expected value of the losses beyond the VaR point. But this

need not concern us too much at present.Q: Fine. How is Credit VaR typically calculated?A: Credit VaR is calculated through a simulation of the basic financial variables underlying

the portfolio under the historical probability measure, commonly referred to as P , up tothe risk horizon. The simulation also includes the default of the counterparties. At the riskhorizon, the portfolio is priced in every simulated scenario of the basic financial variables,including defaults, obtaining a number of scenarios for the portfolio value at the riskhorizon.

Q: So if the risk horizon is one year, we obtain a number of scenarios for what will be thevalue of the portfolio in one year, based on the evolution of the underlying market variablesand on the possible default of the counterparties.

A: Precisely. A distribution of the losses of the portfolio is built based on these scenarios ofportfolio values. When we say “priced” we mean to say is that the discounted future cashflows of the portfolio, after the risk horizon, are averaged conditional on each scenarioat the risk horizon but under another probability measure, the Pricing measure, or Risk-neutral measure, or Equivalent Martingale measure if you want to go technical, commonlyreferred as Q.

Q: Not so clear . . . [Looks confused]A: [Sighing] All right, suppose your portfolio has a call option on equity, traded with a

corporate client, with a final maturity of two years. Suppose for simplicity there is nointerest rate risk, so discounting is deterministic. To get the Credit VaR, roughly, yousimulate the underlying equity under the P measure up to one year, and obtain a numberof scenarios for the underlying equity in one year. Also, you need to simulate the defaultscenarios up to one year, to know in each scenariowhether the counterparties have defaultedor not. This default simulation up to one year is under the measure P as well. And you


Introduction 5

may want to include the “correlation” between default of the counterparty and underlyingequity, that would allow you to model Wrong Way Risk (WWR). But let us leave WWRaside for a moment.

Q: OK. We simulate under P because we want the risk statistics of the portfolio in thereal world, under the physical probability measure, and not under the so-called pricingmeasure Q.

A: That’s right. And then in each scenario at one year, if the counterparty has defaultedthere will be a recovery value and all else will be lost. Otherwise, we price the calloption over the remaining year using, for example, a Black-Scholes formula. But thisprice is like taking the expected value of the call option payoff in two years, conditionalon each scenario for the underlying equity in one year. Because this is pricing, thisexpected value will be taken under the pricing measure Q, not P . This gives the Black-Scholes formula if the underlying equity follows a Geometric Brownian Motion (GMB)under Q.

Q: So default needs to be simulated only under P? Where do you find such probabilities?A: [Frowning] This is a very difficult question. Often one uses probabilities obtained through

aggregation, like the probability associated to the rating of the counterparty, for example.But this is not very precise. Default of a single firm occurs only once, so determining theP probability through direct historical observation is not possible. . .

Q: [Shifts nervously on the chair]. . .A: [Concentrating] Notice also that in a more refined valuation, youmay also want to take into

account the default probability of the counterparty between 1 and 2 years in valuing thecall option. But this would now be the default probability under Q, not under P , becausethis is pricing. But let us leave this aside for the time being, because this leads directly toCredit Valuation Adjustments (CVA) which we will address later. It would be like sayingthat in one year you compute the option price value by taking into account its CVA.

Q: [Frowning] I think I need to understand this P and Q thing better. For example, how arethe default probabilities under P and Q different?

A: The ones under Q, typically inferred from market prices of credit default swaps (CDS)or corporate bonds, are typically larger than those under the measure P . This has beenobserved a number of times. A comparison of the P and Q loss distributions involved inCollateralized Debt Obligations (CDOs) is carried out in [190].

Q: Somemore acronyms . . . In the meantime, where can I readmore about VaR and ExpectedShortfall (ES)?

A: On a basic technical level you have books like [133], whereas at a higher technical levelyou have books like [147]. For the original Credit VaR framework it is a good idea to havea look at the original “Credit Metrics Technical Document” [121], which is available atdefaultrisk.com.

1.3 EXPOSURE, CE, PFE, EPE, EE, EAD

Q: OK, I have more or less understood Credit VaR and ES. But I also keep hearing the word“Exposure” in a lot of meetings. What is that, precisely?

A: Let me borrow [69]. [Calls up a paper on the screen of her tablet] These are not exactlythe definitions and calculations used in Basel, we would need to go into much more detailfor that, but they are enough to give you a good idea of what’s going on.

9

10



Q: Hopefully . . . [Looks at his senior colleague skeptically]A: [Rolls her eyes] Counterparty exposure at any given future time is the larger figure

between zero and the market value of the portfolio of derivative positions with a coun-terparty that would be lost if the counterparty were to default with zero recovery atthat time.

Q: This is clear.A: Current Exposure (CE) is, obviously enough, the current value of the exposure to a

counterparty. This is simply the current value of the portfolio if positive, and zero otherwise.This is typically the expected value under the pricing measure Q of future cashflows,discounted back at the present time and added up, as seen from the present time, ifpositive, and zero otherwise.

Q: OK, I see.A: Potential Future Exposure (PFE) for a given date is the maximum exposure at that date,

with a high degree of statistical confidence. For example, the 95% PFE is the level ofpotential exposure that is exceeded with only 5% P-probability. The curve of PFE in timeis the potential exposure profile, up to the final maturity of the portfolio of trades with thecounterparty.

Q: Why 95? And what about P and Q.A: Just because [Amused]. On P and Q, let’s talk about that later.Q: .. . .A: PFE is usually computed via simulation: for each future date, the price of the port-

folio of trades with a counterparty is simulated. A P-percentile of the distribution ofexposures is chosen to represent the PFE at the future date. The peak of PFE overthe life of the portfolio is called Maximum Potential Future Exposure (MPFE). PFEand MPFE are usually compared with credit limits in the process of permissioningtrades.

Q: But wait . . . isn’t this what you said about Credit VaR? Because earlier you said..A: [Raising her hand] No, be careful . . . here there is no default simulation involved, only the

portfolio is simulated, not the default of the counterparty. With exposure we answer thequestion: IF default happens, what is going to be the loss?

Q: So in a way we assume that default happens for sure and we check what would be the lossin that case. I see. No default simulation or probabilities here.

A: Good. As we have seen above, with Credit VaR instead we answer the question: what is thefinal loss that is not exceeded with a given P probability, over a given time horizon? Thissecond question obviously involves the inclusion of the default event of the counterpartyin generating the loss.

Q: OK I understand. And that’s it about exposure, isn’t it? [Smiling hopefully]A: By no means! [Amused]Q: How many more acronyms do I have to learn???A: Here you go. Expected Exposure (EE) is the average exposure under the P-measure on

a future date. The curve of EE in time, as the future date varies, provides the expectedexposure profile. Expected Positive Exposure (EPE) is the average EE in time up to agiven future date (for example, for dates during a given year).

Q: Gosh. . .A: And did I mention Exposure at Default (EAD)? This is simply defined as the exposure

valued at the (random future) default time of the counterparty.Q: That’s quite enough! [pulling his hair]

11



Q: Hopefully . . . [Looks at his senior colleague skeptically]A: [Rolls her eyes] Counterparty exposure at any given future time is the larger figure

between zero and the market value of the portfolio of derivative positions with a coun-terparty that would be lost if the counterparty were to default with zero recovery atthat time.

Q: This is clear.A: Current Exposure (CE) is, obviously enough, the current value of the exposure to a

counterparty. This is simply the current value of the portfolio if positive, and zero otherwise.This is typically the expected value under the pricing measure Q of future cashflows,discounted back at the present time and added up, as seen from the present time, ifpositive, and zero otherwise.

Q: OK, I see.A: Potential Future Exposure (PFE) for a given date is the maximum exposure at that date,

with a high degree of statistical confidence. For example, the 95% PFE is the level ofpotential exposure that is exceeded with only 5% P-probability. The curve of PFE in timeis the potential exposure profile, up to the final maturity of the portfolio of trades with thecounterparty.

Q: Why 95? And what about P and Q.A: Just because [Amused]. On P and Q, let’s talk about that later.Q: .. . .A: PFE is usually computed via simulation: for each future date, the price of the port-

folio of trades with a counterparty is simulated. A P-percentile of the distribution ofexposures is chosen to represent the PFE at the future date. The peak of PFE overthe life of the portfolio is called Maximum Potential Future Exposure (MPFE). PFEand MPFE are usually compared with credit limits in the process of permissioningtrades.

Q: But wait . . . isn’t this what you said about Credit VaR? Because earlier you said..A: [Raising her hand] No, be careful . . . here there is no default simulation involved, only the

portfolio is simulated, not the default of the counterparty. With exposure we answer thequestion: IF default happens, what is going to be the loss?

Q: So in a way we assume that default happens for sure and we check what would be the lossin that case. I see. No default simulation or probabilities here.

A: Good. As we have seen above, with Credit VaR instead we answer the question: what is thefinal loss that is not exceeded with a given P probability, over a given time horizon? Thissecond question obviously involves the inclusion of the default event of the counterpartyin generating the loss.

Q: OK I understand. And that’s it about exposure, isn’t it? [Smiling hopefully]A: By no means! [Amused]Q: How many more acronyms do I have to learn???A: Here you go. Expected Exposure (EE) is the average exposure under the P-measure on

a future date. The curve of EE in time, as the future date varies, provides the expectedexposure profile. Expected Positive Exposure (EPE) is the average EE in time up to agiven future date (for example, for dates during a given year).

Q: Gosh. . .A: And did I mention Exposure at Default (EAD)? This is simply defined as the exposure

valued at the (random future) default time of the counterparty.Q: That’s quite enough! [pulling his hair]


Introduction 7

1.4 EXPOSURE AND CREDIT VaR

A: [Looking at the junior colleague in a motherly fashion] OK let’s stop there. Basel IIprovided some rules and approximations explaining how such exposures could be approx-imated and calculated. Notice that the default probabilities are not part of this picture.There is no default simulation here, contrary to Credit VaR.

Q: That’s right, you never mentioned default modelling here.A: Essentially exposuremeasures howmuch you are likely to lose if the counterparty defaults.

With Credit VaR we also add the default probability to the picture and get a final value forthe possible loss inclusive of default probability information.

Q: And why is exposure important?A: Banks use to measure counterparty risk internally using mainly two measures: PFE, which

is mainly used internally to monitor when the credit limits with the counterparties arebreached, and EE, which is used, when combined with other quantities, for the calculationof EAD and the capital requirements due to counterparty risk. This last calculation maycombine exposures with default probabilities and recovery estimates, and it produces anapproximation to Credit VaR, which is used as a capital requirement.

Q: So we go back again to a percentile of the loss under a given risk horizon. What is thepercentile and what is the risk horizon?

A: The risk horizon for this approximation of Credit VaR is typically one year and theconfidence level is 99.9%.

Q: That would seem to be quite safe.A: That seems safe, but the approximations and the assumptions introduced by Basel II to

compute the approximated Credit VaR are not realistic and have been heavily criticized.See the Organization for Economic Co-Operation and Development (OECD) paper [27]for an overview of the problems, some of them also affecting Basel III.

1.5 INTERLUDE: P AND Q

Q: More on P and Q? You keep mentioning these two probability measures as if they wereobvious, but I don’t think they are . . . [Looking worriedly at his senior colleague]

A: [Frowning again] Statistical properties of random objects such as future losses depend onthe probability measure we are using. Under two different probabilities a random variablewill usually have two different expected values, variances, medians, modes, etc.

Q: [Frowning in turn] So you are saying that a future random loss can have a differentdistribution under two different measures, such as P and Q? But what is P and what isQ, and why do they differ?

A: P , the historical or physical probability measure, also called real world probability mea-sure, is the probability measure under which we do historical estimation of financialvariables, econometrics, historical volatility estimation, maximum likelihood estimation,and so forth. When we need to simulate the financial variables up to the risk horizon we areusing statistical techniques under P . When we try to make a prediction of future marketvariables, again, we do it under P .

Q: I guess this is because prediction and risk measurement need to be done with the statisticsof the observed world. But why introduce another probability measure Q? Why is itneeded? [Looking puzzled]

12



A: If instead of simulating financial variables for prediction or riskmeasurement we are tryingto price an option or a financial product, when we price products in a no-arbitrage frame-work, the no-arbitrage theory tells us that we need to take expected values of discountedfuture cash flows under a different probability measure, namely Q.

Q: And how is this Q related to P? [Still puzzled]A: The twomeasures are related by a mathematical relationship that depends on risk aversion,

or market price of risk. In the simplest models the real expected rate of return is given bythe risk-free rate plus the market price of risk times the volatility. Indeed the “expected”return of an asset depends on the probability measure that is used. For example, under Pthe average rate of return of an asset is hard to estimate, whereas under Q one knows thatthe rate of return will be the risk-free rate, since dependence on the real rate of return canbe hedged away through replication techniques. [Starts looking tired]

Q: And why should this be interesting? [Ironic]A: Well, maybe it’s not string theory or non-commutative topology (what did you say you

studied for your PhD?), but the fact that arbitrage-free theory removes uncertainty aboutthe expected rate of return by substituting it with the risk-free rate has been a big incentivein developing derivatives.

Q: Why is working under P so difficult? [Puzzled]A: Determining the real world or P expected return of an asset is difficult, and rightly so, or

else we would all be rich by knowing good estimates of expected returns of all stocks inthe future. [Looks at the window dreamingly]

A: This is a lot to take in. . .Q: Let us say that you use P to the risk horizon and then Q to price the portfolio at the risk

horizon.A: I think I am starting to get a grip on this. So let me ask: What is “Basel”?Q: A city in Switzerland?A: Ha ha, very funny. . .

1.6 BASEL

A: OK seriously . . . [pulls her tablet and visualizes a PDF document, handing the tablet to herjunior colleague] “Basel II” is a set of recommendations on banking regulations issued bythe Basel Committee on Banking Supervision. The “II” is because this is a second set ofrules, issued in 2004 and later on updated, following Basel I, the first set, issued in 1998.Basel II was introduced to create a standard that regulators could use to establish howmuch capital a bank needs to set aside to cover financial and operational risks connectedto its lending and investing activities. Banks are often willing to employ as much capitalas possible, and so the more the reserves can be reduced while still covering the risks, thebetter for the banks. In other words, banks often aim at reducing the capital requirements(i.e. the amounts to be set aside) to the minimum. Among Basel II purposes, the two mostinteresting for us are:

– Improve capital requirements by aligning them more with risks and by making themmore risk sensitive;

– Split operational risk and credit risk, quantifying both;

The capital requirements concern overall the three areas of credit – or counterparty –risk, market risk, and operational risks. Here we deal mostly with the first two and in

13



A: If instead of simulating financial variables for prediction or riskmeasurement we are tryingto price an option or a financial product, when we price products in a no-arbitrage frame-work, the no-arbitrage theory tells us that we need to take expected values of discountedfuture cash flows under a different probability measure, namely Q.

Q: And how is this Q related to P? [Still puzzled]A: The twomeasures are related by a mathematical relationship that depends on risk aversion,

or market price of risk. In the simplest models the real expected rate of return is given bythe risk-free rate plus the market price of risk times the volatility. Indeed the “expected”return of an asset depends on the probability measure that is used. For example, under Pthe average rate of return of an asset is hard to estimate, whereas under Q one knows thatthe rate of return will be the risk-free rate, since dependence on the real rate of return canbe hedged away through replication techniques. [Starts looking tired]

Q: And why should this be interesting? [Ironic]A: Well, maybe it’s not string theory or non-commutative topology (what did you say you

studied for your PhD?), but the fact that arbitrage-free theory removes uncertainty aboutthe expected rate of return by substituting it with the risk-free rate has been a big incentivein developing derivatives.

Q: Why is working under P so difficult? [Puzzled]A: Determining the real world or P expected return of an asset is difficult, and rightly so, or

else we would all be rich by knowing good estimates of expected returns of all stocks inthe future. [Looks at the window dreamingly]

A: This is a lot to take in. . .Q: Let us say that you use P to the risk horizon and then Q to price the portfolio at the risk

horizon.A: I think I am starting to get a grip on this. So let me ask: What is “Basel”?Q: A city in Switzerland?A: Ha ha, very funny. . .

1.6 BASEL

A: OK seriously . . . [pulls her tablet and visualizes a PDF document, handing the tablet to herjunior colleague] “Basel II” is a set of recommendations on banking regulations issued bythe Basel Committee on Banking Supervision. The “II” is because this is a second set ofrules, issued in 2004 and later on updated, following Basel I, the first set, issued in 1998.Basel II was introduced to create a standard that regulators could use to establish howmuch capital a bank needs to set aside to cover financial and operational risks connectedto its lending and investing activities. Banks are often willing to employ as much capitalas possible, and so the more the reserves can be reduced while still covering the risks, thebetter for the banks. In other words, banks often aim at reducing the capital requirements(i.e. the amounts to be set aside) to the minimum. Among Basel II purposes, the two mostinteresting for us are:

– Improve capital requirements by aligning them more with risks and by making themmore risk sensitive;

– Split operational risk and credit risk, quantifying both;

The capital requirements concern overall the three areas of credit – or counterparty –risk, market risk, and operational risks. Here we deal mostly with the first two and in


Introduction 9

particular with the first. From this capital adequacy point of view, the counterparty riskcomponent can be measured in three different frameworks of increasing complexity, the“standardized approach”, the foundation Internal Rating-Based Approach (IRBA) and theadvanced IRBA. The standardized approach employs conservative measures of capitalrequirements based on very simple calculations and quantities, so that if a bank followsthat approach it is likely to find higher capital requirements than with the IRBA’s. This isan incentive for banks to develop internal models for counterparty risk and credit rating,although the credit crisis that started in 2007 is generating a lot of doubt and debate onthe effectiveness of Basel II and of banking regulation more generally. Basel regulation iscurrently under revision in view of a new set of rules commonly referred to as Basel III.We will get to Basel III later.

Q: Is the Basel accord considered to be effective? Has there been any criticism?A: You really are a rookie, aren’t you? Of course there has been a lot of criticism. Have a

look again at the OECD paper [27], for example.Q: I’ll do that. So, we mentioned above two broad areas: (i) Counterparty risk measurement

for capital requirements, following Basel II, and the related Credit VaR risk measure, or(ii) counterparty risk from a pricing point of view. Basel II then is concerned with thecapital one bank has to set aside in order to lend money or invest towards a counterpartywith relevant default risk, to cover for that risk, and is related to Credit VaR. What aboutthe other area, i.e. pricing?

A: Pricing concerns updating the value of a specific instrument or portfolio, traded with acounterparty, by altering the price to be charged to the counterparty. This modificationin price is done to account for the default risk of the counterparty. Clearly, all thingsbeing equal, we would always prefer entering a trade with a default-free counterpartythan with a default-risky one. Therefore we charge the default-risky one a supplementaryamount besides the default-free cost of the contract. This is often called Credit ValuationAdjustment, or CVA. Since it is a price, it is computed entirely under the Q probabilitymeasure, the pricing measure. In principle, the P probability measure does not play a rolehere. We are computing a price, not measuring risk statistics.

Q: Has this concept been around for a long time or is it recent?A: It has been around for a while see, for example, [101], [18], [47]. However, it became

more and more important after the 2008 defaults.

1.7 CVA AND MODEL DEPENDENCE

Q: But this CVA term, what does it look like?A: It looks like an option on the residual value of the portfolio, with a random maturity given

by the default time of the counterparty.Q: Why an option? How does it originate?A: If the counterparty defaults and the present value of the portfolio at default is positive to

the surviving party, then the surviving party only gets a recovery fraction of the portfoliovalue from the defaulted entity. If, however, the present value is negative to the survivingparty, the surviving party has to pay it in full to the liquidators of the defaulted entity.This creates an asymmetry that, once one has done all calculations, says that the value ofthe deal under counterparty risk is the value without counterparty risk minus a positiveadjustment, called CVA. This adjustment is the price of an option in the above sense. Seeagain [47] for details and a discussion.

14



Q: A price of an option with randommaturity? Looks like a complicated object . . . [frowning]A: [Smiling] It is, and it is good that you realize it. Indeed, it is quite complicated. First of all,

this is complicated because it introduces model dependence, even in products that weremodel independent to start with. Take, for example, a portfolio of plain vanilla swaps. Youdon’t need a dynamic term structure model to price those, but only the curves at the initialtime.

Q: And what happens with CVA?A: Now you have to price an option on the residual value of the portfolio at default of the

counterparty. To price an option on a swap portfolio you need an interest rate optionmodel. Therefore, even if you portfolio valuation was model independent before includingcounterparty risk, now it is model dependent. This means that quick fixes to pricinglibraries are quite difficult to obtain.

Q: I see . . . model dependence . . . and model risk. So, anyway, volatilities and correlationswould impact this calculation?

A: Yes, and dynamics features more generally. Volatilities of the underlying portfolio vari-ables and also of the counterparty credit spreads all impact valuation importantly. Butalso the statistical dependence (or “correlation”) between default of the counterparty andunderlying financial variables, leading to so-called Wrong Way Risk, can be very impor-tant.

Q: Wrong Way Risk? WWR?A: Yes, I am sure you have heard this before.Q: Well I am not sure about WWR, but before we go there hold on a minute, I have another

question.A: [Sighing] Go ahead.

1.8 INPUT AND DATA ISSUES ON CVA

Q: You mentioned volatilities a correlations, but are they easy to measure?A: That is both a very good and important question. No, they are not easy to measure. We

are pricing under the measure Q, so we would need volatilities and correlation extractedfrom traded prices of products that depend on such parameters.

Q: But where can I extract the correlation between a specific corporate counterparty defaultand the underlying of the trade, for example, oil or a specific Foreign Exchange (FX) rate?And where do I extract credit spread volatilities from?

A: [Looks at the young colleague with increased attention] You are not a rookie then if youask such questions, you must have some experience.

Q: [Sighing] Not really . . . I heard such questions at a meeting of the new products committeeyesterday, I was sitting in a corner as the resident newbie, and started thinking about theseissues.

A: [Sighing in turn] Well at least you learn fast. Let me tell you that the situation is actu-ally worse. For some counterparties it is even difficult to find levels for their defaultprobabilities, not to mention expected recoveries.

Q: Aren’t Q default probabilities deduced from Credit Default Swap (CDS) or corporatebond counterparty data?

A: Yes they are . . . in principle. But for many counterparties we do not have a liquid CDSor even a bond, written on them, that is traded. What if your counterparty is the airport

15



Q: A price of an option with randommaturity? Looks like a complicated object . . . [frowning]A: [Smiling] It is, and it is good that you realize it. Indeed, it is quite complicated. First of all,

this is complicated because it introduces model dependence, even in products that weremodel independent to start with. Take, for example, a portfolio of plain vanilla swaps. Youdon’t need a dynamic term structure model to price those, but only the curves at the initialtime.

Q: And what happens with CVA?A: Now you have to price an option on the residual value of the portfolio at default of the

counterparty. To price an option on a swap portfolio you need an interest rate optionmodel. Therefore, even if you portfolio valuation was model independent before includingcounterparty risk, now it is model dependent. This means that quick fixes to pricinglibraries are quite difficult to obtain.

Q: I see . . . model dependence . . . and model risk. So, anyway, volatilities and correlationswould impact this calculation?

A: Yes, and dynamics features more generally. Volatilities of the underlying portfolio vari-ables and also of the counterparty credit spreads all impact valuation importantly. Butalso the statistical dependence (or “correlation”) between default of the counterparty andunderlying financial variables, leading to so-called Wrong Way Risk, can be very impor-tant.

Q: Wrong Way Risk? WWR?A: Yes, I am sure you have heard this before.Q: Well I am not sure about WWR, but before we go there hold on a minute, I have another

question.A: [Sighing] Go ahead.

1.8 INPUT AND DATA ISSUES ON CVA

Q: You mentioned volatilities a correlations, but are they easy to measure?A: That is both a very good and important question. No, they are not easy to measure. We

are pricing under the measure Q, so we would need volatilities and correlation extractedfrom traded prices of products that depend on such parameters.

Q: But where can I extract the correlation between a specific corporate counterparty defaultand the underlying of the trade, for example, oil or a specific Foreign Exchange (FX) rate?And where do I extract credit spread volatilities from?

A: [Looks at the young colleague with increased attention] You are not a rookie then if youask such questions, you must have some experience.

Q: [Sighing] Not really . . . I heard such questions at a meeting of the new products committeeyesterday, I was sitting in a corner as the resident newbie, and started thinking about theseissues.

A: [Sighing in turn] Well at least you learn fast. Let me tell you that the situation is actu-ally worse. For some counterparties it is even difficult to find levels for their defaultprobabilities, not to mention expected recoveries.

Q: Aren’t Q default probabilities deduced from Credit Default Swap (CDS) or corporatebond counterparty data?

A: Yes they are . . . in principle. But for many counterparties we do not have a liquid CDSor even a bond, written on them, that is traded. What if your counterparty is the airport


Introduction 11

of Duckburg? Where are you going to imply default probabilities from, let alone creditvolatilities and credit-underlying “correlations”? And recoveries?

Q: Recoveries, indeed, aren’t those just 0.4? [Grinning]A: [Rolling eyes] Right. Just like that. However, let me mention that when the Q statistics

are not available, a first attempt one can consider is using P-statistics instead. One canestimate credit spread volatility historically if no CDS or corporate bond option impliedvolatility is available. Also historical correlations between the counterparty credit spreadsand the underlying portfolio of the trade can be much easier to access than implied ones.It is clearly an approximation but it is better than no idea at all. Even default probabilities,when not available under Q, may be considered under P and then perhaps adjusted for anaggregate estimate of credit risk premia. Rating information can provide rough aggregatedefault probabilities for entities such as the airport of Duckburg if one has either an internalor external rating for small medium enterprises (SME).

Q: Aren’t there a lot of problems with rating agencies?A: Yes there are, and I am open to better ideas if you have anything to propose.Q: Not easy . . . But leaving aside default probabilities, credit correlations, credit-underlying

correlations, and recoveries. . .A: You are leaving aside quite a lot of material. . .Q: . . . what about the underlying contract Q dynamics, is that clear for all asset classes?A: For a number of asset classes, traditional derivatives markets provide you with underlying

market levels, volatilities and market-market “correlations”. But not always.Q: Can you provide an example where this does not work?

1.9 EMERGING ASSET CLASSES: LONGEVITY RISK

A: Let me think . . . yes, that could be a good example, Longevity Risk.Q: I was never sure how to pronounce that in English.A: It is longevity, [lon-jev-i-tee], as I pronounced it, “ge” like in “George” rather than “get”.Q: Longevity . . . but what kind of risk is that? I wouldn’t mind living a long time, provided

the quality of life is good.A: It is not a risk for you, it is a risk for your pension provider. If you live longer than expected

then the pension fund needs extra funding to keep your pension going.Q: Right [touching the wooden table].A: [Laughing] If you find the name disturbing, we may call it mortality risk. Anyway with

longevity swaps the problem is also finding the underlying Q-dynamics, both in levelsand volatilities, namely levels and volatilities of mortality rates. . .

Q: Wait a minute. Longevity swaps? What is a longevity swap? Sounds like a pact with thedevil for longer life in exchange for your soul or. . .

A: [Raising her hand] Can’t you be professional for a minute? A longevity swap is a contractwhere one party (typically a pension fund) pays a pre-assigned interest rate in exchangefor a floating rate linked to the realized mortality rate in a given country, or area, over apast window of time.

Q: Sorry for the interruptions, OK this makes sense. So I guess the problem is the calibrationof the mortality rate dynamics in pricing the future cash flows of the swap?

A: Indeed, the problem is that for this product there is basically almost no information fromwhich one can deduce the Q dynamics . . . I wonder actually if it even makes sense to

16



talk about Q-dynamics. If swaps were very liquid we could imply a term structure ofmortality rates from the prices, and also possibly implied volatilities if options on theseswaps became liquid.

Q: And I imagine that, being linked to pensions, these contracts have large maturities, so thatcounterparty risk is relevant?

A: Precisely. Now this is an emerging area for counterparty risk, with almost no literature,except the excellent initial paper [21]. In terms of Q-dynamics, a first approach could beto use the P-dynamics and assume there is no market price of risk, at least until the marketdevelops a little further.

Q: Here I think it may be really hard to find data for the statistical dependence between theunderlying mortality rates and the default of the counterparty, which brings us back to thesubject of Wrong Way Risk, on which I have many general questions.

1.10 CVA AND WRONG WAY RISK

A: [Shifting on the chair] Oh I’m sure you do! Let me try and anticipate a few of them.WWR is the additional risk you have when the underlying portfolio and the default of thecounterparty are “correlated” in the worst possible way for you.

Q: For example?A: Suppose you are trading an oil swapwith an airline and you are receiving floating (variable)

oil and paying fixed. We may envisage a positive correlation between the default of theairline and the price of oil, since higher prices of oil will put the airline under more stress tofinance its operations. When the correlation is extremely high, so that at a marked increaseof oil there is a corresponding marked increase in the airline default probability, we havethe worst possible loss at default of the airline. Indeed, with high oil price increases theoil swap now has a much larger value for us, and there is a higher probability of defaultfrom the airline due to the correlation. If the airline defaults now, it will do so in a statewhere the mark-to-market is quite high in our favour, so that we face a large loss. This isan example of wrong way risk.

Q: Has Wrong Way Risk been studied?A: Yes, see, for example, the following references for such issues in different asset classes:

[47], [55], [61], [62] for equity, [57], [58] for interest rates, [36] for commodities (Oil),[43] for Credit Default Swap (CDS).

Q: So there has been literature available on wrong way risk. Going back to the option structureof Credit Valuation Adjustment (CVA), since options are priced under Q, I would guessthat CVA calculations occur mostly under Q. But can one really work only under Q?

A: Before the crisis started in 2007, in a front office environment it had been relativelycommon to work under Q, forgetting about P . One would postulate models for marketprocesses and then calibrate them to prices that are expectations under Q. At that pointsimulations to compute prices of other products as expected values would still be doneunder Q. Similarly, to compute hedge ratios Q used to be enough. P used to be ignoredexcept for risk measurement and possibly stress testing and model validation.

Q: And was this a good thing? [Perplexed]A: [Frowning] It was good because it allowed you to avoid modelling the same processes

under two probability measures, which could be rather tricky, since the real world Pstatistics are often hard to obtain, as we explained above. But on the other hand one

17



talk about Q-dynamics. If swaps were very liquid we could imply a term structure ofmortality rates from the prices, and also possibly implied volatilities if options on theseswaps became liquid.

Q: And I imagine that, being linked to pensions, these contracts have large maturities, so thatcounterparty risk is relevant?

A: Precisely. Now this is an emerging area for counterparty risk, with almost no literature,except the excellent initial paper [21]. In terms of Q-dynamics, a first approach could beto use the P-dynamics and assume there is no market price of risk, at least until the marketdevelops a little further.

Q: Here I think it may be really hard to find data for the statistical dependence between theunderlying mortality rates and the default of the counterparty, which brings us back to thesubject of Wrong Way Risk, on which I have many general questions.

1.10 CVA AND WRONG WAY RISK

A: [Shifting on the chair] Oh I’m sure you do! Let me try and anticipate a few of them.WWR is the additional risk you have when the underlying portfolio and the default of thecounterparty are “correlated” in the worst possible way for you.

Q: For example?A: Suppose you are trading an oil swapwith an airline and you are receiving floating (variable)

oil and paying fixed. We may envisage a positive correlation between the default of theairline and the price of oil, since higher prices of oil will put the airline under more stress tofinance its operations. When the correlation is extremely high, so that at a marked increaseof oil there is a corresponding marked increase in the airline default probability, we havethe worst possible loss at default of the airline. Indeed, with high oil price increases theoil swap now has a much larger value for us, and there is a higher probability of defaultfrom the airline due to the correlation. If the airline defaults now, it will do so in a statewhere the mark-to-market is quite high in our favour, so that we face a large loss. This isan example of wrong way risk.

Q: Has Wrong Way Risk been studied?A: Yes, see, for example, the following references for such issues in different asset classes:

[47], [55], [61], [62] for equity, [57], [58] for interest rates, [36] for commodities (Oil),[43] for Credit Default Swap (CDS).

Q: So there has been literature available on wrong way risk. Going back to the option structureof Credit Valuation Adjustment (CVA), since options are priced under Q, I would guessthat CVA calculations occur mostly under Q. But can one really work only under Q?

A: Before the crisis started in 2007, in a front office environment it had been relativelycommon to work under Q, forgetting about P . One would postulate models for marketprocesses and then calibrate them to prices that are expectations under Q. At that pointsimulations to compute prices of other products as expected values would still be doneunder Q. Similarly, to compute hedge ratios Q used to be enough. P used to be ignoredexcept for risk measurement and possibly stress testing and model validation.

Q: And was this a good thing? [Perplexed]A: [Frowning] It was good because it allowed you to avoid modelling the same processes

under two probability measures, which could be rather tricky, since the real world Pstatistics are often hard to obtain, as we explained above. But on the other hand one


Introduction 13

should really do a combined estimation of a pricing model based on the observed historyof prices. The prices are Q expectations but they move in time, following the evolutionof basic market variables under the P measure. Kalman and more generally non-linearfiltering techniques can be used to obtain a joint estimation of the underlying marketprocesses, which would incorporate market history (P) AND risk-neutral expectations(Q) at the same time. This implicitly estimates also market aversion, connecting P and Q.

Q: So all the attention to counterparty risk now is about P (Credit VaR) or Q (CVA)?A: [Looking at the ceiling] At the moment most attention is on CVA, but now with Basel III

the distinction is blurring.

1.11 BASEL III: VaR OF CVA ANDWRONG WAY RISK

Q: What do you mean? Give me a break! It is already complicated enough!A: Relax. Let us say that Credit VaR measures the risk of losses you face due to the possible

default of some counterparties you are doing business with. CVA measures the pricingcomponent of this risk, i.e. the adjustment to the price of a product due to this risk.

Q: This is clear.A: But now suppose you revalue and mark-to-market CVA in time. Suppose that CVA moves

in time and moves against you, so that you have to book negative losses NOT becausethe counterparty actually defaults, but because the pricing of this risk has changed for theworse for you. So in this sense you are being affected by CVA volatility.

Q: Ah. . .A: To quote Basel III: [Visualizes a document on her tablet]

Under Basel II, the risk of counterparty default and credit migration risk were addressedbut mark-to-market losses due to credit valuation adjustments (CVA) were not. During theglobal financial crisis, however, roughly two-thirds of losses attributed to counterparty creditrisk were due to CVA losses and only about one-third were due to actual defaults.

Q: So in a way the variability of the price of this risk over time has made more damage thanthe risk itself?

A: I guess you could put it that way, yes. This is why Basel is considering setting up quitesevere capital charges against CVA.

Q: And why did you say that this blurs the picture?A: Because, now, you may decide that you need a VaR estimate for your CVA, especially

after the above Basel III statement.Q: How would this be computed?A: You could simulate basic market variables under P , up to the risk horizon. Then, in each

scenario, you price the residual CVA until final maturity using a Q expectation. You putall the prices at the horizon time together in a histogram and obtain a profit and lossdistribution for CVA at the risk horizon. On this P distribution you select a quantile at thechosen confidence level and now you will have computed VaR of CVA. But this does notmeasure the default risk directly, it measures the risk to have a mark-to-market loss dueeither to default or to adverse CVA change in value over time.

Q: . . . while Credit VaR only measures the default risk, i.e. the risk of a loss due to a directdefault of the counterparty. Let’s go back to counterparty risk as a whole now. Where isour focus in all of this?

Upstream Petroleum Fiscal and Valuation Modeling in ExcelA Worked Examples ApproachKen Kasriel & David Wood 978-0-470-68682-9 • Hardback • 370 pages • March 2013 Buy Now!


£100.00 £60.00 / €120.00 €72.20 / $160.00 $96.00

JWBK569-c05 JWBK569-Kasriel Printer: Yet to Come February 20, 2013 17:17 Trim: 244mm × 168mm

5

Abandonment

5.1 INTRODUCTION

Basic Concepts and Terms

As discussed in Chapter 1, abandonment costs are the costs of abandoning wells and facilitiesand cleaning up and restoring the production site after production ends. They are also referredto as “decommissioning” or “site restoration” costs.

Although rules for funding abandonment take many forms, there are two basic kinds of aban-donment regimes. One requires a single “lumpsum” payment at the end of the production.We term this payment an abandonment payment. For any given project, we will alwaysexpress this in the singular. The abandonment payment can occur in the last year of eco-nomic production (or “commercial production” – we use the terms interchangeably) – orsometimes later, if there is a delay between this last year and the actual decommissioningactivity.

The other kind of abandonment regime also requires a single abandonment payment to bemadeat the end of production, but requires – or permits – the payment to be funded in advance,by periodic contributions which the producer makes over the production period, before theactual abandonment payment is due. We term these periodic contributions abandonmentcontributions.

Avoid Double-Counting Cash Outflows

Whenmodeling a regime in which there are no abandonment contributions, but rather only onelumpsum abandonment payment, the payment is counted as a cash outflow from the producer’sperspective, and is discounted accordingly when determining project NPV.

In contrast, whenmodeling a regime inwhich abandonment contributions fund a later abandon-ment payment, it is important to bear in mind that – while we calculate both the contributionsand the payment – we only count the periodic contributions as cash outflows. To count boththe contributions and the payment would be double-counting:

� Once a producer has made an abandonment contribution to an account – either a normalbank account (or a purpose-specific escrow account, trust fund, bond, etc.) – the producermay no longer use it; it is no longer part of the producer’s discretionary cash. Thus the dateswhen contributions are made are when the cash outflows, from the producer’s perspective,occur; these contributions are what are discounted when calculating the producer’s NPV.

http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470686820.html

19


5

Abandonment

5.1 INTRODUCTION

Basic Concepts and Terms

As discussed in Chapter 1, abandonment costs are the costs of abandoning wells and facilitiesand cleaning up and restoring the production site after production ends. They are also referredto as “decommissioning” or “site restoration” costs.

Although rules for funding abandonment take many forms, there are two basic kinds of aban-donment regimes. One requires a single “lumpsum” payment at the end of the production.We term this payment an abandonment payment. For any given project, we will alwaysexpress this in the singular. The abandonment payment can occur in the last year of eco-nomic production (or “commercial production” – we use the terms interchangeably) – orsometimes later, if there is a delay between this last year and the actual decommissioningactivity.

The other kind of abandonment regime also requires a single abandonment payment to bemadeat the end of production, but requires – or permits – the payment to be funded in advance,by periodic contributions which the producer makes over the production period, before theactual abandonment payment is due. We term these periodic contributions abandonmentcontributions.

Avoid Double-Counting Cash Outflows

Whenmodeling a regime in which there are no abandonment contributions, but rather only onelumpsum abandonment payment, the payment is counted as a cash outflow from the producer’sperspective, and is discounted accordingly when determining project NPV.

In contrast, whenmodeling a regime inwhich abandonment contributions fund a later abandon-ment payment, it is important to bear in mind that – while we calculate both the contributionsand the payment – we only count the periodic contributions as cash outflows. To count boththe contributions and the payment would be double-counting:

� Once a producer has made an abandonment contribution to an account – either a normalbank account (or a purpose-specific escrow account, trust fund, bond, etc.) – the producermay no longer use it; it is no longer part of the producer’s discretionary cash. Thus the dateswhen contributions are made are when the cash outflows, from the producer’s perspective,occur; these contributions are what are discounted when calculating the producer’s NPV.

20



� Whereas when the abandonment payment – which is made up of money to which theproducer has already said goodbye – is made later, the payment does flow out of the accountto pay the decommissioning contractor, but this is not an outflow from the producer’sperspective, and is not discounted when calculating project NPV.

The only exceptions to these principles occur if, for whatever reason, the cumulative abandon-ment contributions either are too small to meet the actual abandonment costs, or exceed thosecosts. In these cases, adjustments that do constitute cashflows to the producer are necessary:

� If the abandonment contributions are too small, then the difference, to be made up atabandonment time, will be a cash outflow for the producer.

� If the abandonment contributions exceed requirements, then the difference will constitutea cash inflow for the producer in the form of cash returned, unless regulations state thatthose contributions are already assigned to the government to conduct the abandonmentoperations. Then, surplus funds may not return to the producer.

As the examples in this chapter show how abandonment contributions can be calibrated toensure they match the amount needed for the abandonment payment, we do not treat theseexceptional cases. But you should be aware of them. After all, our examples here are based onforecasts, which are inherently fallible.

How We Will Handle the Economic Limit in This Chapter

An abandonment payment occurs after economic production ends, which in turn depends onthe economic limit, i.e., the last year in which production is economic. As we have seen inChapter 1, determining the economic limit requires its own calculation (i.e., the calculationof the economic limit test, or “ELT”). Because in this chapter we want to concentrate onthe mechanics of calculating abandonment funding, however, here we will simply statethe economic limit as an input assumption. This is of course not sound practice for fulleconomic models, but for these abandonment-focused illustrative models, it allows us to avoidunnecessary, distracting detail.

Thus in this chapter’s models, you will see message boxes, with arrows pointing to input cellsfor the last economic production year, which say “normally this would be calculated,” or wordsto this effect.

This will get our present lessons across, as the calculations we explain here depend on theeconomic limit date, not on whether that date is merely stated or properly calculated. (Justremember that when doing full modeling, the date does need to be properly calculated!)

5.2 LUMPSUM ABANDONMENT PAYMENTS

An example calculation of a lumpsum abandonment payment at the end of production, with noprior abandonment contributions, is shown in the file “Ch5_aband_lumpsum_w inflation.xls.”

21



� Whereas when the abandonment payment – which is made up of money to which theproducer has already said goodbye – is made later, the payment does flow out of the accountto pay the decommissioning contractor, but this is not an outflow from the producer’sperspective, and is not discounted when calculating project NPV.

The only exceptions to these principles occur if, for whatever reason, the cumulative abandon-ment contributions either are too small to meet the actual abandonment costs, or exceed thosecosts. In these cases, adjustments that do constitute cashflows to the producer are necessary:

� If the abandonment contributions are too small, then the difference, to be made up atabandonment time, will be a cash outflow for the producer.

� If the abandonment contributions exceed requirements, then the difference will constitutea cash inflow for the producer in the form of cash returned, unless regulations state thatthose contributions are already assigned to the government to conduct the abandonmentoperations. Then, surplus funds may not return to the producer.

As the examples in this chapter show how abandonment contributions can be calibrated toensure they match the amount needed for the abandonment payment, we do not treat theseexceptional cases. But you should be aware of them. After all, our examples here are based onforecasts, which are inherently fallible.

How We Will Handle the Economic Limit in This Chapter

An abandonment payment occurs after economic production ends, which in turn depends onthe economic limit, i.e., the last year in which production is economic. As we have seen inChapter 1, determining the economic limit requires its own calculation (i.e., the calculationof the economic limit test, or “ELT”). Because in this chapter we want to concentrate onthe mechanics of calculating abandonment funding, however, here we will simply statethe economic limit as an input assumption. This is of course not sound practice for fulleconomic models, but for these abandonment-focused illustrative models, it allows us to avoidunnecessary, distracting detail.

Thus in this chapter’s models, you will see message boxes, with arrows pointing to input cellsfor the last economic production year, which say “normally this would be calculated,” or wordsto this effect.

This will get our present lessons across, as the calculations we explain here depend on theeconomic limit date, not on whether that date is merely stated or properly calculated. (Justremember that when doing full modeling, the date does need to be properly calculated!)

5.2 LUMPSUM ABANDONMENT PAYMENTS

An example calculation of a lumpsum abandonment payment at the end of production, with noprior abandonment contributions, is shown in the file “Ch5_aband_lumpsum_w inflation.xls.”


Abandonment 193

The basic strategy is as follows:

1. To use the economic life flag (ELF) to time the abandonment payment. Recall fromChapter 1 that the ELF is an expression of the economic limit, in the form of a rowof annual 1s and 0s (“a binary flag”), where a 1 means the field is still economic and thus“alive,” and a 0 means it is no longer economic and thus “dead.”

2. To adjust the size of the payment according to an assumed inflation rate.

Refer to the file “Ch5_aband_lumpsum_w inflation.xls,” the Base Scenario of which isreproduced in Figure 5.1, found on page 1 of the file “Ch5_aband_supplement.pdf.”

Our assumptions include:

� a production forecast (before considering the economic limit) in row 4;

� the economic limit in cell D5;

� whether the abandonment payment is paid in the same year as the last economic productionyear, or one year later (cell D7);

� the abandonment payment in Real 2015 $ mm (cell D8) – recall from Chapter 1 that this isthe format in which analysts are most likely to receive abandonment cost estimates; and

� an inflation rate (cell D9), used to convert Real 2015 dollars intoMOD (“money-of-the-day,”or inflated) dollars.

In the Calculations section:

� The formulas in row 11 make the ELF a 1 in the years up to and including the last economicproduction year (cell D5, or 2021 in our Base Scenario example), and a 0 in the yearsthereafter. We have named the range F11:N11, “ELF”.

� Post-ELF production in each year (row 13) equals pre-ELF production (row 4) times theELF; this has the effect of truncating post-ELF production, in our example, to end in 2021.

� The timing of the abandonment payment is calculated in cell D14 as the sum of the lasteconomic production year (cell D5) and any delay in making the abandonment payment(cell D7; or one year, in our example, meaning the payment will occur in 2022).

� The formulas in row 15 place the abandonment payment, in Real 2015 dollars (Real 2015$50 mm in our example), in time according to the result in cell D14.

� The MOD dollar abandonment payment in row 17 (MOD $60.2 mm, in our example) isthe inflated version of the results in row 15, calculated using a mid-year inflation index, asdescribed in Section 1.2 of Chapter 1.

Split the screen so that the spinners which control the last production year, the abandonmentpayment delay factor and the inflation rate are visible at the top of the screen, and the interactivechart starting in row 27 (reproduced in Figure 5.2) is visible at the bottom. This will show youthat the model is working as it should.

22



––––––

(60.2)

–

(80)(60)(40)(20)

–20406080

100

2024202320222021202020192018201720162015

Abandonment payment (MOD $mm)Production (mm bbl)

Economic cutoff: 20211 yr. payment delay

Inflation: 2.5%

Abandonment payment (MOD $mm) & economic production (mm bbl)

Figure 5.2 Basic lumpsum abandonment calculation, from the file “Ch5_aband_lumpsum_w infla-tion.xls”Note: Reflects the Base Scenario settings.

(Note that the scale on the Y-axis (from −80 to 100) is in MOD $ mm when referring to thegray column, and is in mm bbl when referring to the black diamonds.)

Does production respond properly to changes in the economic limit? Does the payment timing?Does it make sense that the earlier the payment occurs, the lower its value is?

5.3 EQUAL ABANDONMENT CONTRIBUTIONS MADE OVERTHE PRODUCTION PERIOD

Asmentioned, producers are often required to fund the abandonment payment through periodicabandonment contributions, made prior to the actual decommissioning. According to one basicvariant of this approach, the contributions must be the same size, and must be made each yearof the economic production period.

It is important, in both this and the following sections, to clarify the term “production period.”In an annual model, we define the economic production period as all years starting fromthe first year in which there is economic production, through the last year in which there iseconomic production, inclusive.

This might sound obvious, but we spell this out to emphasize that the economic productionperiod is not defined simply as any period during which economic production occurs, becausethis definition would then exclude any intervening production “gap period(s)” during whichthere is no production, due to maintenance or some other interruption. (Granted, in an annualmodel, any year-long production gap(s) would be very unusual; nonetheless, it is good practiceto make the model robust enough to handle them.)

23



––––––

(60.2)

–

(80)(60)(40)(20)

–20406080

100

2024202320222021202020192018201720162015

Abandonment payment (MOD $mm)Production (mm bbl)

Economic cutoff: 20211 yr. payment delay

Inflation: 2.5%

Abandonment payment (MOD $mm) & economic production (mm bbl)

Figure 5.2 Basic lumpsum abandonment calculation, from the file “Ch5_aband_lumpsum_w infla-tion.xls”Note: Reflects the Base Scenario settings.

(Note that the scale on the Y-axis (from −80 to 100) is in MOD $ mm when referring to thegray column, and is in mm bbl when referring to the black diamonds.)

Does production respond properly to changes in the economic limit? Does the payment timing?Does it make sense that the earlier the payment occurs, the lower its value is?

5.3 EQUAL ABANDONMENT CONTRIBUTIONS MADE OVERTHE PRODUCTION PERIOD

Asmentioned, producers are often required to fund the abandonment payment through periodicabandonment contributions, made prior to the actual decommissioning. According to one basicvariant of this approach, the contributions must be the same size, and must be made each yearof the economic production period.

It is important, in both this and the following sections, to clarify the term “production period.”In an annual model, we define the economic production period as all years starting fromthe first year in which there is economic production, through the last year in which there iseconomic production, inclusive.

This might sound obvious, but we spell this out to emphasize that the economic productionperiod is not defined simply as any period during which economic production occurs, becausethis definition would then exclude any intervening production “gap period(s)” during whichthere is no production, due to maintenance or some other interruption. (Granted, in an annualmodel, any year-long production gap(s) would be very unusual; nonetheless, it is good practiceto make the model robust enough to handle them.)


Abandonment 195

This is important to get right because the number of abandonment contributions equals thenumber of years in the economic production period, not the number of years of economicproduction. For example, if the economic production period is 10 years, and includes one yearof no production, there will be 10 equal abandonment contributions, not nine.

Calculation

Refer to the file “Ch5_aband_eq pmnts over prod life.xls,” the Base Scenario of which isreproduced in Figure 5.3, found on page 3 of the file “Ch5_aband_supplement.pdf.”

As shown in Figure 5.3, the Assumptions section is the same as in the previous model. In theCalculations section, the basic strategy is:

� To use (as in the last example) the ELF (again, the economic life flag) to time the Real $abandonment payment, thereby inflating it to MOD $.

� To define the economic production period, which allows us to:

� divide the MOD $ value of the abandonment payment into the number of years in thisperiod;

� then use this to determine the number, timing and MOD $ value of equal annual aban-donment contributions.

The steps shown in Figure 5.3 are as follows:

� The ELF and the post-ELF production profile (ending in 2021) are calculated straightfor-wardly in rows 10 and 12.

� Each of the annual cells in row 13 use the same formula to determine the first year of theeconomic production period.

� For example, the formula for 2016 (cell G13) is

=IF(AND(G12>0, SUM($E12:F12)=0), year, 0) .

� This means that if production in 2016 (cell G12 ) is greater than 0, AND if the sum ofproduction in all previous years – that is, the sum of cells $E12:F12 – equals 0, then theyear corresponding to G12 is the first year of “non-zero” production; i.e. it is the yearproduction starts.

• When both conditions are met, the result of the formula is the corresponding yearwithin the named range, year (cells F2:N2). Because both conditions are met in ourexample formula in cell G13, the answer in cell G13 is 2016.

• In each of the other annual cells in row13, both conditions are nevermet simultaneouslymet, so the answer in each of these cells is 0.

24



� Therefore, there will only one non-zero value in the annual cells of row 13, and this valuewill be the year of first production. This example’s answer of 2016 is then “captured” incell D13, with the formula =SUM(F13:N13) .

� Note that the annual formulae in row 13 all refer to the blank cell E12. This is intentional.This cell should be kept blank.

� Cell D14 equates the last year of the economic production period to the last economicproduction year as defined in cell D5 (so, 2021), unless there is no economic production atall, in which case the last economic production year is defined as 0. The latter provision isthere in case the model user carelessly changes the production assumptions in row 4 to endbefore the last economic assumption year in cell D5.

� The annual cells in row 15 create binary flags to show whether a given year falls within theeconomic production period (as distinct from showing each year of economic production;as mentioned above, we would not want the model to be “fooled” by any gaps in economicproduction). If the year is between the economic production period start and end years,inclusive, the flag is a 1, meaning the year is within the economic production period;otherwise it is a 0. We will call this formula the Period-flag formula . The period flagsare then summed in cell D15 to give the number of years in the period (six years inthis example).

� The timing of the abandonment payment and its conversion from Real 2015 $ to MOD $are determined in rows 16–19, in the same way as in the example from Section 5.2.

� The MOD $ value of each equivalent annual abandonment contribution is calculated incell D20. It is equal to the MOD $ value of the abandonment payment (cell D19), dividedby the number of years in the economic production period. In our example, this is MOD$60.17mm/ 6=MOD$10.03mm. (Note in cell D20, for example, the use of the Error-trap

expression =IF(D15=0, 0, . . . to suppress errormessages in case total economic productionis 0.)

� Note further that the abandonment payment delay factor of one year (cell D6) will notaffect the timing of the annual abandonment contributions – these occur over each yearof the economic production period, regardless of when the actual abandonment paymentis made.

� The delay factor, however, will affect the equal value of each annual abandonmentcontribution, because this value is based on the MOD $ value of the abandonmentpayment, which, due to inflation, will be lower in early years and higher in lateryears.

� The formulas in the annual cells in row 21 calculate the abandonment contributions as thevalue reached in cell D20, times the relevant year’s economic production period flag (inrow 15). The result in our example is that payments of MOD $10.03 mm are made between2016 and 2021, inclusive.

� Crucially, note that the checksum formula in cell A21 ensures that the sum of the MOD $abandonment contributions (cell D21) equals the MOD value of the abandonment payment(cell D17). Reaching that result is the point of the whole exercise!

25



� Therefore, there will only one non-zero value in the annual cells of row 13, and this valuewill be the year of first production. This example’s answer of 2016 is then “captured” incell D13, with the formula =SUM(F13:N13) .

� Note that the annual formulae in row 13 all refer to the blank cell E12. This is intentional.This cell should be kept blank.

� Cell D14 equates the last year of the economic production period to the last economicproduction year as defined in cell D5 (so, 2021), unless there is no economic production atall, in which case the last economic production year is defined as 0. The latter provision isthere in case the model user carelessly changes the production assumptions in row 4 to endbefore the last economic assumption year in cell D5.

� The annual cells in row 15 create binary flags to show whether a given year falls within theeconomic production period (as distinct from showing each year of economic production;as mentioned above, we would not want the model to be “fooled” by any gaps in economicproduction). If the year is between the economic production period start and end years,inclusive, the flag is a 1, meaning the year is within the economic production period;otherwise it is a 0. We will call this formula the Period-flag formula . The period flagsare then summed in cell D15 to give the number of years in the period (six years inthis example).

� The timing of the abandonment payment and its conversion from Real 2015 $ to MOD $are determined in rows 16–19, in the same way as in the example from Section 5.2.

� The MOD $ value of each equivalent annual abandonment contribution is calculated incell D20. It is equal to the MOD $ value of the abandonment payment (cell D19), dividedby the number of years in the economic production period. In our example, this is MOD$60.17mm/ 6=MOD$10.03mm. (Note in cell D20, for example, the use of the Error-trap

expression =IF(D15=0, 0, . . . to suppress errormessages in case total economic productionis 0.)

� Note further that the abandonment payment delay factor of one year (cell D6) will notaffect the timing of the annual abandonment contributions – these occur over each yearof the economic production period, regardless of when the actual abandonment paymentis made.

� The delay factor, however, will affect the equal value of each annual abandonmentcontribution, because this value is based on the MOD $ value of the abandonmentpayment, which, due to inflation, will be lower in early years and higher in lateryears.

� The formulas in the annual cells in row 21 calculate the abandonment contributions as thevalue reached in cell D20, times the relevant year’s economic production period flag (inrow 15). The result in our example is that payments of MOD $10.03 mm are made between2016 and 2021, inclusive.

� Crucially, note that the checksum formula in cell A21 ensures that the sum of the MOD $abandonment contributions (cell D21) equals the MOD value of the abandonment payment(cell D17). Reaching that result is the point of the whole exercise!


Abandonment 197

– – – – –(50.0)

12.5 12.5 12.5 12.5 – – – – –

(80) (60) (40) (20)

– 20 40 60 80

100 120

2015 2016 2017 2018 2019 2020 2021 2022 2023 2024

Abandonment contributions (MOD $mm)Abandonment payment (MOD $mm)Production (mm bbl)

Abandonment transactions (MOD $mm) & Economic production (mm bbl)

Inflation: 0%

Economic cutoff: 2019

1 yr. payment delay

Figure 5.4 Implementing Step 5 (with economic cutoff set to 2019) in “Ch5_aband_eq pmnts overprod life.xls”

Visual Check

Arrange the screen so that rows 5–8 are visible, along with the chart starting in row 32,shown in Figure 5.4. (Note that only the white columns represent actual cash outflows fromthe producer’s perspective, as discussed in the subsection “Avoid Double-Counting CashOutflows,” above.) Does the chart behave sensibly when you make the following cumulativechanges?

1. Use the button in row 6 to show the Base Scenario. Scroll the economic limit (cell D5)from 2021 to 2016. (Are the absolute values of the two columns equivalent?)

2. Change the abandonment payment delay (cell D6) from 1 year to 0.3. Set the economic cutoff to 2022.4. Set the abandonment payment delay to 1.5. Set inflation (cell D8) to 0%. These are now Real 2015 dollars. You can easily work out

mentally that the abandonment contributions sum to the abandonment payment, whenthe economic cutoff year is set to 2020, 2019, 2017 or 2016.

Handling Cases with Prior Production, or When Forecasts Change

Be sure to account for any production years/abandonment contributions occurring prior tothe period modeled. Just as such prior production was relevant to our calculation of fiscalmechanisms covered in Chapters 2 and 3, such as royalties and bonuses based on cumulativeproduction, respectively, it matters here as well. This is because prior production determinesthe number of total years in the economic production period, thus influencing the size of eachfuture annual contribution. Contributions already paid also influence the size of each futureannual contribution. We will treat this soon in a new example.

26



Interpret the term “equal contributions” loosely. The size of each contribution equals the totalabandonment payment (in MOD), divided by the number of years in the economic productionperiod. This period, as the name suggests, is based on the economic (post-ELT) productionforecast. Thus, in models where there is no prior production to account for (such as ourlast example), the producer must base the size of each annual contribution on its forecast ofwhen the economic limit will kick in, triggering abandonment. In practice, this forecast willoften change over the course of the field life, as more becomes known about actual costs andproduction capacity, as well as in response to the commodity price outlook. If the forecastof the abandonment date changes once production has started, then the annual contributionsactually made will not be equivalent after all.

To illustrate, suppose that three years after a producer made the model shown in thelast example, the producer decided that the economic limit would actually be in 2020,not 2021 as originally forecast. No other assumptions changed. On page 4 of the file,“Ch5_aband_supplement.pdf”, Figure 5.5, from the file “mod_aband_02_eq pmnts over prodlife_v07b_forecast changes.xls,” shows how this new model, dated January 1, 2018, wouldlook.

Refer to the file “Ch5_aband_eq pmnts over prod life_forecast_changes.xls.” Click the“Show Revised Base Scenario” button in row 8 to obtain the view reproduced inFigure 5.5, found on page 4 of the file “Ch5_aband_supplement.pdf.”

As seen in the model, or in Figure 5.5:

� The years have been divided into two groups: History (columns F–H) and New forecast(columns I–N).

� Historic abandonment contributions have been value-pasted into cells F4:H4. Note thatthese match the forecasts made in cells F21:H21 of the previous model, as seen inFigure 5.3 (they were good forecasts).

� The inflation year numbers for the remaining forecast years (2018–2023) have been adjustedto reflect the new model date of January 1, 2018 in cells I5:N5.

� The economic limit, as mentioned, has been lowered from 2021 to 2020 (cell D7; providedyou have clicked the “Show Revised Base Scenario” button in row 8).

� The remaining number of years (three) of the forecast production period are summed incell D17.

� The rest of the model works exactly as before, except that the historic abandonment contri-butions in cells F4:H4 have been carried down to cells F23:H23. The forecast contributions(cells I23:N23) are still calculated as the value of the Real 2015 $ abandonment payment(inflated to 2021, when it will be made), divided by the number of remaining contributionsto be made (i.e., the number of years remaining in the revised economic production lifeforecast). But now, they each equal MOD $11.49 mm, versus MOD $10.03 mm before.

27



Interpret the term “equal contributions” loosely. The size of each contribution equals the totalabandonment payment (in MOD), divided by the number of years in the economic productionperiod. This period, as the name suggests, is based on the economic (post-ELT) productionforecast. Thus, in models where there is no prior production to account for (such as ourlast example), the producer must base the size of each annual contribution on its forecast ofwhen the economic limit will kick in, triggering abandonment. In practice, this forecast willoften change over the course of the field life, as more becomes known about actual costs andproduction capacity, as well as in response to the commodity price outlook. If the forecastof the abandonment date changes once production has started, then the annual contributionsactually made will not be equivalent after all.

To illustrate, suppose that three years after a producer made the model shown in thelast example, the producer decided that the economic limit would actually be in 2020,not 2021 as originally forecast. No other assumptions changed. On page 4 of the file,“Ch5_aband_supplement.pdf”, Figure 5.5, from the file “mod_aband_02_eq pmnts over prodlife_v07b_forecast changes.xls,” shows how this new model, dated January 1, 2018, wouldlook.

Refer to the file “Ch5_aband_eq pmnts over prod life_forecast_changes.xls.” Click the“Show Revised Base Scenario” button in row 8 to obtain the view reproduced inFigure 5.5, found on page 4 of the file “Ch5_aband_supplement.pdf.”

As seen in the model, or in Figure 5.5:

� The years have been divided into two groups: History (columns F–H) and New forecast(columns I–N).

� Historic abandonment contributions have been value-pasted into cells F4:H4. Note thatthese match the forecasts made in cells F21:H21 of the previous model, as seen inFigure 5.3 (they were good forecasts).

� The inflation year numbers for the remaining forecast years (2018–2023) have been adjustedto reflect the new model date of January 1, 2018 in cells I5:N5.

� The economic limit, as mentioned, has been lowered from 2021 to 2020 (cell D7; providedyou have clicked the “Show Revised Base Scenario” button in row 8).

� The remaining number of years (three) of the forecast production period are summed incell D17.

� The rest of the model works exactly as before, except that the historic abandonment contri-butions in cells F4:H4 have been carried down to cells F23:H23. The forecast contributions(cells I23:N23) are still calculated as the value of the Real 2015 $ abandonment payment(inflated to 2021, when it will be made), divided by the number of remaining contributionsto be made (i.e., the number of years remaining in the revised economic production lifeforecast). But now, they each equal MOD $11.49 mm, versus MOD $10.03 mm before.


Abandonment 199

� The important checksum in cell A23 shows that the sumofMODabandonment contributionsstill matches the value of the MOD abandonment payment.

From row 23, you can see that the revised forecast contributions are equal to each other, butnot to the historic contributions. Also, the total value of theMOD contributions (cell D23) fallsto $54.4 mm from $60.2 in the old model, as the Real $ value of the abandonment payment isexposed to less inflation (due to the shorter time until the abandonment payment is made).1

Usually governments “forgive” such inequality of payments if the producer’s reasons forrevision appear reasonable, as governments are mainly concerned that the producer is makinga good-faith, systematic effort to set aside enough money to fund the abandonment paymentwhen that payment is actually required.

If the forecast of the abandonment date changes, then the onlymodel in which the contributionsare forecast to be equivalent would be the first model, before any revisions.

5.4 UNEQUAL ABANDONMENT CONTRIBUTIONS, BASEDON ANNUAL PRODUCTION AS A PERCENTAGE OF

ULTIMATE PRODUCTION

Unlike the annual contributions we have just seen, annual contributions arising under this kindof abandonment funding regime, which we have seen used in Africa, are not equal. The contri-butions’ value in a given year is based on that year’s production, as a percentage of total eco-nomic production expected (i.e., forecast remaining reserves) over the life of the field, or ulti-mate production. This approach is sometimes referred to as the “unit of productionmethod”.

If, for example, a field’s ultimate production is forecast to be 100mmbbl (ormmb), the value ofthe abandonment payment is MOD $100 mm, and production in Year 1 is 10 mm bbl, the Year1 abandonment contribution payment will be (8 mm bbl/100 mm bbl)*MOD $100 mm =

8%*MOD $100 mm = MOD $8 mm . Thus the more the production in a given year, thehigher the annual contribution. If (as is typical) production starts high and then declines, annualcontributions will do the same, leading to a “frontloading” of abandonment contributions inthe early years. In terms of discounted cashflow, this is not favorable for the producer.

Calculation

The basic calculation strategy is:

� to determine the timing and thus the MOD $ value of the abandonment cost, as we havedone before; and then

� to calculate the annual abandonment contribution for each year of economic production, asjust described above.

1 Do not, incidentally, conclude from this that earlier abandonment payments are necessarily better from the producer’s perspectivethan later ones, as we will discuss later.

28



– – – –

(50.0)

–

16.6 14.1 12.0 7.2 – – – – –

(80)

(60)

(40)

(20)

–

20

40

60

80

100

2015 2016 2017 2018 2019 2020 2021 2022 2023 2024



Inflation: 0%


1 yr. payment delay

Figure 5.6 Frontloaded abandonment contributions, from the file “Ch5_aband_depletion_coeffs.xls,”with model set as described below

Exercise

Try this one yourself. On the “Solution setup” sheet of the file “Ch5_aband_depletion_coeffs.xls” are input assumptions. Set the economic cutoff to 2022, the abandonment pay-ment delay to 0 years and inflation to 2.5%. Then fill in the Calculation section, which willcause results to show up in the chart we have prepared for you starting in row 22. Compare yoursolution for annual abandonment contributions against that provided on the “Solution” sheet.

Now set the economic cutoff to 2019, the payment delay to 1 year and the inflation rate to0%. The chart should look like Figure 5.6, above. Compare it to Figure 5.5, which is basedon the same assumptions. Note the marked “frontloading” of abandonment contributions inFigure 5.6.

5.5 EQUAL ABANDONMENT CONTRIBUTIONS, STARTINGWHEN DEPLETION REACHES A SPECIFIED THRESHOLD

This method is based on depletion, which in a given year equals year-end cumulative produc-tion as a percentage of ultimate economic production. Equal annual contributions start oncedepletion passes a threshold, or “trigger” specified by legislation or contract.

29



– – – –

(50.0)

–

16.6 14.1 12.0 7.2 – – – – –

(80)

(60)

(40)

(20)

–

20

40

60

80

100

2015 2016 2017 2018 2019 2020 2021 2022 2023 2024



Inflation: 0%


1 yr. payment delay

Figure 5.6 Frontloaded abandonment contributions, from the file “Ch5_aband_depletion_coeffs.xls,”with model set as described below

Exercise

Try this one yourself. On the “Solution setup” sheet of the file “Ch5_aband_depletion_coeffs.xls” are input assumptions. Set the economic cutoff to 2022, the abandonment pay-ment delay to 0 years and inflation to 2.5%. Then fill in the Calculation section, which willcause results to show up in the chart we have prepared for you starting in row 22. Compare yoursolution for annual abandonment contributions against that provided on the “Solution” sheet.

Now set the economic cutoff to 2019, the payment delay to 1 year and the inflation rate to0%. The chart should look like Figure 5.6, above. Compare it to Figure 5.5, which is basedon the same assumptions. Note the marked “frontloading” of abandonment contributions inFigure 5.6.

5.5 EQUAL ABANDONMENT CONTRIBUTIONS, STARTINGWHEN DEPLETION REACHES A SPECIFIED THRESHOLD

This method is based on depletion, which in a given year equals year-end cumulative produc-tion as a percentage of ultimate economic production. Equal annual contributions start oncedepletion passes a threshold, or “trigger” specified by legislation or contract.


Abandonment 201

Calculation

Refer to the file “Ch5_aband_cuml_prod_trigger.xls,” which is reproduced in Figure 5.7on page 5 of the file “Ch5_aband_supplement.pdf.”

In our example file, the percentage depletion threshold, or “trigger” for abandonment paymentsto start, is assumed to be 45% (cell D8, which is named “Cuml_prod_trigger”).

Because the calculations shown in Figure 5.7 have many steps in common with the model“Ch5_aband_eq pmnts over prod life.xls” from Section 5.3, we will only treat the new stepshere in detail:

� The economic production period is calculated in rows 14–16 using the first-period andperiod-flag formulas.

� Cumulative economic production in millions of barrels (row 17) is calculated in a waydesigned to fall to and stay at 0 for each year after the end of the economic productionperiod (for reasonswewill explain in aminute). For 2019 (cell J17), for example, the first part(in parentheses) of the formula =(I17 + J13)*J16 is the Standard-accumulation formula,i.e., the cumulative value of the prior year + the annual value of the present year, where, inthis case, I17 and J13 are the cumulative and annual values for 2018 and 2019, respectively.The second part of the formula multiplies the result of the first part by the binary period flagin row 16, so that when the flag returns to 0 after production ends, cumulative productionalso returns a 0.Wewill call this modified formula theTruncated-accumulation formula.2

� Annual cumulative economic production as a percentage of the ultimate total is calculatedin a straightforward way in row 18.

� The abandonment payment is timed and inflated in rows 19–22.

� Another binary flag – this one to show when abandonment contributions are due – is inrow 23. For example, for 2019 (cell J23), this is calculated as =IF(J18>=Cuml prod

trigger, 1, 0) , which means that if cumulative percentage production in 2019 (cell J18)equals or exceeds our specified 45% trigger, the answer is 1, meaning a contribution is due;otherwise, it is 0. In this case, cumulative percentage production is 92%, so the answer is 1.

� The size of each equal contribution is calculated in cell D24, as theMOD$mmabandonmentpayment, divided by the number of payments due. In this example, each payment is MOD$10.77 mm.

� Lastly, the annual abandonment contributions are calculated in row 25, as the size of anyequal payment (cell D24) times the binary flag for the appropriate year in row 23. Thus,in this example, there are five payments of MOD $10.77 mm each, spanning 2017–2021,inclusive.

2 Truncated-accumulation formulas do not have to use a flag, but in this case we already had the flag in row 16 handy, so it is easyenough to use it. Instead of a flag, you could multiply the standard accumulation part of the formula by anything that has the sameeffect. For example, you could rewrite cell the J17 formula, =(I17 + J13)*J16 , as =(I17 + J13)*IF(J13>0, 1, 0) .

30



Now for the reason why, in the second step, we used the truncated-accumulation formula. Wedid so to prevent paying out too many contributions. If we had not done so, and instead hadused the standard-accumulation formula, then cumulative production for 2022–2023 wouldhave been recorded in cells M17:N17 as 327 million barrels. This would have caused 2022–2023 cumulative production, as a percentage of ultimate production, to equal 100% in the rowbelow. This in turn would have resulted in abandonment contributions being flagged as due in2022–2023 (cells M23:N23) and therefore to be paid out as two “extra” contributions of MOD$10.7mmeach (cellsM25:N25). So in this case, the truncated-accumulation formula preventedthis error (saving the producer MOD $21.2 mm in the process).

Visual Check

– – – – – – –

(53.9)

– –– –10.8 10.8 10.8 10.8 10.8

– – ––

31

57

79 92 98 100

(100)

(80)

(60)

(40)

(20)

–

20

40

60

80

100

2015 2016 2017 2018 2019 2020 2021 2022 2023 2024

Abandonment contributions (MOD $mm)Abandonment payment (MOD $mm)

Cuml. Production (% of total)Cumulative production "trigger" (% of ultimate)

Abandonment transactions (MOD $mm) & Cuml. Economic production (% of total)

Inflation: 1%

Economic limit: 2021

1 yr. payment delay

Figure 5.8 Results from depletion threshold-based abandonment regime, from the file “Ch5_aband_cuml_prod_trigger.xls”Note: Results reflect the input assumptions shown in Figure 5.7.

The interactive chart starting on row 37 provides a visual check. It is reproduced in Figure 5.8.

Note that the labels on the Y-axis should be read:

� as MOD $mm, with reference to the white abandonment contribution columns and the grayabandonment payment column;

� as percentages (with a range of 0–100%), with reference to:

� the diamonds signifying cumulative production as a percentage of total ultimate produc-tion (again, bear in mind that once production stops, we make this return to 0%); andto

� the black horizontal line showing the “trigger,” expressed as a percentage of ultimateproduction, for abandonment payments to start. You will only see a white column belowa diamond when the diamond is directly on, or higher than, the trigger line. Play with thetrigger control (cell D8) while watching the chart to see this work.

31



Now for the reason why, in the second step, we used the truncated-accumulation formula. Wedid so to prevent paying out too many contributions. If we had not done so, and instead hadused the standard-accumulation formula, then cumulative production for 2022–2023 wouldhave been recorded in cells M17:N17 as 327 million barrels. This would have caused 2022–2023 cumulative production, as a percentage of ultimate production, to equal 100% in the rowbelow. This in turn would have resulted in abandonment contributions being flagged as due in2022–2023 (cells M23:N23) and therefore to be paid out as two “extra” contributions of MOD$10.7mmeach (cellsM25:N25). So in this case, the truncated-accumulation formula preventedthis error (saving the producer MOD $21.2 mm in the process).

Visual Check

– – – – – – –

(53.9)

– –– –10.8 10.8 10.8 10.8 10.8

– – ––

31

57

79 92 98 100

(100)

(80)

(60)

(40)

(20)

–

20

40

60

80

100

2015 2016 2017 2018 2019 2020 2021 2022 2023 2024

Abandonment contributions (MOD $mm)Abandonment payment (MOD $mm)

Cuml. Production (% of total)Cumulative production "trigger" (% of ultimate)

Abandonment transactions (MOD $mm) & Cuml. Economic production (% of total)

Inflation: 1%

Economic limit: 2021

1 yr. payment delay

Figure 5.8 Results from depletion threshold-based abandonment regime, from the file “Ch5_aband_cuml_prod_trigger.xls”Note: Results reflect the input assumptions shown in Figure 5.7.

The interactive chart starting on row 37 provides a visual check. It is reproduced in Figure 5.8.

Note that the labels on the Y-axis should be read:

� as MOD $mm, with reference to the white abandonment contribution columns and the grayabandonment payment column;

� as percentages (with a range of 0–100%), with reference to:

� the diamonds signifying cumulative production as a percentage of total ultimate produc-tion (again, bear in mind that once production stops, we make this return to 0%); andto

� the black horizontal line showing the “trigger,” expressed as a percentage of ultimateproduction, for abandonment payments to start. You will only see a white column belowa diamond when the diamond is directly on, or higher than, the trigger line. Play with thetrigger control (cell D8) while watching the chart to see this work.

Fixed Income Relative Value AnalysisA Practitioners Guide to the Theory, Tools, and TradesDoug Huggins & Christian Schaller 978-1-118-47719-9 • Hardback • 382 pages • May 2013 Buy Now!


£60.00 £36.00 / €72.00 €43.20 / $100.00 $60.00

CHAPTER 1

Relative Value

The Concept of Relative Value

Relative value is a quantitative analytical approach toward financial marketsbased on two fundamental notions of modern financial economics.

Proposition 1: If two securities have identical payoffs in every future state ofthe world, then they should have identical prices today.

Violation of this principle would result in the existence of an arbitrageopportunity, which is inconsistent with equilibrium in financial markets.

This proposition seems relatively straightforward now, but this wasn’talways the case. In fact, Kenneth Arrow and Gérard Debreu won Nobelprizes in economics in 1972 and 1983 in part for their work establishing thisresult. And Myron Scholes and Robert Merton later won Nobel prizes ineconomics in 1997 for applying this proposition to the valuation of options.In particular, along with Fischer Black, they identified a self-financingportfolio that could dynamically replicate the payoff of an option, and theywere able to determine the value of this underlying option by valuing thisreplicating portfolio.

Most of the financial models discussed in this book are based on theapplication of this proposition in various contexts.

Proposition 2: If two securities present investors with identical risks, theyshould offer identical expected returns.

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1


33

CHAPTER 1

Relative Value

The Concept of Relative Value

Relative value is a quantitative analytical approach toward financial marketsbased on two fundamental notions of modern financial economics.

Proposition 1: If two securities have identical payoffs in every future state ofthe world, then they should have identical prices today.

Violation of this principle would result in the existence of an arbitrageopportunity, which is inconsistent with equilibrium in financial markets.

This proposition seems relatively straightforward now, but this wasn’talways the case. In fact, Kenneth Arrow and Gérard Debreu won Nobelprizes in economics in 1972 and 1983 in part for their work establishing thisresult. And Myron Scholes and Robert Merton later won Nobel prizes ineconomics in 1997 for applying this proposition to the valuation of options.In particular, along with Fischer Black, they identified a self-financingportfolio that could dynamically replicate the payoff of an option, and theywere able to determine the value of this underlying option by valuing thisreplicating portfolio.

Most of the financial models discussed in this book are based on theapplication of this proposition in various contexts.

Proposition 2: If two securities present investors with identical risks, theyshould offer identical expected returns.

c01 11 April 2013; 18:37:54

1

34

This result may appear intuitive, but it’s somewhat more difficult toestablish than the first result. Of particular interest for our purposes is thatthe result can be established via the Arbitrage Pricing Theory, which assumesthe existence of unobservable, linear factors that drive returns.

In this case, it’s possible to combine securities into portfolios that exposeinvestors to any one of the risk factors without involving exposure to any ofthe other risk factors. In the limit, as the number of securities in the portfolioincreases, the security-specific risks can be diversified away. And in this case,any security-specific risk that offered a non-zero expected return wouldpresent investors with an arbitrage opportunity, at least in the limit, as theremaining risk factors could be immunized by creating an appropriateportfolio of tradable securities.

For our purposes, this is a powerful result, as it allows us to analyzehistorical data for the existence of linear factors and to construct portfoliosthat expose us either to these specific factors or to security-specific risks, atour discretion. In fact, principal component analysis (PCA) can be applieddirectly in this framework, and we’ll rely heavily on PCA as one of the twomain statistical models we discuss in this book.

The Sources of Relative Value Opportunities

From these two propositions, it’s clear that the absence of arbitrage is theassumption that drives many of the models we use as relative value analysts.This should come as no surprise, since one of the main roles of a relative valueanalyst is to search for arbitrage opportunities.

But for some people, this state of affairs presents a bit of a paradox. If ourmodeling assumptions are correct about the absence of free lunches, why doanalysts and traders search so hard for them?

This apparent paradox can be resolved with two observations. The first isthe recognition that arbitrage opportunities are rare precisely because hard-working analysts invest considerable effort trying to find them. If theseopportunities could never be found, or if they never generated any profits forthose who found them, analysts would stop searching for them. But in thiscase, opportunities would reappear, and analysts would renew their search forthem as reports of their existence circulated.

The second observation that helps resolve this paradox is that evenseemingly riskless arbitrage opportunities carry some risk when pursued inpractice. For example, one of the simpler arbitrages in fixed income markets is

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2 Introduction

35

This result may appear intuitive, but it’s somewhat more difficult toestablish than the first result. Of particular interest for our purposes is thatthe result can be established via the Arbitrage Pricing Theory, which assumesthe existence of unobservable, linear factors that drive returns.

In this case, it’s possible to combine securities into portfolios that exposeinvestors to any one of the risk factors without involving exposure to any ofthe other risk factors. In the limit, as the number of securities in the portfolioincreases, the security-specific risks can be diversified away. And in this case,any security-specific risk that offered a non-zero expected return wouldpresent investors with an arbitrage opportunity, at least in the limit, as theremaining risk factors could be immunized by creating an appropriateportfolio of tradable securities.

For our purposes, this is a powerful result, as it allows us to analyzehistorical data for the existence of linear factors and to construct portfoliosthat expose us either to these specific factors or to security-specific risks, atour discretion. In fact, principal component analysis (PCA) can be applieddirectly in this framework, and we’ll rely heavily on PCA as one of the twomain statistical models we discuss in this book.

The Sources of Relative Value Opportunities

From these two propositions, it’s clear that the absence of arbitrage is theassumption that drives many of the models we use as relative value analysts.This should come as no surprise, since one of the main roles of a relative valueanalyst is to search for arbitrage opportunities.

But for some people, this state of affairs presents a bit of a paradox. If ourmodeling assumptions are correct about the absence of free lunches, why doanalysts and traders search so hard for them?

This apparent paradox can be resolved with two observations. The first isthe recognition that arbitrage opportunities are rare precisely because hard-working analysts invest considerable effort trying to find them. If theseopportunities could never be found, or if they never generated any profits forthose who found them, analysts would stop searching for them. But in thiscase, opportunities would reappear, and analysts would renew their search forthem as reports of their existence circulated.

The second observation that helps resolve this paradox is that evenseemingly riskless arbitrage opportunities carry some risk when pursued inpractice. For example, one of the simpler arbitrages in fixed income markets is

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2 Introduction

the relation between bond prices, repo rates, and bond futures prices. If abond futures contract is too rich, a trader can sell the futures contract, buy thebond, and borrow the purchase price of the bond in the repo market, with thebond being used as collateral for the loan. At the expiration of the contract,the bond will be returned to the trader by his repo counterparty, and thetrader can deliver the bond into the futures contract. In theory, this wouldallow the trader to make a riskless arbitrage profit. But in practice, there arerisks to this strategy.

For example, the repo counterparty may fail to deliver the bonds to thetrader promptly at the end of the repo transaction, in which case the tradermay have difficulty delivering the bonds into the futures contract. Failure todeliver carries significant penalties in some cases, and the risk of incurringthese penalties needs to be incorporated into the evaluation of this seeminglyriskless arbitrage opportunity.

These perspectives help us reconcile the existence of arbitrage opportu-nities in practice with the theoretical assumptions behind the valuationmodels we use. But they don’t explain the sources of these arbitrage or rel-ative value opportunities, and we’ll discuss a few of the more importantsources here.

Demand for Immediacy

In many cases, relative value opportunities will appear when some traderexperiences an unusually urgent need to transact, particularly in large size.Such a trader will transact his initial business at a price that reflects typicalliquidity in the market. But if the trader then needs to transact additionaltrades in the same security, he may have to entice other market participants toprovide the necessary liquidity by agreeing to transact at a more attractiveprice. For example, he may have to agree to sell at a lower price or to buy at ahigher price than would be typical for that security. In so doing, this trader issignaling a demand for immediacy in trading, and he’s offering a premium toother traders who can satisfy this demand.

The relative value trader searches for opportunities in which he can bepaid attractive premiums for satisfying these demands for immediacy. Heuses his capital to satisfy these demands, warehousing the securities until hecan liquidate them at more typical prices, being careful to hedge the risks ofthe transactions in a cost-effective and prudent manner.

Because these markets are so competitive, the premiums paid forimmediacy are often small relative to the sizes of the positions. As a result, the

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Relative Value 3

36

typical relative value fund will be run with leverage that is higher than theleverage of, say, a global macro fund. Consequently, it’s important to payattention to small details and to hedge risks carefully.

Misspecified Models

It sometimes happens that market participants overlook relevant issues whenmodeling security prices, and the use of misspecified models can result inattractive relative value opportunities for those who spot these errors early.

For example, until the mid-1990s, most analysts failed to incorporate theconvexity bias when assessing the relative valuations of Eurodollar futurescontracts and forward rate agreements. As market participants came to realizethe importance of this adjustment, the relative valuations of these twoinstruments changed over time, resulting in attractive profits for those whoidentified this issue relatively early.

As another example, until the late 1990s, most academics and marketparticipants believed vanilla swap rates exceeded the yields of default-freegovernment bonds as a result of the credit risk of the two swap counter-parties. Due in part to our work in this area, this paradigm has been shown tobe flawed. In particular, the difference over time between LIBOR and reporates now is considered to be a more important factor in the relative valua-tions between swaps and government bonds.

In recent years, as credit concerns have increased for many governments,it has become increasingly important to reflect sovereign credit risk as anexplicit factor in swap spread valuation models, and we discuss this issue inconsiderable detail in this book.

Regulatory Arbitrage

The fixed income markets are populated by market participants of manytypes across many different regulatory jurisdictions, and the regulatory dif-ferences between them can produce relative value opportunities for some.

For example, when thinking about the relative valuations of unsecuredshort-term loans and loans secured by government bonds in the repo market,traders at European banks will consider the fact that the unsecured loan willattract a greater regulatory charge under the Basel accords. On the otherhand, traders working for money market funds in the US won’t be subject tothe Basel accords and are likely to focus instead on the relative credit risks ofthe two short-term deposits. The difference in regulatory treatment mayresult in relative valuations that leave the European bank indifferent between

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4 Introduction

37

typical relative value fund will be run with leverage that is higher than theleverage of, say, a global macro fund. Consequently, it’s important to payattention to small details and to hedge risks carefully.

Misspecified Models

It sometimes happens that market participants overlook relevant issues whenmodeling security prices, and the use of misspecified models can result inattractive relative value opportunities for those who spot these errors early.

For example, until the mid-1990s, most analysts failed to incorporate theconvexity bias when assessing the relative valuations of Eurodollar futurescontracts and forward rate agreements. As market participants came to realizethe importance of this adjustment, the relative valuations of these twoinstruments changed over time, resulting in attractive profits for those whoidentified this issue relatively early.

As another example, until the late 1990s, most academics and marketparticipants believed vanilla swap rates exceeded the yields of default-freegovernment bonds as a result of the credit risk of the two swap counter-parties. Due in part to our work in this area, this paradigm has been shown tobe flawed. In particular, the difference over time between LIBOR and reporates now is considered to be a more important factor in the relative valua-tions between swaps and government bonds.

In recent years, as credit concerns have increased for many governments,it has become increasingly important to reflect sovereign credit risk as anexplicit factor in swap spread valuation models, and we discuss this issue inconsiderable detail in this book.

Regulatory Arbitrage

The fixed income markets are populated by market participants of manytypes across many different regulatory jurisdictions, and the regulatory dif-ferences between them can produce relative value opportunities for some.

For example, when thinking about the relative valuations of unsecuredshort-term loans and loans secured by government bonds in the repo market,traders at European banks will consider the fact that the unsecured loan willattract a greater regulatory charge under the Basel accords. On the otherhand, traders working for money market funds in the US won’t be subject tothe Basel accords and are likely to focus instead on the relative credit risks ofthe two short-term deposits. The difference in regulatory treatment mayresult in relative valuations that leave the European bank indifferent between

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4 Introduction

the two alternatives but that present a relative value opportunity for the USmoney market fund.

The Insights from Relative Value Analysis

In some sense, relative value analysis can be defined as the process of gaininginsights into the relationships between different market instruments and theexternal forces driving their pricing. These insights facilitate arbitrage trading,but they also allow us more generally to develop an understanding of themarket mechanisms that drive valuations and of the ways seemingly differentmarkets are interconnected.

As a consequence, relative value analysis, which originated in arbitragetrading, has a much broader scope of applications. It can reveal the origins ofcertain market relations, the reasons a security is priced a certain way, and therelative value of this pricing in relation to the prices of other securities. And inthe event that a security is found to be misvalued, relative value analysissuggests ways in which the mispricing can be exploited through specifictrading positions. In brief, relative value analysis is a prism through which weview the machinery driving market pricing amidst a multitude of changingmarket prices.

As an example, consider the divergence of swap spreads for GermanBunds and US Treasuries in recent quarters, which might appear inextricablewithout considering the effects of cross-currency basis swaps (CCBS), intra-currency basis swaps (ICBS), and credit default swaps (CDS).

In this case, CCBS spreads widened as a result of the difficulties thatEuropean banks experienced in raising USD liabilities against their USDassets. On the other hand, arbitrage between Bunds, swapped into USD, andTreasuries prevented an excessive cheapening of Bunds versus USD LIBOR.As a consequence, Bunds richened significantly against EURIBOR (seeChapter 14 for more details).

However, given the relationship between European banks and sover-eigns, the difficulties of European banks were also reflected in a widening ofEuropean sovereign CDS levels. Hence, Bunds richened versus EURIBOR atthe same time as German CDS levels increased.

An analyst who fails to consider these interconnected valuation relationsmay find the combination of richening Bunds and increasing German CDSopaque and puzzling. But a well-equipped relative value analyst can disen-tangle these valuation relations explicitly to identify the factors that aredriving valuations in these markets. And armed with this knowledge, the

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Relative Value 5

38

analyst can apply these insights to other instruments, potentially uncoveringadditional relative value opportunities.

The Applications of Relative Value Analysis

Relative value analysis has a number of applications.

Trading

One of the most important applications of relative value analysis is relativevalue trading, in which various securities are bought and others sold with thegoal of enhancing the risk-adjusted expected return of a trading book.

Identifying relatively rich and relatively cheap securities is an importantskill for a relative value trader, but additional skills are required to be suc-cessful as a relative value trader. For example, rich securities can and often dobecome richer, while cheap securities can and often do become cheaper.A successful relative value trader needs to be able to identify some of thereasons that securities are rich or cheap in order to form realistic expectationsabout the likelihood of future richening or cheapening. We discuss this andother important skills throughout this book.

Hedging and Immunization

Relative value analysis is also an important consideration when hedging orotherwise immunizing positions against various risks. For example, consider aflow trader who is sold a position in ten-year (10Y) French governmentbonds by a customer. This trader faces a number of alternatives for hedgingthis risk.

He could try to sell the French bond to another client or to an interdealerbroker. He could sell another French bond with a similar maturity. He couldsell Bund futures contracts or German Bunds with similar maturities. Hecould pay fixed in a plain vanilla interest rate swap or perhaps a euro over-night index average (EONIA) swap. He could buy payer swaptions or sellreceiver swaptions with various strikes. He could sell liquid supranational oragency bonds issued by entities such as the European Investment Bank.Depending on his expectations, he might even sell bonds denominated inother currencies, such as US Treasuries or UK Gilts. Or he might choose toimplement a combination of these hedging strategies.

In devising a hedging strategy, a skilled trader will consider the relativevaluations of the various securities that can be used as hedging instruments.

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6 Introduction

39

analyst can apply these insights to other instruments, potentially uncoveringadditional relative value opportunities.

The Applications of Relative Value Analysis

Relative value analysis has a number of applications.

Trading

One of the most important applications of relative value analysis is relativevalue trading, in which various securities are bought and others sold with thegoal of enhancing the risk-adjusted expected return of a trading book.

Identifying relatively rich and relatively cheap securities is an importantskill for a relative value trader, but additional skills are required to be suc-cessful as a relative value trader. For example, rich securities can and often dobecome richer, while cheap securities can and often do become cheaper.A successful relative value trader needs to be able to identify some of thereasons that securities are rich or cheap in order to form realistic expectationsabout the likelihood of future richening or cheapening. We discuss this andother important skills throughout this book.

Hedging and Immunization

Relative value analysis is also an important consideration when hedging orotherwise immunizing positions against various risks. For example, consider aflow trader who is sold a position in ten-year (10Y) French governmentbonds by a customer. This trader faces a number of alternatives for hedgingthis risk.

He could try to sell the French bond to another client or to an interdealerbroker. He could sell another French bond with a similar maturity. He couldsell Bund futures contracts or German Bunds with similar maturities. Hecould pay fixed in a plain vanilla interest rate swap or perhaps a euro over-night index average (EONIA) swap. He could buy payer swaptions or sellreceiver swaptions with various strikes. He could sell liquid supranational oragency bonds issued by entities such as the European Investment Bank.Depending on his expectations, he might even sell bonds denominated inother currencies, such as US Treasuries or UK Gilts. Or he might choose toimplement a combination of these hedging strategies.

In devising a hedging strategy, a skilled trader will consider the relativevaluations of the various securities that can be used as hedging instruments.

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6 Introduction

If he expects Bunds to cheapen relative to the alternatives, he may chooseto sell German Bunds as a hedge. And if he believes Bund futures are likely tocheapen relative to cash Bunds, he may choose to implement this hedge viafutures contracts rather than in the cash market.

By considering the relative value implications of these hedging alter-natives, a skilled flow trader can enhance the risk-adjusted expected return ofhis book. In this way, the value of the book reflects not only the franchisevalue of the customer flow but also the relative value opportunities in themarket and the analytical skills of the trader managing the book.

Given the increasing competitiveness of running a fixed income flowbusiness, firms that incorporate relative value analysis as part of their businesscan expect to increase their marginal revenues, allowing them to generatehigher profits and/or to offer liquidity to customers at more competitive rates.

Security Selection

In many respects, a long-only investment manager faces many of the sameissues as the flow trader in the previous example. Just as a flow trader canexpect to enhance the risk-adjusted performance of his book by incorporatingrelative value analysis into his hedging choices, a long-only investmentmanager can expect to enhance the risk-adjusted performance of his portfolioby incorporating relative value analysis into his security selection process.

For example, an investment manager who wants to increase his exposureto the 10Y sector of the EUR debt market could buy government bondsissued by France, Germany, Italy, Spain, the Netherlands, or any of the otherEMU member states. Or he could buy Bund futures or receive fixed in aEURIBOR or EONIA interest rate swap. Or he might buy a US Treasury inconjunction with a cross-currency basis swap, thereby synthetically creating aUS government bond denominated in euros.

An investment manager who incorporates relative value analysis as part ofhis investment process is likely to increase his alpha and therefore over time tooutperform an otherwise similar manager with the same beta who doesn’tincorporate relative value analysis.

The Craft of Relative Value Analysis

Relative value analysis is neither a science nor an art. Rather, it’s a craft, withelements of both science and art. For a practitioner to complete the journeyfrom apprentice to master craftsman, he needs to learn to use the tools

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Relative Value 7

40

of the trade, and in this book we introduce these tools along with theirfoundations in the mathematical science of statistics and in the social scienceof financial economics.

We also do our best to explain the practical benefits and potential pitfallsof applying these tools in practice. In the development of an apprentice, thereis no substitute for repeated use of the tools of the trade in the presence of amaster craftsman. But we make every effort in this book to convey the benefitof our experience over many years of applying these tools.

Since financial and statistical models are the tools of the trade for arelative value analyst, it’s important that the analyst choose these toolscarefully, with an eye toward usefulness, analytical scope, and parsimony.

Usefulness

In our view, models are neither right nor wrong. Pure mathematicians may beimpressed by truth and beauty, but the craftsman is concerned with use-fulness. To us, various models have varying degrees of usefulness, dependingon the context in which they’re applied.

As Milton Friedman reminds us in his 1966 essay “The Methodology ofPositive Economics”, models are appropriately judged by their implications.The usefulness of a particular model is not a function of the realism of itsassumptions but rather of the quality of its predictions.

For relative value analysts, models are useful if they allow us to identifyrelative misvaluations between and among securities, and if they improve thequality of the predictions we make about the future richening and cheap-ening of these securities.

For example, we agree with critics who note that the Black–Scholesmodel is wrong, in the sense that it makes predictions about option prices thatare in some ways systematically inconsistent with the prices of options asrepeatedly observed in various markets. However, we’ve found the Black–Scholes model to be useful in many contexts, as have a large number ofanalysts and traders. It’s important to be familiar with its problems andpitfalls, and like most tools it can do damage if used improperly. But werecommend it as a tool of the trade that is quite useful in a number of contexts.

Analytical Scope (Applicability)

For our purposes, it’s also useful for a model to have a broad scope, withapplicability to a wide range of situations. For example, principal componentanalysis (PCA) has proven to be useful in a large number of applications,

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8 Introduction

41

of the trade, and in this book we introduce these tools along with theirfoundations in the mathematical science of statistics and in the social scienceof financial economics.

We also do our best to explain the practical benefits and potential pitfallsof applying these tools in practice. In the development of an apprentice, thereis no substitute for repeated use of the tools of the trade in the presence of amaster craftsman. But we make every effort in this book to convey the benefitof our experience over many years of applying these tools.

Since financial and statistical models are the tools of the trade for arelative value analyst, it’s important that the analyst choose these toolscarefully, with an eye toward usefulness, analytical scope, and parsimony.

Usefulness

In our view, models are neither right nor wrong. Pure mathematicians may beimpressed by truth and beauty, but the craftsman is concerned with use-fulness. To us, various models have varying degrees of usefulness, dependingon the context in which they’re applied.

As Milton Friedman reminds us in his 1966 essay “The Methodology ofPositive Economics”, models are appropriately judged by their implications.The usefulness of a particular model is not a function of the realism of itsassumptions but rather of the quality of its predictions.

For relative value analysts, models are useful if they allow us to identifyrelative misvaluations between and among securities, and if they improve thequality of the predictions we make about the future richening and cheap-ening of these securities.

For example, we agree with critics who note that the Black–Scholesmodel is wrong, in the sense that it makes predictions about option prices thatare in some ways systematically inconsistent with the prices of options asrepeatedly observed in various markets. However, we’ve found the Black–Scholes model to be useful in many contexts, as have a large number ofanalysts and traders. It’s important to be familiar with its problems andpitfalls, and like most tools it can do damage if used improperly. But werecommend it as a tool of the trade that is quite useful in a number of contexts.

Analytical Scope (Applicability)

For our purposes, it’s also useful for a model to have a broad scope, withapplicability to a wide range of situations. For example, principal componentanalysis (PCA) has proven to be useful in a large number of applications,

c01 11 April 2013; 18:37:54

8 Introduction

including interest rates, swap spreads, implied volatilities, and the prices ofequities, grains, metals, energy, and other commodities. As with any powerfulmodel, there is a cost to implementing PCA, but the applicability of the modelonce it has been built means that the benefits of the implementation tend to bewell worth the costs.

Other statistical models with broad applicability are those that charac-terize the mean-reverting properties of various financial variables. Overconsiderable periods of time, persistent mean reversion has been observed inquite a large number of financial variables, including interest rates, curveslopes, butterfly spreads, term premiums, and implied volatilities. And in thecommodity markets, mean reversion has been found in quite a number ofspreads, such as those between gold and silver, corn and wheat, crack spreadsin the energy complexes, and crush spreads in the soybean complex.

The ubiquity of mean-reverting behavior in financial markets means thatmean reversion models have a tremendous applicability. As a result, weconsider them some of the more useful tools of a well-equipped relative valueanalyst, and we discuss them in some detail in this book.

Parsimony

From our perspective, it’s also useful for a model to be parsimonious. AsEinstein articulated in his 1933 lecture “On the Method of TheoreticalPhysics”, “It can scarcely be denied that the supreme goal of all theory is tomake irreducible basic elements as simple and as few as possible withouthaving to surrender the adequate representation of a single datum ofexperience”.

In our context, it’s important to note the relative nature of the word“adequate”. In most circumstances, there is an inevitable trade-off betweenthe parsimony of a model and its ability to represent experience. The goal ofpeople developing models is to improve this tradeoff in various contexts. Thegoal of people using models is to select those models that offer the besttradeoff between costs and benefits in specific applications. And it’s in thatsense that we characterize the models in this book as being useful in thecontext of relative value analysis.

Summary of Contents

Relative value analysis models can be divided into two categories: statisticaland financial. Statistical models require no specific knowledge about the

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Relative Value 9

42

instrument that is being modeled and are hence universally applicable. Forexample, a mean reversion model only needs to know the time series, notwhether the time series represents yields, swap spreads, or volatilities, norwhat drives that time series.

Financial models, on the other hand, give insight into the specific drivingforces and relationships of a particular instrument (and are therefore differentfor each instrument). For example, the specific knowledge that swap spreadsare a function of the cost of equity of LIBOR panel banks can explain whytheir time series exhibits a certain statistical behavior.

While we present the models in two separate categories, comprehensiverelative value analysis combines both. The successful relative value traderdescribed above might first use statistical models to identify which instru-ments are rich and cheap relative to each other, and then apply financialmodels in order to gain insights into the reasons for that richness andcheapness, on which basis he can assess the likelihood for the richness andcheapness to correct. If he sees a sufficient probability for the spread positionto be an attractive trade, he can then use statistical models again to calculate,among others, the appropriate hedge ratios and the expected holding horizon.

Statistical Models

The two types of statistical models presented here are designed to capture twoof the most useful statistical properties frequently observed in the fixedincome markets: the tendency for many spreads to revert toward their longer-run means over time and the tendency for many variables to increaseand decrease together. Chapter 2 and Chapter 3 are largely independent andtherefore do not need to be read sequentially. However, Chapter 3 does referto the application of mean-reverting models to the estimated factors and tospecific residuals, so a reader with no preference would do well to read thechapter on mean reversion first.

Mean ReversionMany financial spreads exhibit a persistent tendency to revert toward theirmeans, providing a potential source of return predictability. In this chapter, wediscuss stochastic processes that are useful in modeling this mean reversion,and we present ways in which data can be used to estimate the parameters ofthese processes. Once the parameters have been estimated, we can calculatethe half-life of a process and make probabilistic statements about the valueof the spread at various points in the future.

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10 Introduction

43

instrument that is being modeled and are hence universally applicable. Forexample, a mean reversion model only needs to know the time series, notwhether the time series represents yields, swap spreads, or volatilities, norwhat drives that time series.

Financial models, on the other hand, give insight into the specific drivingforces and relationships of a particular instrument (and are therefore differentfor each instrument). For example, the specific knowledge that swap spreadsare a function of the cost of equity of LIBOR panel banks can explain whytheir time series exhibits a certain statistical behavior.

While we present the models in two separate categories, comprehensiverelative value analysis combines both. The successful relative value traderdescribed above might first use statistical models to identify which instru-ments are rich and cheap relative to each other, and then apply financialmodels in order to gain insights into the reasons for that richness andcheapness, on which basis he can assess the likelihood for the richness andcheapness to correct. If he sees a sufficient probability for the spread positionto be an attractive trade, he can then use statistical models again to calculate,among others, the appropriate hedge ratios and the expected holding horizon.

Statistical Models

The two types of statistical models presented here are designed to capture twoof the most useful statistical properties frequently observed in the fixedincome markets: the tendency for many spreads to revert toward their longer-run means over time and the tendency for many variables to increaseand decrease together. Chapter 2 and Chapter 3 are largely independent andtherefore do not need to be read sequentially. However, Chapter 3 does referto the application of mean-reverting models to the estimated factors and tospecific residuals, so a reader with no preference would do well to read thechapter on mean reversion first.

Mean ReversionMany financial spreads exhibit a persistent tendency to revert toward theirmeans, providing a potential source of return predictability. In this chapter, wediscuss stochastic processes that are useful in modeling this mean reversion,and we present ways in which data can be used to estimate the parameters ofthese processes. Once the parameters have been estimated, we can calculatethe half-life of a process and make probabilistic statements about the valueof the spread at various points in the future.

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10 Introduction

We also present the concept of a first passage time and show ways tocalculate probabilities for first passage times. Once we have these first passagetime densities, we can provide probabilistic answers to some of the moreperplexing questions that are typical on a trading desk. Over what time periodshould I expect this trade to perform? What sort of return target is reasonable overthe next month? How likely am I to hit a stop-loss if placed at this level? Firstpassage time densities can provide probabilistic answers to these questions,and we discuss practical ways in which they can be implemented in a tradingenvironment.

Principal Component AnalysisMany large data sets in finance appear to be driven by a smaller number offactors, and the ability to reduce the dimensionality of these data sets byprojecting them onto these factors is a very useful method for analyzing andidentifying relative value opportunities. In this chapter we discuss PCA insome detail. We address not only the mathematics of the approach but alsothe practicalities involved in applying PCA in real-world applications,including trading the underlying factors and hedging the factor risk whentrading specific securities.

Financial Models

The financial models in this section are relative value models in that theyvalue one security in relation to one or more other securities. To some extent,the chapters build on one another, with the material for one chapter servingas a starting point for the material in another chapter. For example, thechapter comparing risky bonds denominated in multiple currencies synthe-sizes the material on OIS–repo spreads, ICBS, cross-currency basis swaps,swap spreads, and CDS. Not every chapter needs to be read sequentially, butreaders should be alert to the dependencies that exist between the variouschapters, which we do our best to highlight in the subsequent previews.

Some Comments on Yield, Duration, and ConvexityA working knowledge of bond and interest rate mathematics is a prerequisitefor this book. But we believe some of the basic bond math taught to prac-titioners is simply wrong, or at the very least misleading. For example, thebasis point value of a bond is fundamentally a different concept from the valueof a basis point for a swap, yet many practitioners are unclear about this

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Relative Value 11

44

difference. As another example, the Macaulay duration of a bond is oftenreferred to as the weighted average time to maturity of a bond, but this is onlytrue when all the zero-coupon bonds that constitute the coupon-paying bondhave the same yield, a condition that is almost never observed in practice. Wealso discuss the frequent misuse of bond convexity and suggest a morepractical interpretation of the concept.

Bond Futures ContractsA simple no-arbitrage relation applies to the relative values of a cash bond, therepo rate for the bond, and the forward price of the bond. But governmentbond futures contracts typically contain embedded delivery options, whichcomplicate the analysis. We present a multi-factor model for valuing theembedded delivery option, which can be implemented in a spreadsheet usingbasic stochastic simulation.

LIBOR, OIS Rates, and Repo RatesOvernight index swaps (OIS) are based on unsecured overnight lending rates,whereas repo transactions are secured with collateral. In addition to thedifference in credit risks, the two transactions will be subject to differenttreatment with regard to regulatory capital. We present a simple model forOIS rates that incorporates repo rates, the default probability, the presumedrecovery rate, the risk-weighting of the transaction, the amount of regulatorycapital required for the transaction, and the cost of the regulatory capital.

Intra-currency Basis SwapsFor this purpose, an ICBS is one in which the legs of the swap referencefloating rates are in the same currency but with different maturities. Forexample, one party might agree to pay three-month EURIBOR for five yearsin exchange for receiving six-month EURIBOR less a spread for five years.We present a simple model for valuing these swaps based on the conceptspresented in the OIS–repo model of the preceding section.

Theoretical Determinants of Swap SpreadsUp until the mid-1990s, it was widely believed that swap rates tended to begreater than government bond yields because of the credit risk of the twoswap counterparties. Now, swap spreads are seen to be a function of the

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12 Introduction

45

difference. As another example, the Macaulay duration of a bond is oftenreferred to as the weighted average time to maturity of a bond, but this is onlytrue when all the zero-coupon bonds that constitute the coupon-paying bondhave the same yield, a condition that is almost never observed in practice. Wealso discuss the frequent misuse of bond convexity and suggest a morepractical interpretation of the concept.

Bond Futures ContractsA simple no-arbitrage relation applies to the relative values of a cash bond, therepo rate for the bond, and the forward price of the bond. But governmentbond futures contracts typically contain embedded delivery options, whichcomplicate the analysis. We present a multi-factor model for valuing theembedded delivery option, which can be implemented in a spreadsheet usingbasic stochastic simulation.

LIBOR, OIS Rates, and Repo RatesOvernight index swaps (OIS) are based on unsecured overnight lending rates,whereas repo transactions are secured with collateral. In addition to thedifference in credit risks, the two transactions will be subject to differenttreatment with regard to regulatory capital. We present a simple model forOIS rates that incorporates repo rates, the default probability, the presumedrecovery rate, the risk-weighting of the transaction, the amount of regulatorycapital required for the transaction, and the cost of the regulatory capital.

Intra-currency Basis SwapsFor this purpose, an ICBS is one in which the legs of the swap referencefloating rates are in the same currency but with different maturities. Forexample, one party might agree to pay three-month EURIBOR for five yearsin exchange for receiving six-month EURIBOR less a spread for five years.We present a simple model for valuing these swaps based on the conceptspresented in the OIS–repo model of the preceding section.

Theoretical Determinants of Swap SpreadsUp until the mid-1990s, it was widely believed that swap rates tended to begreater than government bond yields because of the credit risk of the twoswap counterparties. Now, swap spreads are seen to be a function of the

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12 Introduction

spreads between the LIBOR and repo rates over the life of the bond beingswapped. We present this model in detail, incorporating the results of theOIS–repo model and the ICBS model of the preceding sections.

Swap Spreads from an Empirical PerspectiveWhile it’s critical to consider the theoretical determinants of swap spreads, it’salso important to consider swap spreads from an empirical perspective. Inparticular, we examine the crucial link between swap spreads and LIBOR–repo spreads and find considerable empirical support for our conceptualframework. We also consider the role of credit quality in the valuation ofsovereign debt relative to swaps in the aftermath of the subprime andEuropean debt crises of recent years.

Swap Spreads as Relative Value Indicators for Government BondsSwap spreads often have been used to assess the relative valuations betweendifferent bonds along an issuer’s yield curve. We discuss the different waysthis can be done and chronicle the numerous pitfalls that accompany theseapproaches. We conclude that none of these approaches is particularly goodfor assessing relative valuations among bonds, and we suggest using fittedbond curves as an alternative approach.

Fitted Bond CurvesThere are many functional forms that are candidates for fitting yield curves,discount curves, and forward curves. In our experience, the particularfunctional form chosen is less important than the careful selection of thebonds used to fit the curve and the weighting methods used in the calibra-tions. In this chapter, we use a basic but widely used functional form toillustrate the important considerations that should apply when fitting bondcurves. We then discuss the way in which the results can be used to identifyrelatively rich and cheap bonds within particular sectors.

A Brief Comment on Interpolated Swap SpreadsThe most popular structure for trading bonds against swaps is the interpo-lated swap spread, with the end date of the swap set equal to the maturity dateof the bond. While this structure has advantages relative to alternative

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46

structures, it can subject a trader to curve steepening or flattening positions,an issue we discuss in the context of an example.

Cross-Currency Basis SwapsFor our purposes, a CCBS is one in which the two legs are floating ratesdenominated in different currencies. For example, one party might agree topay three-month EURIBOR for five years in exchange for receiving three-month USD LIBOR plus a spread for five years. If the tenor of the swap isless than one year, we typically refer to this as an FX swap, and there are nointermediate interest payments. Because the counterparties exchangeprincipal at the beginning and end of the swap, these swaps have been inconsiderable demand in recent years. We discuss the valuation issues inthis chapter.

Relative Values of Bonds Denominated in Different CurrenciesA fundamental proposition of international financial economics is that inopen and integrated capital markets securities should have the same risk-adjusted expected real return regardless of the currency of denomination.One implication of this is that two otherwise identical bonds, denominatedin different currencies, should have identical yields once one is combinedwith the relevant interest rate swap and relevant basis swaps. We apply thisnotion in the context of global asset selection, by incorporating CCBS in thetechniques for fitting bond curves.

Credit Default SwapsThe time has long since passed that we could assume the existence of default-free sovereign debt. CDS can play a role in assessing and adjusting for thesecredit implications, and in this chapter we review the salient features ofthese instruments.

USD Asset Swap Spreads versus Credit Default SwapsThe swap spread model developed in the preceding section assumed thesovereign bond had no default risk. That assumption has become increasinglyless tenable in the current environment, and we discuss ways in which CDScan be used to reflect the default risk of specific issuers.

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14 Introduction

47

structures, it can subject a trader to curve steepening or flattening positions,an issue we discuss in the context of an example.

Cross-Currency Basis SwapsFor our purposes, a CCBS is one in which the two legs are floating ratesdenominated in different currencies. For example, one party might agree topay three-month EURIBOR for five years in exchange for receiving three-month USD LIBOR plus a spread for five years. If the tenor of the swap isless than one year, we typically refer to this as an FX swap, and there are nointermediate interest payments. Because the counterparties exchangeprincipal at the beginning and end of the swap, these swaps have been inconsiderable demand in recent years. We discuss the valuation issues inthis chapter.

Relative Values of Bonds Denominated in Different CurrenciesA fundamental proposition of international financial economics is that inopen and integrated capital markets securities should have the same risk-adjusted expected real return regardless of the currency of denomination.One implication of this is that two otherwise identical bonds, denominatedin different currencies, should have identical yields once one is combinedwith the relevant interest rate swap and relevant basis swaps. We apply thisnotion in the context of global asset selection, by incorporating CCBS in thetechniques for fitting bond curves.

Credit Default SwapsThe time has long since passed that we could assume the existence of default-free sovereign debt. CDS can play a role in assessing and adjusting for thesecredit implications, and in this chapter we review the salient features ofthese instruments.

USD Asset Swap Spreads versus Credit Default SwapsThe swap spread model developed in the preceding section assumed thesovereign bond had no default risk. That assumption has become increasinglyless tenable in the current environment, and we discuss ways in which CDScan be used to reflect the default risk of specific issuers.

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14 Introduction

OptionsWe address the analysis and trading of options in a relative value contextby discussing three broad categories of option trades. In the first, the tradersimply buys or sells an option with a view that the underlying will finishin-the-money or out-of-the-money, with no dynamic trading. In the second,the trader attempts to capitalize on the difference between the impliedvolatility of the option and the actual volatility that the trader anticipates forthe underlying instrument, by trading the option against a dynamic positionin the underlying. In the third, the trader positions for a change in the impliedvolatility of the option, irrespective of the actual volatility of the underlyinginstrument.

Relative Value in a Broader Perspective

We conclude our sometimes rather technical description of relative valueanalysis by taking a broader perspective on its macroeconomic functions. At atime when professionals in the financial services industry increasingly need tojustify their role in society, we present a few thoughts about the benefits ofarbitrage for society.

Throughout the book, we offer pieces of general advice – words ofwisdom that we’ve gleaned over time. We’ve been mentored by some of thebest in the business over the years, with particular thanks to our managersand colleagues in Anshu Jain’s Global Relative Value Group at DeutscheMorgan Grenfell, and especially to David Knott, Pam Moulton, and HenryRitchotte. They were good enough to impart their wisdom to us, and we’rehappy to pass along this treasure trove of useful advice, hopefully with a fewadditional pearls of insight and experience that we’ve been able to add overthe years.1

Please visit the website accompanying this book to gain access to addi-tional material www.wiley.com/go/fixedincome

1When reviewing this book, Christian Carrillo, Martin Hohensee, Antti Ilmanen and KaareSimonsen have provided valuable feedback, enhancing our product.

c01 11 April 2013; 18:37:55

Relative Value 15

The Principles of BankingMoorad Choudhry 978-0-470-82521-1 • Hardback • 350 pages • May 2012 Buy Now!


£60.00 £36.00 / €72.00 €43.20 / $105.00 $63.00


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CHAPTER 16Bank Strategy I: Formulating

Strategy and Direction

The global financial crisis of 2007–2009 had the effect of making allparticipants in the banking industry, from regulators, central banks and

governments to bank boards, directors and trade associations, undertake afundamental review of the principles of banking. Issues such as capital andliquidity management, and systemic risk, became the subject of renewedfocus. In practical terms, legislators realised that they needed to addressthe issue of the ‘‘too-big-to-fail’’ bank; this issue remains unresolved, andultimately the realisation will dawn that the global economy simplycannot withstand certain financial institutions failing. But instead of thisbeing taken to mean that banks can operate perpetually in an environmentin which their profits are privatised and losses are socialised, it should beapparent that these institutions will have to be run on principles thatensure that they survive throughout the business cycle. This will call formore enlightened strategy and management, as well as an inherentconservatism. If bankers wish to run a proprietary trading outfit, or wishto maximise market share and return on capital, or outperform their peers,then they should go and work at a hedge fund. Those who manage a retaildeposit-taking institution will need to remain aware of the responsibilitiesthey bear.

From the point of view of bank practitioners, the most important taskis to address the issues of capital, liquidity and risk management, andwork them into a coherent strategy that is designed to produce sustainablereturns over the business cycle. In this chapter we introduce these topics aspart of a wider discussion on formulating bank strategy, and consider howthis strategy should be worked around the changed requirements of thepost-crisis age.

761

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THE SUSTA INABL E BANK BUS IN ESS MODEL

The basic bank business model has remained unchanged since banks werefirst introduced in modern society. Of course, as it as much an art as ascience, the model parameters themselves can be set to suit the specificstrategy of the individual bank, depending on whether the strategy operatesat a higher or lower risk-reward profile. But the basic model is identicalacross all banks. In essence, banking involves taking risks, and then applyingeffective management of that risk. This risk can be categorised as follows:

& managing the bank’s capital;& managing the liquidity mismatch: a fundamental ingredient of banking

is ‘‘maturity transformation’’, the recognition that loans (assets)generally have a longer tenor than deposits (liabilities).

If we wished to summarise the basic ingredients of the historical bankmodel, we might describe the following terms:

& leverage: a small capital base is levered into an asset pool that can be 10,20, 30 times greater, or even higher;

& the ‘‘gap’’: essentially funding short to lend long. This is a functionof the conventional positively sloping yield curve, and dictated by therecognition of the asset–liability mismatch noted above;

& liquidity: an assumption that a bank will always be able to roll overfunding as it falls due;

& risk management: an understanding of credit or default risk.

These fundamentals remain unchanged. The critical issue for bankmanagement, however, is that some of the assumptions behind theapplication of these fundamentals have changed, as demonstrated by theevents of 2007–2009. The changed landscape in the wake of the crisis hasresulted in some hitherto ‘‘safe’’ or profitable business lines being viewed asrisky. Although more favourable conditions for banking will return in duecourse, for the foreseeable future the challenge for banks will be to set theirstrategy only after first arriving at a true and full understanding of economicconditions as they exist today. The first subject for discussion is to considerwhat a realistic, sustainable return on capital target level should be, andthat it is commensurate to the level of risk aversion desired by the bank’sBoard. The Board should also consider the bank’s capital availability, andwhat sustained amount of business this would realistically support. Thesetwo issues need to be addressed before the remainder of the bank’s strategycan be considered.

762 The Principles of Banking

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THE SUSTA INABL E BANK BUS IN ESS MODEL

The basic bank business model has remained unchanged since banks werefirst introduced in modern society. Of course, as it as much an art as ascience, the model parameters themselves can be set to suit the specificstrategy of the individual bank, depending on whether the strategy operatesat a higher or lower risk-reward profile. But the basic model is identicalacross all banks. In essence, banking involves taking risks, and then applyingeffective management of that risk. This risk can be categorised as follows:

& managing the bank’s capital;& managing the liquidity mismatch: a fundamental ingredient of banking

is ‘‘maturity transformation’’, the recognition that loans (assets)generally have a longer tenor than deposits (liabilities).

If we wished to summarise the basic ingredients of the historical bankmodel, we might describe the following terms:

& leverage: a small capital base is levered into an asset pool that can be 10,20, 30 times greater, or even higher;

& the ‘‘gap’’: essentially funding short to lend long. This is a functionof the conventional positively sloping yield curve, and dictated by therecognition of the asset–liability mismatch noted above;

& liquidity: an assumption that a bank will always be able to roll overfunding as it falls due;

& risk management: an understanding of credit or default risk.

These fundamentals remain unchanged. The critical issue for bankmanagement, however, is that some of the assumptions behind theapplication of these fundamentals have changed, as demonstrated by theevents of 2007–2009. The changed landscape in the wake of the crisis hasresulted in some hitherto ‘‘safe’’ or profitable business lines being viewed asrisky. Although more favourable conditions for banking will return in duecourse, for the foreseeable future the challenge for banks will be to set theirstrategy only after first arriving at a true and full understanding of economicconditions as they exist today. The first subject for discussion is to considerwhat a realistic, sustainable return on capital target level should be, andthat it is commensurate to the level of risk aversion desired by the bank’sBoard. The Board should also consider the bank’s capital availability, andwhat sustained amount of business this would realistically support. Thesetwo issues need to be addressed before the remainder of the bank’s strategycan be considered.


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Bank S t ra t egyThe most important function that a bank Board can undertake is to setthe bank’s strategy. This is not as obvious as it sounds. It would besurprising to a layperson to observe just how often banks, both large andsmall, sophisticated or plain vanilla, have no real articulated strategy, but itis a fact. It is vital that banks put in place a coherent, articulated strategy inplace that sets the tone for the entire business, from the top down.

In the first instance the Board must take into account the currentregulatory environment. This includes, of course, the requirements of theBasel III rules, as well as the requirements of the national regulator. A bankcannot formulate strategy without a clear and genuine understanding of theenvironment in which it operates. Once this is achieved, before proceedingwith a formal strategy, the bank needs to determine what markets it wishesto operate in, what products it sells and what class of customer it wishes toserve. All its individual business lines should be set up to operate within themain strategy, having identified the markets and customers. In other words,all the business lines exist as ingredients of the strategy. If a business line isnot a fit with the strategy, it should be divested; equally, if a bank wishesto enter into a new business, then the strategy should be reviewed andrealigned if it does not naturally suggest the new business. Again, thissounds obvious, but there are many cases of banks entering piecemeal intodifferent businesses, or maintaining business lines that have been inheritedthrough previous growth or acquisition, that do not fit the bank’s culture.

In other words, a bank cannot afford to operate by simply meanderingalong, noting its peer group market share and RoE, and making up strategyas it goes along. This approach, which it would seem is what many banksdo indeed follow, however inadvertently, results in a senior managementand Board that is not fully aware of what the bank’s liabilities and riskexposures are.

The first task then is to understand one’s operating environment. It isthen to incorporate a specific target market and product suite as the basis ofits strategy. Concurrent with this, the bank must set its RoE target, whichdrives much of its culture and ethos. It is important to get this part of theprocess right, and at the start. Prior to the crash, it was common for banksto seek to increase revenue by adding to their risk exposure. Assets wereadded to the balance sheet or higher risk assets were taken on. In the bullmarket environment of 2001–2007, and allied to low funding costs as aresult of low base interest rates, this resulted in ever higher RoE figures, tothe point where it was common for even ‘‘Tier 2’’ banks to target levels of22%–25% RoE in their business appraisal. This process was of course nottenable in the long run.

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The second task, following immediately from the first, is to set arealistic RoE target, or better still, RoA target, that is sustainable over theentire business cycle. This cannot be done without educating boarddirectors as well as shareholders, who must appreciate the new, lower RoEtargets. Managing expectations will contribute to a more dispassionatereview of strategy. As important, risk-adjusted RoE should also be setat a realistic level and not be allowed to increase. Hence, the Board andshareholders must accept that lower RoE levels will become the standard.This should also be allied to lower leverage levels and higher capital ratios.

Also, concurrently with the above process, a bank must ask itself whereits strength lies, and formulate its strategy around that. In other words, it isimportant to focus on core competencies. Again, the experience of thecrash has served to demonstrate that many banks found themselves withrisk exposures they did not understand. This may have been simply theholding of assets (such as structured finance securities) whose creditexposures, valuation and secondary market liquidity they did not appreciate,or embarking on investment strategies such as negative basis trading withoutbeing aware of all the risk measurement parameters of such strategies.1

To properly implement a coherent, articulate strategy, a bank needs tobe aware of exactly what it does and does not have an expertise forundertaking, and not operate in products or markets in which it has nogenuine knowledge base.

Allied to an understanding of core competence is a review of core andnon-core assets. Bank strategy is not a static process or document, butrather a dynamic process. Regular reviews of the balance sheet need to beundertaken to identify any non-core assets, which can then be assessed todetermine whether they remain compatible with the strategy. If they arenot, then a realistic disposal process should be drawn up. In the long run,this is connected with an understanding of where the bank’s real strengthslie. Long-term core assets may well differ from core assets, but this needs

1 Without naming the banks, the author is aware of institutions that purchasedABS and CDO securities under a belief that the senior tranche, rated AAA,would not be downgraded even if there were a default in the underlying assetpool, presumably because the junior note(s) would absorb the losses. Of course,this loss of subordination does erode the initial rating of the senior note, with aconsequent markdown in market value. Another institution, according toanecdotal evidence received by the author in an email from one of its employees,entered into negative basis trades without any consideration for the funding cost ofthe trade package. This resulted in losses irrespective of the performance of thebasis. In this case, it is clear that the trading desks in question entered into arelatively sophisticated trading strategy without being sufficiently aware of itstechnical and risk implications.


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The second task, following immediately from the first, is to set arealistic RoE target, or better still, RoA target, that is sustainable over theentire business cycle. This cannot be done without educating boarddirectors as well as shareholders, who must appreciate the new, lower RoEtargets. Managing expectations will contribute to a more dispassionatereview of strategy. As important, risk-adjusted RoE should also be setat a realistic level and not be allowed to increase. Hence, the Board andshareholders must accept that lower RoE levels will become the standard.This should also be allied to lower leverage levels and higher capital ratios.

Also, concurrently with the above process, a bank must ask itself whereits strength lies, and formulate its strategy around that. In other words, it isimportant to focus on core competencies. Again, the experience of thecrash has served to demonstrate that many banks found themselves withrisk exposures they did not understand. This may have been simply theholding of assets (such as structured finance securities) whose creditexposures, valuation and secondary market liquidity they did not appreciate,or embarking on investment strategies such as negative basis trading withoutbeing aware of all the risk measurement parameters of such strategies.1

To properly implement a coherent, articulate strategy, a bank needs tobe aware of exactly what it does and does not have an expertise forundertaking, and not operate in products or markets in which it has nogenuine knowledge base.

Allied to an understanding of core competence is a review of core andnon-core assets. Bank strategy is not a static process or document, butrather a dynamic process. Regular reviews of the balance sheet need to beundertaken to identify any non-core assets, which can then be assessed todetermine whether they remain compatible with the strategy. If they arenot, then a realistic disposal process should be drawn up. In the long run,this is connected with an understanding of where the bank’s real strengthslie. Long-term core assets may well differ from core assets, but this needs

1 Without naming the banks, the author is aware of institutions that purchasedABS and CDO securities under a belief that the senior tranche, rated AAA,would not be downgraded even if there were a default in the underlying assetpool, presumably because the junior note(s) would absorb the losses. Of course,this loss of subordination does erode the initial rating of the senior note, with aconsequent markdown in market value. Another institution, according toanecdotal evidence received by the author in an email from one of its employees,entered into negative basis trades without any consideration for the funding cost ofthe trade package. This resulted in losses irrespective of the performance of thebasis. In this case, it is clear that the trading desks in question entered into arelatively sophisticated trading strategy without being sufficiently aware of itstechnical and risk implications.


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to be articulated explicitly. The decision on whether an asset is core ornon-core, or core or long-term core, is a function of the bank’s overallstrategy of what its expertise is and what markets and customers it wishesto service. This will be embedded in the strategy and the bank’s businessmodel. This drives the choice of products and business lines that the bankfeels it can add value in.

Leverage Ra t i o sElsewhere we discuss bank capital structure. There is no doubt that the newmodel for banking assumes higher capital ratios and buffers for all banks inthe longer term. The higher level of capital will be substantial in some cases,because under the Basel III rules trading businesses will be required to holdup to three times as much capital as vanilla banking business. Basel III alsoimposes a limit on the leverage ratio, and indeed some national regulatorsalready are doing so; this follows the example of the regulators in Canadaand Australia, two jurisdictions that had imposed leverage ratio limits andwhich, not coincidentally, did not suffer a bank crash in 2008.

A leverage ratio is the total value of a bank’s assets relative to its equitycapital. The financial crash highlighted the extent of risk taking by certainbanks when measured using leverage ratios. As a measure of the ratio ofassets to owner’s equity, they are an explicit indication of risk exposure.Lehman Brothers leverage ratio increased from approximately 24:1 in 2003to over 31:1 by 2007. Such aggressive asset growth generated tremendousprofits during the boom years, but exposed the bank to such an extentthat even a 3% or 4% decline in the value of its assets would eliminatecompletely its equity. This duly happened.

This is why Basel III has introduced a limit on leverage ratios as anadded safety measure, alongside minimum capital requirements. In theaftermath of the crash it is accepted that bank leverage ratios have toadjust downwards, and the prevailing sentiment today dictates thatboards should be wary of a business model that ramps up the ratio toan excessive level. Figure 16.1 shows levels during 2007–2009; prudentmanagement suggests average levels will be much lower than thesefigures over the next 10–15 years. This is not only business best-practice, but will also contribute to greater systemic stability.

Bank management will have to adjust to a concept of an explicitleverage ratio limit, the rationale for which is clear. The experience of thelast and previous crises has shown that during a period of upside growth,banks’ risk models tend to underestimate their exposure. This has twoconsequences: first, the bank takes on ever greater risk, as it targets greaterrevenue and profit during a bull market, and second the amount of capital


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set aside is below what is adequate at the time the crash occurs. Figure 16.2,which shows a sample of ‘‘bulge-bracket’’ banks, suggests that banksfocused on trading assets as they expanded their balance sheets.

In such an environment, capital ratio requirements are an insufficientsafeguard against instability, and it becomes necessary to monitor leverageratios. Hence, in the post-crash environment banks need to adjust theirbusiness strategy to allow for this constraint.

0

10

20

30

40

50

60

Bank ofAmerica

Barclays BNPParibas

Citigroup CreditSuisse

DeutscheBank

HSBC JPMorgan RBS SociétéGénérale

UBS0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Total assets/Tier 1 capital (LHS scale)Trading assets/Total assets (RHS scale)

FIGURE 16.2 Selected bank ratio of total assets to Tier 1 capital and trading assetsto total assets, 2008.Source: Bank of England (2009).

0

10

20

30

40

50

60

2007 2008 2009 Q2 2009 Q3

US banks European banks UK banks

FIGURE 16.1 Bank median leverage ratios, 2007–2009.Source: Bank of England (2009).


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set aside is below what is adequate at the time the crash occurs. Figure 16.2,which shows a sample of ‘‘bulge-bracket’’ banks, suggests that banksfocused on trading assets as they expanded their balance sheets.

In such an environment, capital ratio requirements are an insufficientsafeguard against instability, and it becomes necessary to monitor leverageratios. Hence, in the post-crash environment banks need to adjust theirbusiness strategy to allow for this constraint.

0

10

20

30

40

50

60

Bank ofAmerica

Barclays BNPParibas

Citigroup CreditSuisse

DeutscheBank

HSBC JPMorgan RBS SociétéGénérale

UBS0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Total assets/Tier 1 capital (LHS scale)Trading assets/Total assets (RHS scale)

FIGURE 16.2 Selected bank ratio of total assets to Tier 1 capital and trading assetsto total assets, 2008.Source: Bank of England (2009).

0

10

20

30

40

50

60

2007 2008 2009 Q2 2009 Q3

US banks European banks UK banks

FIGURE 16.1 Bank median leverage ratios, 2007–2009.Source: Bank of England (2009).


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As we noted above in the case of Lehmans, excessively high leverageresults in a higher sensitivity of the balance sheet to trading and/or defaultlosses. Limiting the amount of leverage acts as an additional risk controlmeasure, backing up the safety net provided by a regulatory capital buffer.But when one thinks about it, this is a sensible measure on its own. It shouldnot have to be imposed by regulatory fiat. In advance of the introduction ofthe standardised ratio as part of Basel III, banks should have addressed thisissue anyway as part of their prudential capital and risk management.

A number of jurisdictions already employ a leverage ratio limit,although there is no uniform definition (see Figure 16.3). Under Basel III therules will incorporate a limit, with a common definition of capital and anagreed measure of all assets, both on- and off-balance sheet.

Cap i t a l S t ruc t ureThe efficient management of capital is a vital function of bank seniormanagement. In the aftermath of any recession, capital is of course a scarcecommodity. However, this fact itself leads to one of the lessons learnedfrom the crisis: the need for ‘‘countercyclical’’ capital management. In otherwords, boards should treat capital as scare at all times, and build up capitalbases even as a bull market is helping to generate higher profits. The level ofcapital needs to be sufficient to cushion the fallout from ‘‘stress events’’,which are the outlier events that normal distribution models used in financedo not capture.

Elsewhere in this book we have discussed the value of contingentcapital instruments that can convert to equity at any time should the issuingbank’s capital ratio fall below a pre-specified level. Going forward, thisshould be the only ‘‘sophisticated’’ financial instrument in the bank’s capital

Canada Tier 1 and Tier 2 capital must be at least 5% of on-balance sheetassets plus qualifiying off-balance sheet assets.

Switzerland Tier 1 capital must be at least 3% of on-balance sheet assets lessSwiss domestic lending for bank holding companies, and at least4% for individual institutions. This rule applies only to CreditSuisse and UBS.

US Tier 1 capital must be at least 3% of on-balance sheet assets for‘‘strong’’ bank holding companies and at least 4% for all otherbank holding companies.

FIGURE 16.3 Summary of selected regulatory leverage ratio limits.Source: Bank of England (2009).


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structure. It will assist efficient capital management, as well as investortransparency, if a bank’s capital is held in the form of simple instrumentsonly, essentially common equity and retained profits (reserves). Of course,long-dated debt instruments can also form part of capital, but again it ismore transparent if these are vanilla instruments.

Capital itself on its own is an insufficient protection against firm failure.Bank management must take additional measures, over and above capitalbuffers, to safeguard the institution in the event of systemic stress or othermarket crash events, because the capital base on its own will be insufficientto preserve the firm as a going concern. Hence, leverage ratio limits androbust liquidity management is as important as capital buffers. A reportfrom the BoE (2009) suggests that on average a Tier 1 capital ratio of 8.5%would have been needed by banks to avoid falling below the Basel minimumof 4% during the last crisis. This suggests that the current requirementis far too low to act as a genuine risk-based capital reserve. Of course, afinancial crisis will affect different banks in different ways; the BoE reportgoes on to state that even if all the banks in its study sample had indeedpossessed a Tier 1 ratio of 8.5%, as much 40% of those banks would stillhave breached their 4% limit during the crash. For some firms the ‘‘inhindsight’’ sufficient level of capital was as high as 18%.

The implications of the BoE report are clear: minimum capital require-ments must be higher, and banks also need to build in an element of flexibilityinto their capital structure, perhaps by means of contingent capitalinstruments. Contingent capital is any instrument that would convert intocommon equity on occurrence of a pre-specified trigger. This is illustrated inFigure 16.4. An issue of bonds by Lloyds Banking Group in 2009, Enhanced

Tier 1 trigger level

Contingent capital Tier 1 capital

Initial position Post-conversionLosses incurred

FIGURE 16.4 Illustration of contingent capital note triggering.Source: Bank of England (2009).


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structure. It will assist efficient capital management, as well as investortransparency, if a bank’s capital is held in the form of simple instrumentsonly, essentially common equity and retained profits (reserves). Of course,long-dated debt instruments can also form part of capital, but again it ismore transparent if these are vanilla instruments.

Capital itself on its own is an insufficient protection against firm failure.Bank management must take additional measures, over and above capitalbuffers, to safeguard the institution in the event of systemic stress or othermarket crash events, because the capital base on its own will be insufficientto preserve the firm as a going concern. Hence, leverage ratio limits androbust liquidity management is as important as capital buffers. A reportfrom the BoE (2009) suggests that on average a Tier 1 capital ratio of 8.5%would have been needed by banks to avoid falling below the Basel minimumof 4% during the last crisis. This suggests that the current requirementis far too low to act as a genuine risk-based capital reserve. Of course, afinancial crisis will affect different banks in different ways; the BoE reportgoes on to state that even if all the banks in its study sample had indeedpossessed a Tier 1 ratio of 8.5%, as much 40% of those banks would stillhave breached their 4% limit during the crash. For some firms the ‘‘inhindsight’’ sufficient level of capital was as high as 18%.

The implications of the BoE report are clear: minimum capital require-ments must be higher, and banks also need to build in an element of flexibilityinto their capital structure, perhaps by means of contingent capitalinstruments. Contingent capital is any instrument that would convert intocommon equity on occurrence of a pre-specified trigger. This is illustrated inFigure 16.4. An issue of bonds by Lloyds Banking Group in 2009, Enhanced

Tier 1 trigger level

Contingent capital Tier 1 capital

Initial position Post-conversionLosses incurred

FIGURE 16.4 Illustration of contingent capital note triggering.Source: Bank of England (2009).


C16 04/04/2012 3:43:25 Page 769

Capital Notes, was of this type. Such instruments enable a bank to purchasecatastrophe insurance from the private sector, rather than from the publicsector via the lender of last resort. They also allow a bank to hold a Tier 1equity reserve at a lower cost, in theory at least, than equity itself.

EXAMPLE 16 .1 FUTURE BANK CAP I TA LSTRUCTURE

The financial crash resulted in a major review of the hitherto conven-tional bank funding model, with results that were exemplified by theUK FSA’s consultative papers of 2008 and 2009 on liquidity and thepublication of the Basel III guidelines in 2010. Further regulatoryreform impacting the liquidity structure of banks is inevitable. Anexample of this is the FSA’s Bail-In regime for UK banks, designed toensure an orderly wind-down of banks that have become a ‘‘goneconcern’’. The impact of such regulatory changes, together with thechange in emphasis for bank funding away from short-term wholesalefunding to long-term funding and more core customer funding, meansthat the future bank capital structure will look different in somerespects from what it has done recently.

The following factors are influencing change:

& a move away from short-term unsecured wholesale funding: theliquidity crisis of 2008 reinforced the lessons from earlier bankliquidity crises, that an excess reliance on wholesale funding isoverly risky;

& a move towards secured funding away from unsecured funding: theexperience of 2008–2009 demonstrated that, provided collateralquality was acceptable, repo funding remained available for bankswhere unsecured funding had frozen. A greater share of the bankfunding model will comprise secured funding in the form of repo,TRS, ABS/RMBS and Covered Bonds;

& the FSA Bail-In regime will classify senior unsecured debt as a classof liabilities that absorbs losses following the erosion of Tier 1equity. While this simply reinforces what was always in legaltheory the case (senior debt lies above equity and subordinateddebt in the capital structure, so would be expected to absorb lossesat some point), the expectation now is that the Central Bankbackstop or taxpayer-funded bailout will not be invoked so

(continued )


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Core Compe t ence : ‘ ‘ K now Your R i sk ’ ’Regulatory authorities noticed a considerable decline in cross-borderlending flows in the aftermath of the Lehman bankruptcy; for instance, seethe BoE’s Financial Stability Report dated June 2009. This is significant.During the bull market of 2001–2007, international lending volumes hadexpanded steadily (see Figure 16.6), as banks grew their balance sheets andsought higher yield opportunities overseas.

It is evident that during and after the bank crisis, when inter-bank marketliquidity had dried up, banks pulled back from overseas markets, irrespectiveof whether these were deemed peripheral or not, and concentrated on coremarkets. This reflects informational advantages in core markets compared tooverseas and non-core markets. The UK corporate lending sector makes acase in point: between 2002 and 2009, lending volume from UK banks fellby approximately 16% (the figure between 2006 and 2009 was a decline of14%). However, the equivalent figures for foreign subsidiaries was a fall of10.5% and 20%, while for foreign branches the decline was even more

readily, thus the risk premium demanded from investors to holdsuch liabilities will increase;

& subordinated debt may be difficult for most banks to place withinvestors, in which case it will be discontinued. Senior unsecureddebt would be issued, at a relatively higher yield spread thanpreviously, in the 1- to 10-year tenor; longer dated issuance ismore likely to be the preserve of high-rated banks.

For all but the most well-capitalised and/or highest rated banks,we can expect to see a capital structure on the liabilities’ side asillustrated in Figure 16.5.

Senior unsecured debt

Secured funding (Covered Bonds,term repo, etc.)

Equity

Customer deposits (beyond government guaranteed level)

FIGURE 16.5 Future bank liabilities structure.


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Core Compe t ence : ‘ ‘ K now Your R i sk ’ ’Regulatory authorities noticed a considerable decline in cross-borderlending flows in the aftermath of the Lehman bankruptcy; for instance, seethe BoE’s Financial Stability Report dated June 2009. This is significant.During the bull market of 2001–2007, international lending volumes hadexpanded steadily (see Figure 16.6), as banks grew their balance sheets andsought higher yield opportunities overseas.

It is evident that during and after the bank crisis, when inter-bank marketliquidity had dried up, banks pulled back from overseas markets, irrespectiveof whether these were deemed peripheral or not, and concentrated on coremarkets. This reflects informational advantages in core markets compared tooverseas and non-core markets. The UK corporate lending sector makes acase in point: between 2002 and 2009, lending volume from UK banks fellby approximately 16% (the figure between 2006 and 2009 was a decline of14%). However, the equivalent figures for foreign subsidiaries was a fall of10.5% and 20%, while for foreign branches the decline was even more

readily, thus the risk premium demanded from investors to holdsuch liabilities will increase;

& subordinated debt may be difficult for most banks to place withinvestors, in which case it will be discontinued. Senior unsecureddebt would be issued, at a relatively higher yield spread thanpreviously, in the 1- to 10-year tenor; longer dated issuance ismore likely to be the preserve of high-rated banks.

For all but the most well-capitalised and/or highest rated banks,we can expect to see a capital structure on the liabilities’ side asillustrated in Figure 16.5.

Senior unsecured debt

Secured funding (Covered Bonds,term repo, etc.)

Equity

Customer deposits (beyond government guaranteed level)

FIGURE 16.5 Future bank liabilities structure.


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dramatic, at 17% and 46%.2 Foreign banks would, on average, have lessdepth and breadth of corporate relationships, while branches would beexpected to have even less developed relationships in the domestic market.

The lessons for the bank business model are clear: during an expansionaryphase, it is important to remain focused on areas on core competence,and sectors in which the bank possesses actual knowledge and strength.Concentrating on areas in which the bank carries competitive advantagemakes it less likely that loan origination standards will decline, resultingin lower losses during an economic downturn. There is also a technicalreason for ensuring that overseas lending standards are maintained strictly,and limits set carefully, because it is often undertaken in foreign currency.A bank’s ability to fund such lending is more dependent on externalmarkets and wholesale counterparties relative to domestic currencylending, thus making the bank more vulnerable to a market downturn. Forexample, the cross-currency swap market in US dollars came under pressure,resulting in higher swap prices, following the Lehman default, and many banksstruggled to obtain dollar funding during this period.

Corpora t e GovernanceWe introduce here bank corporate governance in the context of bank strategy;the subject is discussed in greater detail in Chapter 18. The governancestructure of a bank is a vital part of ensuring effective overall control and risk

–2000

–1500

–1000

–500

0

500

1000

1500

2000

2500

3000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

USD billion

FIGURE 16.6 Cross-border bank lending volumes, 2000–2009.Source: Bank of England (2009).

2 Source: Bank of England (2009).


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management. An inadequate set-up will result in ineffective decision-making.The crash has highlighted the importance of addressing, in robust fashion, thefollowing:

& What should the makeup of the Board itself be? What is the rightnumber of executive directors and NEDs?

& How should the Board’s performance be measured?& Is the knowledge base, expertise and experience of the Board adequate?

Does the CEO possess the right background in banking?3

& Are the board executives actually challenged in their decision-making?

Other questions to address include: (i) Is the Board provided withsufficient and adequate management reporting, in accessible fashion, on thebank’s performance and risk exposures? (ii) Are there controls built intothe firms’ cultures such that they are adhered to when the bank’s businessstrategy is in conflict with them?

The role of NEDs came under scrutiny in the wake of the 2008 crash.That some NEDs were not up to the standard required is evident; however,this should not detract from the vital function, in theory at least, that theydo undertake. In the first instance, business best-practice dictates that therisk management function should report to a NED on the Board. Thisclearly implies that the NED in question must be sufficiently experiencedand capable. The national regulator should always interview the relevantNED to ensure that this person meets the standards required.

It is rare to observe genuine control at all levels of a bank that alsoboasts true innovation, creativity and efficiency. It may be, for instance,that some institutions are simply too big to manage effectively, especiallywhen things start to go wrong. However, this does not mean we should notattempt to implement an effective strategy at the top level and still maintainefficiency at the ‘‘coal face’’. The bank crisis demonstrated that in somecases bank boards were not able to maintain effective control of thebusiness as they expanded. Certain desks originated risk that went beyondthe stated (or believed) risk-appetite of the parent banks; in other cases, therisk management department was marginalised or ignored, and at boardlevel there was a ‘‘rubber stamp’’ mentality. These instances have significantimplications for bank corporate governance.

3 The CEOs of two British banks, HBOS and Bradford & Bingley plc, hadbackgrounds in supermarket retail and not banking. They also had managementconsulting backgrounds.


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management. An inadequate set-up will result in ineffective decision-making.The crash has highlighted the importance of addressing, in robust fashion, thefollowing:

& What should the makeup of the Board itself be? What is the rightnumber of executive directors and NEDs?

& How should the Board’s performance be measured?& Is the knowledge base, expertise and experience of the Board adequate?

Does the CEO possess the right background in banking?3

& Are the board executives actually challenged in their decision-making?

Other questions to address include: (i) Is the Board provided withsufficient and adequate management reporting, in accessible fashion, on thebank’s performance and risk exposures? (ii) Are there controls built intothe firms’ cultures such that they are adhered to when the bank’s businessstrategy is in conflict with them?

The role of NEDs came under scrutiny in the wake of the 2008 crash.That some NEDs were not up to the standard required is evident; however,this should not detract from the vital function, in theory at least, that theydo undertake. In the first instance, business best-practice dictates that therisk management function should report to a NED on the Board. Thisclearly implies that the NED in question must be sufficiently experiencedand capable. The national regulator should always interview the relevantNED to ensure that this person meets the standards required.

It is rare to observe genuine control at all levels of a bank that alsoboasts true innovation, creativity and efficiency. It may be, for instance,that some institutions are simply too big to manage effectively, especiallywhen things start to go wrong. However, this does not mean we should notattempt to implement an effective strategy at the top level and still maintainefficiency at the ‘‘coal face’’. The bank crisis demonstrated that in somecases bank boards were not able to maintain effective control of thebusiness as they expanded. Certain desks originated risk that went beyondthe stated (or believed) risk-appetite of the parent banks; in other cases, therisk management department was marginalised or ignored, and at boardlevel there was a ‘‘rubber stamp’’ mentality. These instances have significantimplications for bank corporate governance.

3 The CEOs of two British banks, HBOS and Bradford & Bingley plc, hadbackgrounds in supermarket retail and not banking. They also had managementconsulting backgrounds.


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Coun t ercyc l i c a l F und i n gOne additional lesson learned from the crash is that banks should takeadvantage of ‘‘benign’’ conditions to improve their funding structures.Figure 16.7 shows the rise and fall in Libor spreads during 2007–2009,giving an idea of the market conditions that may prevail and suggestingwhen a bank may wish to take on more funding to take advantage ofLibor rates.4 In the first instance this would involve reducing the relianceon short-term funding. The definition of ‘‘short-term’’ is not universal;depending on which person one asks, it may mean up to one week or up tothree months. Irrespective of the view that an individual bank takes, and thisshould reflect the bank’s particular business model and current funding gap,best business practice suggests that a time of low funding spreads is theopportune moment to change the liability structure by increasing averagematurity tenor. For instance, in the UK, overall banks had reduced theirreliance on funding of up to 1-week from 15% of unsecured wholesalefunding in December 2008 to 9% by October 2009. The aggregate customerfunding gap (the difference between customer loans and customer deposits)was at GBP610 billion by Q2 2009, compared to GBP842 billion at the end

0

50

100

150

200

250

300

Apr-07

Jun-07

Aug-07

Oct-07

Dec-07

Feb-08

Apr-08

Jun-08

Aug-08

Oct-08

Dec-08

Feb-09

Apr-09

Jun-09

Aug-09

Oct-09

bps

FIGURE 16.7 Sterling Libor–OIS spread, 2007–2009.Source: Bloomberg L.P.

4 See Chapter 10 in Choudhry (2007a), which discusses the fair value of the Liborterm premium.


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of Q4 in 2008. This was 18% of all loans, the lowest proportion since 2003.5

This is shown at Figure 16.8.This is a critical feature of the new bank business model. The main

lesson of the 2007–2009 crisis was the importance of liquidity riskmanagement. To mitigate the impact of the next recession, bank fundingstructures need to be set up to reduce the reliance on short-term fundingand unstable wholesale funding. They also need to extend the maturity ofthe liability side of the balance sheet. Excluding notable exceptions such asthe banks in Australia and Canada, many country banks’ customer fundinggaps are uncomfortably high (see Figure 16.9). Banks must address tworequirements, which are (i) to reduce the reliance on wholesale funding,which is not ‘‘sticky’’ and is less stable than retail customer deposits, and(ii) to increase the average tenor of their liabilities. The UK bank sector, forexample, remains vulnerable in this regard: the BoE reported in 2009 thatabout 50% of UK bank aggregate wholesale funding was lower than sixmonths in maturity.6

Bank funding strategy should therefore include targeting increased useof retail funding. Retail deposits are treated by regulators as being morestable, with greater expectation of being rolled over and not withdrawn on

5 Source: Bank of England (2009).6 Source: Ibid.

–5

0

5

10

15

20

25

30

35

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

FIGURE 16.8 UK banks customer funding gap 1998–2009, median value.Source: British Bankers Association.


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of Q4 in 2008. This was 18% of all loans, the lowest proportion since 2003.5

This is shown at Figure 16.8.This is a critical feature of the new bank business model. The main

lesson of the 2007–2009 crisis was the importance of liquidity riskmanagement. To mitigate the impact of the next recession, bank fundingstructures need to be set up to reduce the reliance on short-term fundingand unstable wholesale funding. They also need to extend the maturity ofthe liability side of the balance sheet. Excluding notable exceptions such asthe banks in Australia and Canada, many country banks’ customer fundinggaps are uncomfortably high (see Figure 16.9). Banks must address tworequirements, which are (i) to reduce the reliance on wholesale funding,which is not ‘‘sticky’’ and is less stable than retail customer deposits, and(ii) to increase the average tenor of their liabilities. The UK bank sector, forexample, remains vulnerable in this regard: the BoE reported in 2009 thatabout 50% of UK bank aggregate wholesale funding was lower than sixmonths in maturity.6

Bank funding strategy should therefore include targeting increased useof retail funding. Retail deposits are treated by regulators as being morestable, with greater expectation of being rolled over and not withdrawn on

5 Source: Bank of England (2009).6 Source: Ibid.

–5

0

5

10

15

20

25

30

35

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

FIGURE 16.8 UK banks customer funding gap 1998–2009, median value.Source: British Bankers Association.


C16 04/04/2012 3:43:25 Page 775

maturity. To reduce its funding gap (whatever it is), a bank would seek togrow its retail deposits.

At a tactical level, this raises the question of what interest rate to pay toattract more such deposits. Figure 16.10 shows the change in averagespread on retail savings products offered by UK banks from 2005 to 2009.

–40

–30

–20

–10

0

10

20

30

40

50

Canada Japan US France UnitedKingdom

Germany Spain Italy

Customer loans lesscustomer deposits %

FIGURE 16.9 Selected country bank funding gaps.Source: Bank of England (2009).

–400

–300

–200

–100

0

100

200

300

Q4 2005 Q4 2007 Q4 2009

Notice accountTax-free savings accountCall accountFixed-rate deposit

FIGURE 16.10 UK banks retail deposit spread.Source: Money Observer.


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From a spread below Libor, the spread was increased to almost 200 bps overLibor. Partly this reflects the fact that absolute base interest rates had fallento a very low level, but it also reflects the increased demand for such depositsfrom banks. It is important not to pay a rate that is excessively above that inthe market, partly for reputation reasons, but also so as to not convey theimpression that the bank is in difficulty and desperate for funds.

The overall impact of the new modified strategy will be a higherfunding cost. In adopting a more robust funding structure, there will beadded costs associated with raising longer dated liabilities (assuming apositive-sloping yield curve) and paying more to attract stable retaildeposits. However, the object of this strategy is to reduce the vulnerabilityof the bank should there be another external shock, or systemic instability.

EXAMPLE 16 .2 THE UN I T ED K INGDOMINDEPENDENT COMMISS I ON ON BANK ING ( I CB )

The UK ICB was set up by the UK government to provide recommen-dations on the future of banking, and published its report inSeptember 2011. Its high-level objective was to describe a frameworkthat ensured a more stable banking system in the UK. Its highestimpact findings can be summarised as follows:

& establishment of a ‘‘ring-fence’’ separating the retail arm of a bankfrom an investment banking (IB) arm;

& a higher minimum required loss-absorbing capital base.

For banks that operate in both retail and IB sectors, the ring-fencingmust be organised along the following business lines:

& mandatory businesses: individual deposits; SME deposits; overdrafts;& permitted businesses: corporate banking; private banking; trade

finance and project finance; retail assets; European Economic Area(EEA) business;

& prohibited business (and therefore outside ring-fence): trading andwholesale markets; proprietary derivatives trading; non-EEAbusiness.

The organisation must ensure that each part of the bank, inside andoutside the ring-fence, is able to meet capital and liquidity requirementson a stand-alone basis. The part inside the ring-fence can deal with thepart outside up to a 25% of Tier 1 capital large exposure limit, andotherwise as simply another third-party entity.


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From a spread below Libor, the spread was increased to almost 200 bps overLibor. Partly this reflects the fact that absolute base interest rates had fallento a very low level, but it also reflects the increased demand for such depositsfrom banks. It is important not to pay a rate that is excessively above that inthe market, partly for reputation reasons, but also so as to not convey theimpression that the bank is in difficulty and desperate for funds.

The overall impact of the new modified strategy will be a higherfunding cost. In adopting a more robust funding structure, there will beadded costs associated with raising longer dated liabilities (assuming apositive-sloping yield curve) and paying more to attract stable retaildeposits. However, the object of this strategy is to reduce the vulnerabilityof the bank should there be another external shock, or systemic instability.

EXAMPLE 16 .2 THE UN I T ED K INGDOMINDEPENDENT COMMISS I ON ON BANK ING ( I CB )

The UK ICB was set up by the UK government to provide recommen-dations on the future of banking, and published its report inSeptember 2011. Its high-level objective was to describe a frameworkthat ensured a more stable banking system in the UK. Its highestimpact findings can be summarised as follows:

& establishment of a ‘‘ring-fence’’ separating the retail arm of a bankfrom an investment banking (IB) arm;

& a higher minimum required loss-absorbing capital base.

For banks that operate in both retail and IB sectors, the ring-fencingmust be organised along the following business lines:

& mandatory businesses: individual deposits; SME deposits; overdrafts;& permitted businesses: corporate banking; private banking; trade

finance and project finance; retail assets; European Economic Area(EEA) business;

& prohibited business (and therefore outside ring-fence): trading andwholesale markets; proprietary derivatives trading; non-EEAbusiness.

The organisation must ensure that each part of the bank, inside andoutside the ring-fence, is able to meet capital and liquidity requirementson a stand-alone basis. The part inside the ring-fence can deal with thepart outside up to a 25% of Tier 1 capital large exposure limit, andotherwise as simply another third-party entity.


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STRATEGY INPUTS

Notwithstanding that all banks are ultimately similar beasts, the strategyformulated for an individual bank will be unique to it and reflects its particularmarket, business model, customer base and operating environment. Unlikesome of the other subjects dealt with in this book, it would be difficult (and ofquestionable value) to come up with a ‘‘template’’ strategy document. Instead,in this section we will illustrate business best-practice with a description of therelevant inputs to a coherent strategy. These would then be modified for eachspecific case.

It is important that a bank articulates its strategic vision, and publiclyannounces its quantitative and qualitative targets. This may sound obvious,

Under the ICB regime UK banks will have to set aside a highercore Tier 1 equity level and also a higher total capital base, referred toas the primary loss absorbing capacity (PLAC), which includes otherTier 1 capital and required buffers. This is illustrated in Figure 16.11.The PLAC can include up to 3.5% of ‘‘bail-inable’’ debt; in practice, itis likely to be senior unsecured bonds designated as such, and whichwould absorb losses after equity has been wiped out (in other words,once the bank is no longer a going concern), and CoCo bonds. If thereis no resolution regime in place for the bank, the so-called ‘‘LivingWill’’ that describes the mechanism for an orderly wind-down of abank that is now a gone concern, then a further 3.0% buffer is required.

The date for UK banks to demonstrate implementation ofthe ICB’s requirements will be in 2019. Of course, irrespective of thechanges in the UK banking market as a result of the ICB report, theprinciples of banking described in this book will remain unchanged.

3.0

3.5

3.0

7.0

Resolution buffer (bail‐in)

PLAC to 17% (Bail‐In debt / CoCo)

Basel III other Tier 1 (non‐equity)

Ring‐fence buffer (equity), total equity 10%

Basel III core Tier 1

3.5

FIGURE 16.11 UK ICB regulatory capital regime.


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but one would be surprised how many financial institutions do not actuallydo this beyond bland platitudes, and simply bumble along from one year tothe next.

V i s i o n S t a t emen tThe concept of a vision statement is beloved of management consultants andtherefore care must be taken to avoid writing one that is simply verbiage andplatitudes, and thereby a worthless, pointless document. To be of value, itshould capture succinctly and accurately what the bank aspires to be. In atop-down strategy origination process, it would drive the quantitative andqualitative elements of the bank strategy; hence, if the statement is wellformulated it becomes a worthwhile input to the strategy. It can set therisk-reward culture at the bank. If the bank wishes to deviate from this culture,it would then look to revise the statement (and its strategy). In other words, avision statement serves as a statement of intent, so that all the bank’sstakeholders knowwhat its business model and objectives are.

For example, a framework vision statement might encompass one ormore of the following:

& to be a stable commercial bank serving the requirements of customers inthe EMEA region;

& to achieve a consistent RoE of 12%–14% and RoA of 4%–5% through-out the business cycle;

& to maintain an AA�/Aa2 credit rating;& to generate revenue from customer business, within core business lines;& to focus on customer requirements, emphasising a robust risk

management culture;& to limit cost base, including employee remuneration, to [ ]% of revenue

base.

Note how the above almost explicitly restricts proprietary tradingbusiness. A bank whose primary focus lay outside some or all of the abovewould craft a different vision statement. Equally, if the bank that draftedthe above statement wished to move into new businesses or products thatwere not covered by its current vision, it would modify it, thereby givingintent of its new focus.

With the vision set, the bank should drill down from it and articulate itsstrategic plan. This is still a general statement; it is the next layer down thatwill describe detailed target metrics. For example, the hypothetical bankthat drafted our vision statement above might describe its strategic plan inthe following terms:


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but one would be surprised how many financial institutions do not actuallydo this beyond bland platitudes, and simply bumble along from one year tothe next.

V i s i o n S t a t emen tThe concept of a vision statement is beloved of management consultants andtherefore care must be taken to avoid writing one that is simply verbiage andplatitudes, and thereby a worthless, pointless document. To be of value, itshould capture succinctly and accurately what the bank aspires to be. In atop-down strategy origination process, it would drive the quantitative andqualitative elements of the bank strategy; hence, if the statement is wellformulated it becomes a worthwhile input to the strategy. It can set therisk-reward culture at the bank. If the bank wishes to deviate from this culture,it would then look to revise the statement (and its strategy). In other words, avision statement serves as a statement of intent, so that all the bank’sstakeholders knowwhat its business model and objectives are.

For example, a framework vision statement might encompass one ormore of the following:

& to be a stable commercial bank serving the requirements of customers inthe EMEA region;

& to achieve a consistent RoE of 12%–14% and RoA of 4%–5% through-out the business cycle;

& to maintain an AA�/Aa2 credit rating;& to generate revenue from customer business, within core business lines;& to focus on customer requirements, emphasising a robust risk

management culture;& to limit cost base, including employee remuneration, to [ ]% of revenue

base.

Note how the above almost explicitly restricts proprietary tradingbusiness. A bank whose primary focus lay outside some or all of the abovewould craft a different vision statement. Equally, if the bank that draftedthe above statement wished to move into new businesses or products thatwere not covered by its current vision, it would modify it, thereby givingintent of its new focus.

With the vision set, the bank should drill down from it and articulate itsstrategic plan. This is still a general statement; it is the next layer down thatwill describe detailed target metrics. For example, the hypothetical bankthat drafted our vision statement above might describe its strategic plan inthe following terms:


C16 04/04/2012 3:43:26 Page 779

BANK STRATEGIC PLAN

& Business focus– home market, euro-zone and Gulf Co-operation Council (GCC)region;

– customer base for corporate and institutional banking: corporate andfinancial institutions;

– customer base for retail banking: high net worth individuals (HNWIs)in home market and GCC region;

– limit balance sheet to EUR [ ] billion;– limit wholesale funding share to 20%.

& Management focus– limit cost base to [ ]% of revenue base;– explicit metric for balance sheet usage;– return target set at 12%–14% on a sustained basis;– robust risk management organisation, policy and reporting line;– incentivise long-term customer-focused business.

The above can be built on and developed into greater detail. The nextinput to the strategy is the next level down, the target metrics.

S tra t egy Se t t i n g :Per f ormance Parame tersThe second tier of strategy development is the formulation of a bank-widebusiness plan and target return metrics. This should set key performanceindicators (KPIs) in actual quantitative terms. The base KPIs are:

& capital: return on capital; return on equity; RAROC; assets-to-capitalratio;

& liquidity: loan-to-deposit ratio; liquidity ratio; wholesale funding ratio;& cost base: front-office/back-office ratio; cost–income ratio;& risk appetite: provisions/lending; NPLs/lending; VaR;& growth: asset growth; liability growth.

We emphasise that the targets are not necessarily minimum levels, andin some cases they can be maximum levels. A sustained performance of12% RoE over a 10–15-year period is infinitely preferable, from anaggregate market viewpoint (or from society’s viewpoint), to several yearsof 22% RoE followed by losses for a year or two. Equally, a market sharetarget of 10% does not mean that a level of 20% is desirable: an emphasison market share as a KPI was one of the forces that drove Northern Rock


Continues...


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69

2 AN INTRODUCTION TO VALUE-AT-RISK

The risk management department was one of the fastest growingareas in investment and commercial banks during the 1990s,

and again after the crash of 2008. A string of high-profile bankinglosses and failures, typified by the fall of Barings Bank in 1995,highlighted the importance of risk management to bank managersand shareholders alike. In response to the volatile and complexnature of risks that they were exposed to, banks set up specialistrisk management departments, whose functions included bothmeasuring and managing risk. As a value-added function, riskmanagement can assist banks not only in managing risk, but alsoin understanding the nature of their profit and loss, and so helpincrease return on capital. It is now accepted that senior directorsof banks need to be thoroughly familiar with the concept of riskmanagement. One of the primary tools of the risk manager is value-at-risk (VaR), which is a quantitative measure of the risk exposureof an institution. For a while VaR was regarded as somewhatinaccessible, and only the preserve of mathematicians and quanti-tative analysts. Although VaR is indeed based on statistical tech-niques that may be difficult to grasp for the layman, its basic premisecan, and should, be explained in straightforward fashion, in a waythat enables non-academics to become comfortable with theconcept. The problem with VaR is that while it was only ever ameasure, based on some strong assumptions, of approximatemarket risk exposure (it is unsuited to measuring risk exposure inthe banking book), it suffers in the eyes of its critics in having thecachet of science. This makes it arcane and inaccessible, whileparadoxically being expected to be much more accurate than itwas ever claimed to be. Losses suffered by banks during the crash of2007–08 were much larger than any of their VaR values, which iswhere the measure comes in for criticism. But we can leave thataside for now, and concentrate just on introducing the technicalities.

Later in the book we describe and explain the calculation andapplication of VaR. We begin here with a discussion of risk.

DEFINING RISK

Any transaction or undertaking with an element of uncertainty as toits future outcome carries an element of risk: risk can be thought ofas uncertainty. To associate particular assets such as equities, bondsor corporate cash flows with types of risk, we need to define ‘risk’itself. It is useful to define risk in terms of a risk horizon, the point at

70

INTRODUCTION TO RISK 3

which an asset will be realised, or turned into cash. All marketparticipants, including speculators, have an horizon, which maybe as short as a half-day. Essentially then, the horizon is the timeperiod relating to the risk being considered.

Once we have established a notion of horizon, a working definitionof risk is the uncertainty of the future total cash value of an invest-ment on the investor’s horizon date. This uncertainty arises frommany sources. For participants in the financial markets risk isessentially a measure of the volatility of asset returns, although ithas a broader definition as being any type of uncertainty as to futureoutcomes. The types of risk that a bank or securities house is exposedto as part of its operations in the bond and capital markets arecharacterised below.

THE ELEMENTS OF RISK:CHARACTERISING RISK

Banks and other financial institutions are exposed to a number ofrisks during the course of normal operations. The different types ofrisk are broadly characterised as follows:

. Market risk – risk arising from movements in prices in financialmarkets. Examples include foreign exchange (FX) risk, interestrate risk and basis risk. In essence market risk applies to‘tradeable’ instruments, ones that are marked-to-market in atrading book, as opposed to assets that are held to maturity,and never formally repriced, in a banking book.

. Credit risk – something called issuer risk refers to risk that acustomer will default. Examples include sovereign risk, marginalrisk and force majeure risk.

. Liquidity risk – this refers to two different but related issues: for aTreasury or money markets’ person, it is the risk that a bank hasinsufficient funding to meet commitments as they arise. That is,the risk that funds cannot be raised in the market as and whenrequired. For a securities or derivatives trader, it is the risk thatthemarket for assets becomes too thin to enable fair and efficienttrading to take place. This is the risk that assets cannot be sold orbought as and when required. We should differentiate thereforebetween funding liquidity and trading liquidity whenever usingthe expression liquidity.

71


which an asset will be realised, or turned into cash. All marketparticipants, including speculators, have an horizon, which maybe as short as a half-day. Essentially then, the horizon is the timeperiod relating to the risk being considered.

Once we have established a notion of horizon, a working definitionof risk is the uncertainty of the future total cash value of an invest-ment on the investor’s horizon date. This uncertainty arises frommany sources. For participants in the financial markets risk isessentially a measure of the volatility of asset returns, although ithas a broader definition as being any type of uncertainty as to futureoutcomes. The types of risk that a bank or securities house is exposedto as part of its operations in the bond and capital markets arecharacterised below.

THE ELEMENTS OF RISK:CHARACTERISING RISK

Banks and other financial institutions are exposed to a number ofrisks during the course of normal operations. The different types ofrisk are broadly characterised as follows:

. Market risk – risk arising from movements in prices in financialmarkets. Examples include foreign exchange (FX) risk, interestrate risk and basis risk. In essence market risk applies to‘tradeable’ instruments, ones that are marked-to-market in atrading book, as opposed to assets that are held to maturity,and never formally repriced, in a banking book.

. Credit risk – something called issuer risk refers to risk that acustomer will default. Examples include sovereign risk, marginalrisk and force majeure risk.

. Liquidity risk – this refers to two different but related issues: for aTreasury or money markets’ person, it is the risk that a bank hasinsufficient funding to meet commitments as they arise. That is,the risk that funds cannot be raised in the market as and whenrequired. For a securities or derivatives trader, it is the risk thatthemarket for assets becomes too thin to enable fair and efficienttrading to take place. This is the risk that assets cannot be sold orbought as and when required. We should differentiate thereforebetween funding liquidity and trading liquidity whenever usingthe expression liquidity.


. Operational risk – risk of loss associated with non-financialmatters such as fraud, system failure, accidents and ethics.Table 1.1 assigns sources of risk for a range of fixed interest,FX, interest rate derivative and equity products. The classifica-tion has assumed a 1-year horizon, but the concepts apply to anytime horizon.

Forms of market risk

Market risk reflects the uncertainty as to an asset’s price when it issold. Market risk is the risk arising from movements in financialmarket prices. Specific market risks will differ according to the typeof asset under consideration:

Table 1.1 Characterising risk.

Market

Reinvestm

ent

Credit

Sovereign

FX

Basis

Prepayment

Counterparty

Government bondDeveloped countryDeveloping country

Zero-coupon bond

Corporate bond

Asset-backed bond

Bank deposit

FRA

Futures contract

Forward contract

Interest rate swap

Repo

Equity (listed exchange)

72


. Currency risk – this arises from exposure to movements in FXrates. A version of currency risk is transaction risk, wherecurrency fluctuations affect the proceeds from day-to-daytransactions.

. Interest rate risk – this arises from the impact of fluctuatinginterest rates and will directly affect any entity borrowing orinvesting funds. The most common exposure is simply to thelevel of interest rates but some institutions run positions that areexposed to changes in the shape of the yield curve. The basic riskarises from revaluation of the asset after a change in rates.

. Equity risk – this affects anyone holding a portfolio of shares,which will rise and fall with the level of individual share pricesand the level of the stock market.

. Other market risk – there are residual market risks which fall inthis category. Among these are volatility risk, which affectsoption traders, and basis risk, which has a wider impact. Basisrisk arises whenever one kind of risk exposure is hedged withan instrument that behaves in a similar, but not necessarilyidentical manner. One example would be a company using3-month interest rate futures to hedge its commercial paper(CP) programme. Although eurocurrency rates, to which futuresprices respond, are well correlated with CP rates, they do notinvariably move in lock step. If CP rates moved up by 50 basispoints but futures prices dropped by only 35 basis points, the15-bps gap would be the basis risk in this case.

Other risks

. Liquidity risk – in banking, this refers to the risk that a bankcannot raise funds to refinance loans as the original borrowingbecomes past due. It is sometimes also referred to as rollover risk.In other words, it refers to the risk of an inability to continue toraise funds to replace maturing liabilities. There is also another(related) liquidity risk, which refers to trading liquidity. This isthe risk that an asset on the balance sheet cannot be sold at apreviously perceived fair value, or cannot be sold at all, and henceexperiences illiquidity.

. Credit risk – the risk that an obligor (the entity that has borrowedfunds from you) defaults on the loan repayments.

. Counterparty risk – all transactions involve one or both parties incounterparty risk, the potential loss that can arise if one party

73


. Currency risk – this arises from exposure to movements in FXrates. A version of currency risk is transaction risk, wherecurrency fluctuations affect the proceeds from day-to-daytransactions.

. Interest rate risk – this arises from the impact of fluctuatinginterest rates and will directly affect any entity borrowing orinvesting funds. The most common exposure is simply to thelevel of interest rates but some institutions run positions that areexposed to changes in the shape of the yield curve. The basic riskarises from revaluation of the asset after a change in rates.

. Equity risk – this affects anyone holding a portfolio of shares,which will rise and fall with the level of individual share pricesand the level of the stock market.

. Other market risk – there are residual market risks which fall inthis category. Among these are volatility risk, which affectsoption traders, and basis risk, which has a wider impact. Basisrisk arises whenever one kind of risk exposure is hedged withan instrument that behaves in a similar, but not necessarilyidentical manner. One example would be a company using3-month interest rate futures to hedge its commercial paper(CP) programme. Although eurocurrency rates, to which futuresprices respond, are well correlated with CP rates, they do notinvariably move in lock step. If CP rates moved up by 50 basispoints but futures prices dropped by only 35 basis points, the15-bps gap would be the basis risk in this case.

Other risks

. Liquidity risk – in banking, this refers to the risk that a bankcannot raise funds to refinance loans as the original borrowingbecomes past due. It is sometimes also referred to as rollover risk.In other words, it refers to the risk of an inability to continue toraise funds to replace maturing liabilities. There is also another(related) liquidity risk, which refers to trading liquidity. This isthe risk that an asset on the balance sheet cannot be sold at apreviously perceived fair value, or cannot be sold at all, and henceexperiences illiquidity.

. Credit risk – the risk that an obligor (the entity that has borrowedfunds from you) defaults on the loan repayments.

. Counterparty risk – all transactions involve one or both parties incounterparty risk, the potential loss that can arise if one party


were to default on its obligations. Counterparty risk is mostrelevant in the derivatives market, where every contract ismarked-to-market daily and so a positive MTM is taken to theprofit & loss (P&L) account. If the counterparty defaults beforethe contract has expired, there is risk that the actual P&Lwill notbe realized. In the credit derivatives market, a counterparty thathas sold protection on the third-party reference name on thecredit derivative contract and which subsequently defaultswill mean the other side to the trade is no longer protectedagainst the default of that third party.

. Reinvestment risk – if an asset makes any payments before theinvestor’s horizon, whether it matures or not, the cash flowswill have to be reinvested until the horizon date. Since thereinvestment rate is unknown when the asset is purchased,the final cash flow is uncertain.

. Sovereign risk – this is a type of credit risk specific to agovernment bond. Post 2008, there is material risk of defaultby an industrialised country. A developing country maydefault on its obligation (or declare a debt ‘moratorium’) ifdebt payments relative to domestic product reach unsustainablelevels.

. Prepayment risk – this is specific to mortgage-backed andasset-backed bonds. For example, mortgage lenders allow thehomeowner to repay outstanding debt before the statedmaturity.If interest rates fall prepayment will occur, which forcesreinvestment at rates lower than the initial yield.

. Model risk – some financial instruments are heavily dependenton complex mathematical models for pricing and hedging. If themodel is incorrectly specified, is based on questionable assump-tions or does not accurately reflect the true behaviour of themarket, banks trading these instruments could suffer extensivelosses.

Risk estimation

There are a number of different ways of approaching the estimationof market risk. The key factors determining the approach are theuser’s response to two questions:

. Can the user accept the assumption of normality – is it reason-able to assume that market movements follow the normal dis-tribution? If so, statistical tools can be employed.

74


. Does the value of positions change linearly with changes inmarket prices? If not (as is typical for option positions wheremarket movements are not very small), simulation techniqueswill be more useful.

Were the answers to both questions to be ‘yes’ then we could becomfortable using standard measures of risk such as duration andconvexity (these concepts are covered later). If the answers are ‘no’then we are forced to use scenario analysis combined with simula-tion techniques. If, as is more likely, the answer to the first questionis ‘yes’ and the second ‘no’, then a combination of statistical toolsand simulation techniques will be required.

For most banks and securities houses the portfolio will almostcertainly behave in a non-linear manner because that is thenature of financial markets. Hence, a combination of statisticaltools and simulation is likely to be the most effective risk measure-ment approach. The scenarios used in simulations are often amixture of observed rate and price changes from selected periodsin the past, and judgement calls by the risk manager. The variousalternative methods are examined in Chapter 3.

RISK MANAGEMENT

The risk management function grew steadily in size and importancewithin commercial and investment banks during the 1990s. Riskmanagement departments exist not to eliminate the possibility of allrisk, should such action indeed be feasible or desirable; rather, tocontrol the frequency, extent and size of such losses in such a wayas to provide the minimum surprise to senior management andshareholders.

Risk exists in all competitive business although the balance betweenfinancial risks of the type described above and general and manage-ment risk varies with the type of business engaged in. The keyobjective of the riskmanagement functionwithin a financial institu-tion is to allow for a clear understanding of the risks and exposuresthe firm is engaged in, such that monetary loss is deemed acceptableby the firm. The acceptability of any loss should be on the basis thatsuch (occasional) loss is to be expected as a result of the firmbeing engaged in a particular business activity. If the bank’s riskmanagement function is effective, there will be no over-reaction to

75


. Does the value of positions change linearly with changes inmarket prices? If not (as is typical for option positions wheremarket movements are not very small), simulation techniqueswill be more useful.

Were the answers to both questions to be ‘yes’ then we could becomfortable using standard measures of risk such as duration andconvexity (these concepts are covered later). If the answers are ‘no’then we are forced to use scenario analysis combined with simula-tion techniques. If, as is more likely, the answer to the first questionis ‘yes’ and the second ‘no’, then a combination of statistical toolsand simulation techniques will be required.

For most banks and securities houses the portfolio will almostcertainly behave in a non-linear manner because that is thenature of financial markets. Hence, a combination of statisticaltools and simulation is likely to be the most effective risk measure-ment approach. The scenarios used in simulations are often amixture of observed rate and price changes from selected periodsin the past, and judgement calls by the risk manager. The variousalternative methods are examined in Chapter 3.

RISK MANAGEMENT

The risk management function grew steadily in size and importancewithin commercial and investment banks during the 1990s. Riskmanagement departments exist not to eliminate the possibility of allrisk, should such action indeed be feasible or desirable; rather, tocontrol the frequency, extent and size of such losses in such a wayas to provide the minimum surprise to senior management andshareholders.

Risk exists in all competitive business although the balance betweenfinancial risks of the type described above and general and manage-ment risk varies with the type of business engaged in. The keyobjective of the riskmanagement functionwithin a financial institu-tion is to allow for a clear understanding of the risks and exposuresthe firm is engaged in, such that monetary loss is deemed acceptableby the firm. The acceptability of any loss should be on the basis thatsuch (occasional) loss is to be expected as a result of the firmbeing engaged in a particular business activity. If the bank’s riskmanagement function is effective, there will be no over-reaction to


any unexpected losses, which may increase eventual costs to manytimes the original loss amount.

The risk management function

While there is no one agreed organisation structure for the riskmanagement function, the following may be taken as beingreflective of the typical bank set-up:

. an independent, ‘middle office’ department responsible fordrawing up and explicitly stating the bank’s approach to risk,and defining trading limits and the areas of the market that thefirm can have exposure to;

. the head of the risk function reporting to an independent seniormanager, who is a member of the executive board;

. monitoring the separation of duties between front, middle andback office, often in conjunction with an internal audit function;

. reporting to senior management, including firm’s overallexposure and adherence of the front office to the firm’s overallrisk strategy;

. communication of risks and risk strategy to shareholders;

. where leading edge systems are in use, employment of the riskmanagement function to generate competitive advantage in themarket as well as control.

The risk management function is more likely to deliver effectiveresults when there are clear lines of responsibility and account-ability. It is also imperative that the department interacts closelywith other areas of the front and back office.

In addition to the above the following are often accepted asingredients of a risk management framework in an institutionengaged in investment banking and trading activity:

. proactive management involvement in risk issues;

. daily overview of risk exposure profile and profit & loss (P&L)reports;

. VaR as a common measure of risk exposure, in addition to othermeasures including ‘jump risk’ to allow for market corrections;

. defined escalation procedures to deal with rising levels of tradingloss, as well as internal ‘stop-loss’ limits;

. independent daily monitoring of risk utilisation by middle-officerisk management function;

76


. independent production of daily P&L, and independent review offront-office closing prices on a daily basis;

. independent validation of market pricing, and pricing and VaRmodels.

These guidelines, adopted universally in the investment bankingcommunity, should assist in the development of an influentialand effective riskmanagement function for all financial institutions.We say ‘should’, but of course the experience of JPMorgan, Soc Genand UBS in the 21st century, shows that the existence of large andseemingly sophisticated risk management infrastructures does notpreclude multi-billion dollar trading losses.

Managing risk

The different stakeholders in a bank or financial institution willhave slightly different perspectives on risk and its management. Ifwe were to generalise, shareholders will wish for stable earnings aswell as the highest possible return on capital. From the point ofview of business managers though, the perspective may be slightlydifferent and possibly shorter term. For them, risk managementoften takes the following route:

. create as diversified a set of business lines as possible, and withineach business line diversify portfolios to maximum extent;

. establish procedures to enable some measure of forecasting ofmarket prices;

. hedge the portfolio to minimise losses when market forecastssuggest that losses are to be expected.

The VaR measurement tool falls into the second and third areas ofthis strategy. It is used to give an idea of risk exposure (generally, tomarket and credit risk only) so that banks can stay within tradinglimits, and to feed into the hedge calculation.

QUANTITATIVE MEASUREMENT OFRISK–REWARD

Before introducing the concept of VaR we will consider threestandard measures of risk–reward exposure used in the investmentcommunity.

77


. independent production of daily P&L, and independent review offront-office closing prices on a daily basis;

. independent validation of market pricing, and pricing and VaRmodels.

These guidelines, adopted universally in the investment bankingcommunity, should assist in the development of an influentialand effective riskmanagement function for all financial institutions.We say ‘should’, but of course the experience of JPMorgan, Soc Genand UBS in the 21st century, shows that the existence of large andseemingly sophisticated risk management infrastructures does notpreclude multi-billion dollar trading losses.

Managing risk

The different stakeholders in a bank or financial institution willhave slightly different perspectives on risk and its management. Ifwe were to generalise, shareholders will wish for stable earnings aswell as the highest possible return on capital. From the point ofview of business managers though, the perspective may be slightlydifferent and possibly shorter term. For them, risk managementoften takes the following route:

. create as diversified a set of business lines as possible, and withineach business line diversify portfolios to maximum extent;

. establish procedures to enable some measure of forecasting ofmarket prices;

. hedge the portfolio to minimise losses when market forecastssuggest that losses are to be expected.

The VaR measurement tool falls into the second and third areas ofthis strategy. It is used to give an idea of risk exposure (generally, tomarket and credit risk only) so that banks can stay within tradinglimits, and to feed into the hedge calculation.

QUANTITATIVE MEASUREMENT OFRISK–REWARD

Before introducing the concept of VaR we will consider threestandard measures of risk–reward exposure used in the investmentcommunity.


Standard deviation

We defined ‘risk’ above as a prelude to considering its measurementin a VaR context. Investment ‘risk’ tends to be viewed differently byacademics and investors. Academics consider risk within modernportfolio theory to be defined as standard deviation or volatility. Toinvestors risk usually is the probability of loss. Standard deviation isa traditional measure often used by investment professionals. Itmeasures an investment’s variability of returns; that is, its volatilityin relation to its average return.

While standard deviation has the cachet of science it is a narrowmeasure and may not provide sufficient information by itself. It issimply a measure of volatility and as a measure of the probability ofloss is of limited use. However, its usefulness is increased if one pairsit with returns, as in the Sharpe Ratio or the Van Ratio. Moving onfrom here, the concept of VaR is built on obtaining probabilities ofloss based on the distribution of returns from a market investmentinstrument.

Sharpe Ratio

The Sharpe Ratio is a reward–risk ratio. It measures the extent towhich the return of an investment (above the risk-free return)exceeds its volatility. The higher the ratio, the more reward aninvestment provides for the risk incurred. The ratio is calculatedaccording to the following equation:

Sharpe Ratio ¼ Rm � Rf

Vmð1:1Þ

where Rm ¼ Rate of return of investment m;Rf ¼ Risk-free rate of return (e.g., T-Bill);Vm ¼ Standard deviation of instrument m.

A ratio of 0.5 is considered fair return for risk incurred. For aninvestor it is more useful as a relative measure, in comparing theratio of one investment with that of another. For bank trading desksit is a useful measure of the return generated against the riskincurred, for which the return and volatility of individual tradingbooks can be compared with that on the risk-free instrument (or abank book trading only T-bills).

78


Van Ratio

The Van Ratio expresses the probability of an investment suffering aloss for a defined period, usually 1 year. For example, a Van Ratio of20% indicates that there is a 1 in 5 chance of a loss during every four-quarter rolling window. The ratio first uses the following fraction tocalculate this probability:

Compound annual return for the measurement period

Average four-quarter standard deviation for the measurement period

ð1:2ÞThe probability of a loss is then calculated using standard normalcurve probability tables.

The Van Ratio provides an intuitive measure of absolute risk, theconcept of the probability of a loss. To this end its calculationhas assumed a normal distribution of returns. The assumptionof normality of returns is important in the concept of VaR ascalculated by most of the models and methodologies in use infinancial institutions.

79


Van Ratio

The Van Ratio expresses the probability of an investment suffering aloss for a defined period, usually 1 year. For example, a Van Ratio of20% indicates that there is a 1 in 5 chance of a loss during every four-quarter rolling window. The ratio first uses the following fraction tocalculate this probability:

Compound annual return for the measurement period

Average four-quarter standard deviation for the measurement period

ð1:2ÞThe probability of a loss is then calculated using standard normalcurve probability tables.

The Van Ratio provides an intuitive measure of absolute risk, theconcept of the probability of a loss. To this end its calculationhas assumed a normal distribution of returns. The assumptionof normality of returns is important in the concept of VaR ascalculated by most of the models and methodologies in use infinancial institutions.


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81

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1

Credit Securitizations and Derivatives

Daniel Roesch1 and Harald Scheule2

1University of Hannover2University of Technology, Sydney

The Global Financial Crisis (GFC) led to an unprecedented and, by most of us, unexpectedincrease of impairment and loss rates for securitizations and derivatives. The disappointmentof investors manifested in the criticism of models applied for measuring credit portfolio riskin relation to credit securities and derivatives.

Credit portfolio securitizations and derivatives are primarily OTC market instruments withexposures totaling approximately $40 trillion. Securitizations involve the sale of assets intobankruptcy-remote special purpose vehicles, which are funded by investors of different senior-ities (tranches). Based on the nature of the securitized asset portfolios, important transactiontypes include asset-backed securities, collateralized debt obligations, home equity loan-backedsecurities and mortgage-backed securities. On the other side, credit derivatives are generallyunfunded contracts and share similar structures and appraisal challenges with securitizations.

This exciting and timely book provides regulators with an overview of the risk inherentin credit securitizations and derivatives. The book aims to help quantitative analysts improverisk models and managers of financial institutions evaluate the performance of existing riskmodels and future model needs. The book addresses challenges in relation to the evaluationof credit portfolio securitizations and derivatives and covers the following areas:

� credit portfolio risk measurement,� credit portfolio risk tranching,� credit ratings,� credit default swaps, indices and tranches,� counterparty credit risk and clearing of derivatives contracts,� liquidity risk,� regulation.

The following provides a first introduction to some of these areas.

1.1 ECONOMIC CYCLES AND CREDIT PORTFOLIO RISK

The Global Financial Crisis (GFC) had its origin in the US mortgage market. During the GFCvarious changes in key macroeconomic variables were observed: (i) declining house prices,where changes in house prices often exceeded their equity finance, (ii) higher mortgage resetrates despite declining risk-free interest rates, (iii) decreases in GDP coinciding with higherunemployment rates and lower per capita earnings. This economic downturn spread to other

82


4 Credit Securitizations and Derivatives

0

2

4

6

8

10

12

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Del

inq

uen

cy R

ate

in %

Business Loans Consumer Loans Credit Card Loans Single-family Residential Mortgages

Figure 1.1 Delinquency rates, all commercial US banks, seasonally adjusted.Note: This chart shows the delinquency rates for business loans, consumer loans, credit card loans andsingle-family residential mortgages. Delinquency rates are the ratios of the dollar amount of a bank’sdelinquent loans to the dollar amount of total loans outstanding in that category.Source: Board of Governors of the US Federal Reserve System.

asset classes, financial products and eventually financial markets in many other countriesthrough various mechanisms.

Figure 1.1 shows the delinquency rates for business loans, consumer loans, credit card loansand single-family residential mortgages. Traditionally, credit risk moves in parallel for thevarious loan classes. This trend was reversed in 2007 when delinquency rates for single-familyresidential mortgages dramatically increased to historically unprecedented levels (gray linewith black markers).

Demyanyk et al. (2011) and others confirm that house prices are a major driver of mortgagecredit risk. Figure 1.2 compares the delinquency rates for single-family residential mort-gages with the growth rate of the Case–Shiller house price index for 10 major MetropolitanStatistical Areas in the United States (Greater Boston, Chicago metropolitan area, Denver-Aurora Metropolitan Area, Las Vegas metropolitan area, Greater Los Angeles, South Floridametropolitan area, New York metropolitan area, San Diego County, California, San Francisco–Oakland–Fremont, CA and Washington Metropolitan Area). The negative correlation betweenthe two variables is apparent. More interestingly, the decrease in growth rates in 2006/07 antic-ipates the subsequent increase in mortgage delinquency rates.

83


Credit Securitizations and Derivatives 5

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1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

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Figure 1.2 Delinquency rates for single-family residential mortgages with the Case–Shiller houseprice index.Note: This chart shows the negative relationship between delinquency rates for single-family residentialmortgages and the Case–Shiller house price index.

The cyclical movement of credit risk poses a challenge to practitioners, prudential regula-tors and academics as cyclical patterns may be included to various degrees in risk measures.Rosch and Scheule (2005) highlight the two extremes. The first extreme is the through-the-cycle (TTC) approach, which averages over the business cycle and is often promoted bybanks in order to avoid cyclical regulatory capital requirements. The problem with cyclicalregulatory capital requirements is that banks may be exposed to raise capital during eco-nomic downturns (when risk is high) when share prices are low and when capital supplyis limited.

The second extreme is the point-in-time approach (PIT), which makes a prediction for futureperiods. PIT models are more accurate as they are generally based on forecast models, whichexplain the credit risk for a future point in time by information which is available at the timewhen the forecast is made.

Similar model approaches are common for other risk dimensions such as loss rates givendefault, and exposures given default (compare Bade, Rosch and Scheule, 2011 and Rosch andScheule, 2010). Many recent current contributions in literature aim to improve the measurementof mortgage risk by building PIT risk models which include dynamic risk drivers such as realestate prices.

84



1.2 CREDIT PORTFOLIO RISK MEASUREMENT

Credit portfolio risk models measure the risk for loan portfolios. Such models are generallybased on a set of parameters such as probabilities of default, loss rates given default, exposuresat default and default correlations. Mortgage portfolios are retail portfolios and are charac-terized by a large number of mortgages. The US delinquency rates, which are presented inFigure 1.1, may be used as proxies for the portfolio default rate as they average over manyindividual exposures. Default rates are low in economic booms and high in economic down-turns. Financial institutions generate default rate distributions around the current default rateand derive key portfolio measures, such as expected loss or value at risk. In addition, economicand regulatory capital may be derived from such distributions.

Figure 1.3 shows the default rate distribution for delinquency rates for single-family resi-dential mortgages in the first quarter of 2006, which represents the economic boom state and2011, which represents the economic downturn state. The application of TTC models willlead to time-invariant measures of portfolio risk while the application of PIT models will leadto time-varying measures of portfolio risk. Real-world models have mixed properties and thePIT-character of risk models accelerated the need for financial institutions to recapitalize dur-ing the GFC. The current discussion in literature focuses on the trade-off between (i) achieving

Figure 1.3 Credit portfolio loss distributions.Note: The application of TTC models will lead to time-invariant measures of portfolio risk while theapplication of PIT models will lead to time-varying measures of portfolio risk.Source: Own calculations based on delinquency rates for single-family residential mortgages in thefirst quarter of 2006 (expected default rate: 1.59%), which represents the economic book state, and2011 (expected default rate: 10.37%), which represents the economic downturn state. A Basel II assetcorrelation for residential mortgage loans of 15% and the Vasicek density was assumed in deriving thenumbers underlying the figure.



model accuracy and therefore capital adequacy, and (ii) a reduction of capital cyclicality. ABasel II asset correlation for residential mortgage loans of 15% and the Vasicek density wasassumed in deriving the numbers underlying the figure. The vertical lines indicate the expecteddefault rates of 1.59% and 10.37% for the two states.

1.3 CREDIT PORTFOLIO RISK TRANCHING

Credit derivatives and securitizations are often subject to tranching, which is highly sensitive tothe systematic exposure. The interaction between states of the economy and the risk exposurefor tranches is forcefully shown in Figure 1.3. The attachment risk increases for senior tranchesmore so than for junior tranches from economic booms to economic downturns. For example,if a structure has an equity, mezzanine and junior tranche with attachment levels 0%, 5%and 20%, then the attachment probability for the mezzanine tranche is 5.18% in a boom and74.55% in a recession. The attachment probability for the senior tranche is 0.02% in a boomand 10.53% in a recession. The attachment probability for the equity tranche is convergingto one for large portfolios in both economic scenarios. Rosch and Scheule (2012) analyze therisk, capital adequacy and policy implications in relation to securitizations.

1.4 CREDIT RATINGS

The disappointment of investors also manifested in the criticism of models applied by creditrating agencies (CRAs). First contributions analyze the ratings of securitizations in moregeneral terms or in relation to different asset classes such as collateralized debt obligations.Benmelech and Dlugosz (2009) analyze collateralized loan obligations (CLOs) rated by Stan-dard & Poor’s and find a mismatch between credit ratings and the quality of the underlying loanportfolios. Bolton et al. (2011) analyze CRA securitization rating performance with regard tothe business cycle. Griffin and Tang (2012) compare CRA model methodologies with CRAratings for collateralized debt obligations. Coval et al. (2009) argue that model risk and theexposure to systemic risk of securitization may explain the increase of impairment rates duringthe GFC.

1.5 ACTUARIAL VS. MARKET CREDIT RISK PRICING

So far, we have focused on actuarial, so-called real-world risk measures. Credit risks arepriced in many markets such as lending markets, deposit markets, corporate bond markets,securitization markets or credit derivatives markets. Many risk models rely on market pricesto measure the inherent level of risk. However, Figure 1.4 shows that a gap between actuarialand market priced losses exists and that this gap widens during an economic downturn. Inaddition, the volatility of market-based risk measures is larger than the volatility of real-worldrisk measures.

Market participants as well as researchers are currently scrutinizing the accuracy of market-based risk models and implications on financial institutions’ risk measurement, managementand reporting.

85



model accuracy and therefore capital adequacy, and (ii) a reduction of capital cyclicality. ABasel II asset correlation for residential mortgage loans of 15% and the Vasicek density wasassumed in deriving the numbers underlying the figure. The vertical lines indicate the expecteddefault rates of 1.59% and 10.37% for the two states.

1.3 CREDIT PORTFOLIO RISK TRANCHING

Credit derivatives and securitizations are often subject to tranching, which is highly sensitive tothe systematic exposure. The interaction between states of the economy and the risk exposurefor tranches is forcefully shown in Figure 1.3. The attachment risk increases for senior tranchesmore so than for junior tranches from economic booms to economic downturns. For example,if a structure has an equity, mezzanine and junior tranche with attachment levels 0%, 5%and 20%, then the attachment probability for the mezzanine tranche is 5.18% in a boom and74.55% in a recession. The attachment probability for the senior tranche is 0.02% in a boomand 10.53% in a recession. The attachment probability for the equity tranche is convergingto one for large portfolios in both economic scenarios. Rosch and Scheule (2012) analyze therisk, capital adequacy and policy implications in relation to securitizations.

1.4 CREDIT RATINGS

The disappointment of investors also manifested in the criticism of models applied by creditrating agencies (CRAs). First contributions analyze the ratings of securitizations in moregeneral terms or in relation to different asset classes such as collateralized debt obligations.Benmelech and Dlugosz (2009) analyze collateralized loan obligations (CLOs) rated by Stan-dard & Poor’s and find a mismatch between credit ratings and the quality of the underlying loanportfolios. Bolton et al. (2011) analyze CRA securitization rating performance with regard tothe business cycle. Griffin and Tang (2012) compare CRA model methodologies with CRAratings for collateralized debt obligations. Coval et al. (2009) argue that model risk and theexposure to systemic risk of securitization may explain the increase of impairment rates duringthe GFC.

1.5 ACTUARIAL VS. MARKET CREDIT RISK PRICING

So far, we have focused on actuarial, so-called real-world risk measures. Credit risks arepriced in many markets such as lending markets, deposit markets, corporate bond markets,securitization markets or credit derivatives markets. Many risk models rely on market pricesto measure the inherent level of risk. However, Figure 1.4 shows that a gap between actuarialand market priced losses exists and that this gap widens during an economic downturn. Inaddition, the volatility of market-based risk measures is larger than the volatility of real-worldrisk measures.

Market participants as well as researchers are currently scrutinizing the accuracy of market-based risk models and implications on financial institutions’ risk measurement, managementand reporting.

86



0

0.005

0.01

0.015

0.02

0.025

2005 2006 2007 2008

Cred

it R

isk

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Actuarial Loss Market Premium

Figure 1.4 Actuarial losses and market premiums.Note: Actuarial loss rates are calculated as default rates multiplied by average loss rates given default foron BAA-rated bonds. Market premium is calculated as the average credit spread of credit default swapsof BAA-rated bonds.Source: Bloomberg and Moody’s rating agency.

1.6 REGULATION

Prudential regulators of financial institutions aim to ensure that, under all reasonable cir-cumstances, financial promises made by the institutions are met within a stable, efficientand competitive financial system. The enhancement of prudential regulations is an importantelement in ensuring the stability of financial institutions, markets and instruments.

In response to the GFC, the G-20 countries have proposed a new set of regulatory require-ments with regard to (a) capital, (b) accounting and (c) liquidity of financial institutions, alsoknown as Basel III. These revised requirements are based on national feedback such as theTurner Review (FSA 2009). For example, the Turner Review outlined various changes forprudential regulation: (i) increasing the quantity and quality of bank capital, (ii) increasing thetrading book capital, (iii) avoiding pro-cyclicality in relation to bank capital regulations,(iv) creating counter-cyclical capital buffers, (v) offsetting pro-cyclicality in publishedaccounts, (vi) implementing a gross leverage ratio backstop and (vii) containing liquidityrisks in individual banks and at the systemic level.

These new rules have been expressed under Basel III, which aims to increase capital andliquidity of banks as well as in national regulations such as the Dodd–Frank Wall Street Reformand Consumer Protection Act of 2010 in the US.

Surprisingly, few measures relate to minimum standards for financial risk models. It is thisarea where research may make a major contribution. New policies require the understandingof the characteristics of financial risks with regard to level, idiosyncratic and systematic risk,

87



0

0.005

0.01

0.015

0.02

0.025

2005 2006 2007 2008

Cred

it R

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Actuarial Loss Market Premium

Figure 1.4 Actuarial losses and market premiums.Note: Actuarial loss rates are calculated as default rates multiplied by average loss rates given default foron BAA-rated bonds. Market premium is calculated as the average credit spread of credit default swapsof BAA-rated bonds.Source: Bloomberg and Moody’s rating agency.

1.6 REGULATION

Prudential regulators of financial institutions aim to ensure that, under all reasonable cir-cumstances, financial promises made by the institutions are met within a stable, efficientand competitive financial system. The enhancement of prudential regulations is an importantelement in ensuring the stability of financial institutions, markets and instruments.

In response to the GFC, the G-20 countries have proposed a new set of regulatory require-ments with regard to (a) capital, (b) accounting and (c) liquidity of financial institutions, alsoknown as Basel III. These revised requirements are based on national feedback such as theTurner Review (FSA 2009). For example, the Turner Review outlined various changes forprudential regulation: (i) increasing the quantity and quality of bank capital, (ii) increasing thetrading book capital, (iii) avoiding pro-cyclicality in relation to bank capital regulations,(iv) creating counter-cyclical capital buffers, (v) offsetting pro-cyclicality in publishedaccounts, (vi) implementing a gross leverage ratio backstop and (vii) containing liquidityrisks in individual banks and at the systemic level.

These new rules have been expressed under Basel III, which aims to increase capital andliquidity of banks as well as in national regulations such as the Dodd–Frank Wall Street Reformand Consumer Protection Act of 2010 in the US.

Surprisingly, few measures relate to minimum standards for financial risk models. It is thisarea where research may make a major contribution. New policies require the understandingof the characteristics of financial risks with regard to level, idiosyncratic and systematic risk,



as well as the impact on the capital adequacy of banks and risk transfer mechanisms such assecuritizations.

1.7 THANK YOU

It is apparent from these examples that many global challenges for credit securitizationsand derivatives persist and that more knowledge on these issues is required. This book isa first step into this direction. Leading academics and practitioners from many institutionsand places have come together over the past two years to share their insights and recentresearch findings on credit securitizations and derivatives. This book aims to transfer thisknowledge to the wider community. This research was supported by the Centre for InternationalFinance and Regulation (project number E001) which is funded by the Commonwealth andNSW Governments and supported by other Consortium members (see www.cifr.edu.au). Wewould like to thank the Centre for International Finance and Regulation and the Hong KongInstitute for Monetary Research for their support. We hope you have a great reading time andthat the book will provide further stimulus for research and impact in the practice of creditsecuritizations and derivatives.

REFERENCES

Bade, B., Rosch, D., Scheule, H., 2011. Default and recovery risk dependencies in a simple credit risk model. EuropeanFinancial Management, 17 (1), 120–144.

Benmelech, E., Dlugosz, J., 2009. The alchemy of CDO credit ratings. Journal of Monetary Economics, 56, 617–634.Bolton, P., Freixas, X., Shapiro, J., 2011. The Credit Ratings Game. Journal of Finance, 67(1), 85–112.Coval, J., Jurek, J., Stafford, E., 2009. The economics of structured finance. Journal of Economic Perspectives, 23,

3–25.Demyanyk, Y., Koijen, R., Hemert, O. V., 2011. Understanding the subprime mortgage crisis, 24(6), 1848–1880.Fitch Ratings. 2006. Exposure Draft: Introducing the Fitch VECTOR Default Model Version 3.0.FSA. 2009. The Turner review: A regulatory response to the global banking crisis. Financial Services Authority, UK,

March.Griffin, J. M., Tang, D., 2012. Did subjectivity play a role in CDO credit ratings? Forthcoming Journal of Finance.International Swaps and Derivative Association 2009. ISDA Market Survey Historical Data. www.isda.org.Moody’s 2006. CDOROM v2.3 User Guide.Rosch, D., Scheule, H., 2005. A multi-factor approach for systematic default and recovery risk. Journal of Fixed

Income, 15(2), 63–75.Rosch, D., Scheule, H., 2010. Downturn credit portfolio risk, regulatory capital and prudential incentives. International

Review of Finance, 10(2), 185–207.Rosch, D., Scheule, H., 2012. Capital Incentives and Adequacy for Securitizations, 2012. Journal of Banking and

Finance, 36, 733–748.Standard & Poor’s 2005. CDO Evaluator Version 3.0: Technical Document.

Mastering IlliquidityRisk management for portfolios of limited partnership fundsThomas Meyer, Peter Cornelius, Christian Diller & Didier Guennoc 978-1-119-95242-8 • Hardback • 304 pages • May 2013 Buy Now!


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1

Introduction

Investing in private equity, hedge funds and real assets – such as infrastructure, real estate,forestry and farmland, energy and commodities – has gained considerable momentum inrecent years. These assets are often called “alternatives” as their investment history is stillrelatively short and, unlike traditional asset classes, they are rarely traded in public mar-kets.1 Investors have been attracted by the superior returns that alternative assets may offer.Moreover, as returns are found to be correlated less with traditional asset classes, alternativeassets have been regarded as attractive investments helping asset allocators diversify theirportfolios. At the same time, it has been argued that the potential returns of traditional assetclasses have diminished. Specifically, public stock markets have become increasingly efficient,limiting investors’ potential to achieve excess returns by investing in undervalued stocks. Inthe bond market, yields have declined substantially since the 1980s thanks to successfulcentral bank policies aimed at reducing inflation expectations and restoring confidence inmonetary policy.

1.1 ALTERNATIVE INVESTING AND THE NEED TO UPGRADERISK MANAGEMENT SYSTEMS

At the end of 2011, private equity funds, hedge funds and funds investing in real assetswere estimated to be managing around USD 4 trillion. This amount may still seem smallcompared with the size of the global equity and debt securities markets, whose volumetotalled almost USD 150 trillion in 2010. However, the market for alternatives has grownmuch faster than traditional investments. Just three decades ago alternative assets totalled onlya few billion US dollars, implying a compound annual growth rate of more than 25%. Forsome investors, especially endowments, foundations and family offices, alternative investingis no longer considered a niche strategy, but instead is part of their core portfolio. In fact, someasset allocators have invested as much as half their capital in alternatives, a few individualinstitutions even more. Pension plans, the largest investors in private equity, real assets andhedge funds, generally have a comparatively less pronounced exposure in terms of the totalamount of assets under management (AuM). However, some of the largest pension fundsworldwide, such as the California Public Employees’ Retirement System (CalPERS), theCanadian Pension Plan Investment Board or the Washington State Investment Board, haveinvested 20% and more of their assets in alternatives.

The United States has remained the largest market for alternative investing, absorbing morethan 50% of the capital deployed in private equity, real assets and hedge funds. At the same time,US investors have been the world’s largest capital source for alternative investments. However,Europe and, more recently, advanced Asia and emerging economies have been playing catch-up, both as a destination and source of capital. As regards the latter, sovereign wealth funds

1 Note that there is no universally accepted definition of alternative assets. Although often too small for institutional investors,alternatives may also include arts, rare books and maps, vintage cars and wine/vineyards.

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2 Mastering Illiquidity

(SWFs) have played a particularly important role, helping recycle their countries’ currentaccount surpluses and raising foreign exchange reserves by investing in asset classes whoseliquidity characteristics make them inaccessible for central banks. Thus, alternative investinghas become a global business, with cross-border transactions helping regional markets becomeincreasingly integrated.

However, it appears that the development of investors’ risk management capabilities hasnot always kept pace with their growing exposure to alternative assets. During the globalfinancial crisis in 2008–2009, a significant number of investors, and especially those witha substantial exposure to alternative assets, were faced with an acute lack of liquidity. Thesudden shortage of liquidity took investors by surprise. The majority of them had based theirliquidity planning on cash flow models whose parameters were essentially static. However, asfinancial markets shut in the wake of the collapse of Lehman Brothers in the autumn of 2008,the model parameters shifted rapidly due to sharply reduced distributions from private equityfunds and similar partnerships investing in real assets, the suspension of redemptions by hedgefunds, and increased margin calls and collateral. Many institutional investors thus found thattheir short-term liabilities either proved to be much more inflexible than they had thought orrose unexpectedly in the face of the crisis.

The financial turmoil that spread rapidly around the globe made a key characteristic oflong-term investing in private equity funds and similar structures suddenly highly transpar-ent. Organized as limited partnerships, such funds are designed to shield fledgling portfoliocompanies in their early stages and those in need of being restructured from disruptive marketinfluences, and to assure these companies’ continued financing. This requires patient capital,with long-term investors in limited partnerships essentially locking away their capital for 10years or even longer. While investors, or limited partners in private equity funds, were awareof the fact that they had to make long-term capital commitments in order to be able to harvestan illiquidity risk premium, during the crisis it turned out that many of them had underes-timated liquidity risk in two important ways. First, capital calls, or so-called contributions,of committed capital to private equity funds and similar structures are unknown in terms oftheir timing and size. Although capital calls slowed substantially during the Great Recession,distributions fell even faster as exit markets essentially closed. Thus, limited partners wereexposed to funding risk, which represents a key challenge in terms of liquidity management.Second, investors who had relied on the secondary market as a means to liquidate (parts of)their portfolios found out that transaction volumes fell sharply precisely when liquidity wasneeded most.

University endowments in the USA were hit particularly hard, and given their payout require-ments several of them were forced into distressed sales of assets. However, the problems wereby no means confined to university endowments. In fact, as we discuss throughout this book,even some of the largest pension funds were confronted with significant liquidity problems asfunding risk and market liquidity risk in the secondary market surged to unprecedented highs.As investors attempted to avoid defaulting on their commitments amid an increasingly illiquidsecondary market, they decided to sell liquid parts of their portfolios, such as public stocks, togenerate liquidity (Ang et al., 2011). In some cases, the pressure to divest was amplified by asubstantially larger-than-expected decline in the mark-to-market value of investors’ portfolios,triggering “sell” signals by their asset allocation models. In the event, many investors incurredsignificant losses (Ang and Kjaer, 2011; whose analysis is summarized in Chapter 6).

To be sure, the crisis did not generally undermine investors’ belief in the benefits of alter-native investing. While some investors did reduce their allocation to alternatives in an effort

91



(SWFs) have played a particularly important role, helping recycle their countries’ currentaccount surpluses and raising foreign exchange reserves by investing in asset classes whoseliquidity characteristics make them inaccessible for central banks. Thus, alternative investinghas become a global business, with cross-border transactions helping regional markets becomeincreasingly integrated.

However, it appears that the development of investors’ risk management capabilities hasnot always kept pace with their growing exposure to alternative assets. During the globalfinancial crisis in 2008–2009, a significant number of investors, and especially those witha substantial exposure to alternative assets, were faced with an acute lack of liquidity. Thesudden shortage of liquidity took investors by surprise. The majority of them had based theirliquidity planning on cash flow models whose parameters were essentially static. However, asfinancial markets shut in the wake of the collapse of Lehman Brothers in the autumn of 2008,the model parameters shifted rapidly due to sharply reduced distributions from private equityfunds and similar partnerships investing in real assets, the suspension of redemptions by hedgefunds, and increased margin calls and collateral. Many institutional investors thus found thattheir short-term liabilities either proved to be much more inflexible than they had thought orrose unexpectedly in the face of the crisis.

The financial turmoil that spread rapidly around the globe made a key characteristic oflong-term investing in private equity funds and similar structures suddenly highly transpar-ent. Organized as limited partnerships, such funds are designed to shield fledgling portfoliocompanies in their early stages and those in need of being restructured from disruptive marketinfluences, and to assure these companies’ continued financing. This requires patient capital,with long-term investors in limited partnerships essentially locking away their capital for 10years or even longer. While investors, or limited partners in private equity funds, were awareof the fact that they had to make long-term capital commitments in order to be able to harvestan illiquidity risk premium, during the crisis it turned out that many of them had underes-timated liquidity risk in two important ways. First, capital calls, or so-called contributions,of committed capital to private equity funds and similar structures are unknown in terms oftheir timing and size. Although capital calls slowed substantially during the Great Recession,distributions fell even faster as exit markets essentially closed. Thus, limited partners wereexposed to funding risk, which represents a key challenge in terms of liquidity management.Second, investors who had relied on the secondary market as a means to liquidate (parts of)their portfolios found out that transaction volumes fell sharply precisely when liquidity wasneeded most.

University endowments in the USA were hit particularly hard, and given their payout require-ments several of them were forced into distressed sales of assets. However, the problems wereby no means confined to university endowments. In fact, as we discuss throughout this book,even some of the largest pension funds were confronted with significant liquidity problems asfunding risk and market liquidity risk in the secondary market surged to unprecedented highs.As investors attempted to avoid defaulting on their commitments amid an increasingly illiquidsecondary market, they decided to sell liquid parts of their portfolios, such as public stocks, togenerate liquidity (Ang et al., 2011). In some cases, the pressure to divest was amplified by asubstantially larger-than-expected decline in the mark-to-market value of investors’ portfolios,triggering “sell” signals by their asset allocation models. In the event, many investors incurredsignificant losses (Ang and Kjaer, 2011; whose analysis is summarized in Chapter 6).

To be sure, the crisis did not generally undermine investors’ belief in the benefits of alter-native investing. While some investors did reduce their allocation to alternatives in an effort


Introduction 3

Table 1.1 Allocation of pension funds to alternative assetclasses, as a percentage of total assets under management

2006 2008 2010

Real estate 5.2 6.7 5.6Private equity 2.7 4.5 4.6Commodities 0.4 0.6 1.0Hedge funds 1.5 2.2 2.2Other 1.0 1.7 2.1

Total 10.9 15.7 15.6

Source: IMF (2011).

to align assets more closely with liabilities and to comply with accounting and regulatorypressures, others maintained their allocations or even raised them, for example, to addressunderfunded liabilities (WEF, 2011). As far as pension funds are concerned, a recent surveyby the International Monetary Fund (IMF, 2011) found that their overall exposure to alternativeassets was virtually unchanged between 2008 and 2010 (see Table 1.1), as new investmentsessentially kept pace with distributions by limited partnership funds or offset other divest-ments. Importantly, the share of alternative assets in pension funds’ total AuM thus remainedsignificantly higher than prior to the crisis, when many investors increased their allocationsto alternatives substantially. As a result, pension funds’ average exposure to alternative assetsin 2010 exceeded their relative allocation in 2006 by more than 40%, with private equitycontributing particularly strongly to this increase.

Arguably, the most recent turmoil in Europe’s sovereign debt market might have contributedto institutional investors’ continuous commitment to alternatives. As the IMF (2012) points out,the debt crisis has reinforced the notion that no asset can be viewed as truly safe. Instead, recentrating downgrades of sovereigns previously considered to be virtually riskless have reaffirmedthat even highly rated assets are subject to significant risks. The IMF (2012) estimates that thedecline in the number of sovereigns whose debt is considered safe could remove some USD9 trillion from the supply of safe assets by 2016, or roughly 16% of the projected total. Thisdecline is accentuated by a reduction in the private supply of safe assets as poor securitizationin the USA has tainted these securities and more stringent regulation has impaired the easewith which private sector issuers may produce assets that are deemed “safe”.

At the same time, heightened uncertainty, regulatory reforms and crisis-related responsesby central banks have driven up demand for safe assets. Given the shrinking set of assetsperceived to be safe, growing global supply/demand imbalances are feared to increase theprice of safety and compel investors to move down the safety scale as they scramble to obtainscarce assets. The IMF (2012) warns that safe asset scarcity could lead to global financialinstability resulting from short-term volatility jumps, herding behaviour and runs on sovereigndebt. In this environment, where global supply/demand imbalances may seriously distortthe benchmark pricing of sovereign debt, investors may be compelled further to invest inalternatives to generate higher returns. Note, in this context, that in the first nine months of2012 10-year US Treasury bonds averaged around 1.8%, implying significantly negative yieldsin real terms. Yields on 2-year US Treasuries averaged 0.28% during this period, while strongdemand for German and Swiss 2-year bonds drove even nominal yields into negative territory.A third round of quantitative easing in the United States, unconventional monetary policy

92



measures in the euro area, the United Kingdom and Japan, and further monetary easing inseveral emerging markets indicate that policy makers are committed to keeping interest rateslow in the foreseeable future.

While investors have remained committed to alternatives, their experience in the recentglobal financial crisis has led many of them to reconsider their investment strategies withregard to private equity, hedge funds and real assets. Generally, this review has focused on twoaspects of the allocation process. First, from a top-down perspective investors have revisitedtheir asset allocation models in light of their liability profiles and risk appetite (WEF, 2011).Second, from an asset-specific point of view a growing number of investors have thoughtabout alternative ways to achieve their target exposure to specific asset classes. As a growingnumber of investors have begun to adjust their asset allocation strategies, they have fosteredvisible changes in the alternative investment industry.

As far as portfolio construction is concerned, in the pre-crisis era most investors reliedon models that were designed to construct efficient portfolios on the basis of historicalasset returns, their variance and their correlation with returns in other asset classes. How-ever, in the Great Recession such mean/variance approaches proved to be too static, as sys-temic risk rapidly pushed correlations upwards. As a result, gains from diversification oftenproved to be illusive, and investor portfolios turned out to be far less robust than the modelshad suggested.

Against this background, several investors have begun to implement less granular asset allo-cation frameworks that focus more on asset-specific risks as differentiating factors generatingdiversification benefits – as opposed to (less-than-perfect) return correlations that play a keyrole in the standard mean/variance approach. This applies to both traditional and alternativeasset classes. As far as the latter are concerned, the risk factor allocation approach recognizesthat private equity, hedge funds and real assets are subject to fundamentally different risks.Private equity, for instance, is subject to liquidity risk, in addition to equity risk. By compar-ison, investing in hedge funds is generally less illiquid than commitments to private equityfunds. At the same time, however, hedge funds tend to be highly leveraged and hence subjectto credit risk. As far as real estate is concerned, investors expect to be compensated for theterm risk they take – a risk component which is absent in private equity investments. It is thisheterogeneity of investment risk and the associated risk premiums that offers diversificationgains and hence helps improve risk-adjusted portfolio returns.

1.2 SCOPE OF THE BOOK

Harvesting different risk premiums requires specific risk management approaches. In thisbook, we focus primarily on the illiquidity risk premium that structurally illiquid asset classesmay offer. Two clarifications are in order. First of all, a broad range of asset markets maybecome illiquid in periods of severe financial stress. In the recent global financial crisis, themarkets for corporate debt, collateralized debt obligations and securitization virtually shutdown. There is a rapidly expanding literature on cyclical illiquidity, discussing its causesand effects and especially the role of banks (e.g., Shin, 2010; Tirole, 2011 and the literaturediscussed therein). In contrast to asset classes that may become illiquid thanks to financialturmoil and heightened risk aversion, investors in structurally illiquid asset classes, such asprivate equity and real assets, are aware ex ante of the risk they take. In fact, as we arguein this book, it is precisely this risk, and more specifically the associated risk premium, that

93



measures in the euro area, the United Kingdom and Japan, and further monetary easing inseveral emerging markets indicate that policy makers are committed to keeping interest rateslow in the foreseeable future.

While investors have remained committed to alternatives, their experience in the recentglobal financial crisis has led many of them to reconsider their investment strategies withregard to private equity, hedge funds and real assets. Generally, this review has focused on twoaspects of the allocation process. First, from a top-down perspective investors have revisitedtheir asset allocation models in light of their liability profiles and risk appetite (WEF, 2011).Second, from an asset-specific point of view a growing number of investors have thoughtabout alternative ways to achieve their target exposure to specific asset classes. As a growingnumber of investors have begun to adjust their asset allocation strategies, they have fosteredvisible changes in the alternative investment industry.

As far as portfolio construction is concerned, in the pre-crisis era most investors reliedon models that were designed to construct efficient portfolios on the basis of historicalasset returns, their variance and their correlation with returns in other asset classes. How-ever, in the Great Recession such mean/variance approaches proved to be too static, as sys-temic risk rapidly pushed correlations upwards. As a result, gains from diversification oftenproved to be illusive, and investor portfolios turned out to be far less robust than the modelshad suggested.

Against this background, several investors have begun to implement less granular asset allo-cation frameworks that focus more on asset-specific risks as differentiating factors generatingdiversification benefits – as opposed to (less-than-perfect) return correlations that play a keyrole in the standard mean/variance approach. This applies to both traditional and alternativeasset classes. As far as the latter are concerned, the risk factor allocation approach recognizesthat private equity, hedge funds and real assets are subject to fundamentally different risks.Private equity, for instance, is subject to liquidity risk, in addition to equity risk. By compar-ison, investing in hedge funds is generally less illiquid than commitments to private equityfunds. At the same time, however, hedge funds tend to be highly leveraged and hence subjectto credit risk. As far as real estate is concerned, investors expect to be compensated for theterm risk they take – a risk component which is absent in private equity investments. It is thisheterogeneity of investment risk and the associated risk premiums that offers diversificationgains and hence helps improve risk-adjusted portfolio returns.

1.2 SCOPE OF THE BOOK

Harvesting different risk premiums requires specific risk management approaches. In thisbook, we focus primarily on the illiquidity risk premium that structurally illiquid asset classesmay offer. Two clarifications are in order. First of all, a broad range of asset markets maybecome illiquid in periods of severe financial stress. In the recent global financial crisis, themarkets for corporate debt, collateralized debt obligations and securitization virtually shutdown. There is a rapidly expanding literature on cyclical illiquidity, discussing its causesand effects and especially the role of banks (e.g., Shin, 2010; Tirole, 2011 and the literaturediscussed therein). In contrast to asset classes that may become illiquid thanks to financialturmoil and heightened risk aversion, investors in structurally illiquid asset classes, such asprivate equity and real assets, are aware ex ante of the risk they take. In fact, as we arguein this book, it is precisely this risk, and more specifically the associated risk premium, that


Introduction 5

attracts investors to these asset classes. Not all investors are able to harvest this risk premium,however. As a matter of principle, only long-term investors can, whose liability profile allowsthem to lock capital in for a prolonged period of time, usually 10 years or more. Harvestingthe illiquidity risk premium requires specific risk management techniques, however, which arethe subject of this book.

Second, we shall not consider hedge funds. While they are generally considered to be partof the alternative investment universe, they show a different risk profile compared with privateequity and real assets. Although redemptions may be suspended in certain circumstances, theorganization of hedge funds is fundamentally different from private equity funds and limitedpartnerships investing in real assets, making the former less illiquid. At the same time, hedgefunds are subject to risks that are idiosyncratic to this asset class, requiring different riskmanagement tools whose discussion is beyond the scope of this book.

This leaves us with long-term investing in private equity and real assets as two highlyilliquid alternative asset classes. But this is still too broad a focus for what this book attemptsto achieve. Instead, it is important to recognize that there are different ways to invest inprivate equity and real assets. As investors have revisited their exposure to alternative assets,and more specifically to private equity and real assets, some of them have decided to pursuealternative routes to fund investing. To begin with, some large investors have engaged in directinvestments, essentially competing with partnerships in acquiring assets. Others have putincreased emphasis on co-investments alongside funds they have committed capital to. Whilethere is little systematic evidence on the significance of co-investments and direct investmentsin investors’ portfolios, anecdotal evidence suggests that at least in individual cases (notablysome Canadian pension funds) these forms play an important role. Yet others (i.e., somesovereign wealth funds) have acquired stakes in the management company of private equityfirms. Finally, a rising number of investors have sought to set up managed accounts with assetmanagers instead of committing capital to limited partnerships.

As investors have looked into alternative ways of investing in private equity and real assets,many fund managers have adjusted their own business models. Several large private equityfirms – such as the Blackstone Group, Carlyle Group or Kohlberg Kravis Roberts – havetransformed themselves into alternative asset managers, offering their clients a broad rangeof products, including through managed accounts. A growing number of firms have gonepublic, enabling shareholders to get exposure to alternative investing without investing in theirfunds. Meanwhile, there is a range of derivative instruments on listed private equity, includingexchange-traded funds (ETFs).

As important as these structural changes in the alternative investment arena are, the mostcommon form of investing in private equity and real assets remains the limited partnership.In a limited partnership, investors serve as limited partners (LPs) committing capital to afund, which is raised and managed by a general partner (GP). Such limited partnership fundstypically have a lifespan of 10 years, with the possible extension of 2 years. For this period,LPs essentially lock in their capital, notwithstanding the emergence of a secondary market inrecent years. At any given point in time, LPs have to be in a position to respond to capital callsby the GP, subjecting fund investments to significant funding risk.

Unfortunately, studies on managing illiquidity risk associated with investments in limitedpartnerships have remained rare. This may seem surprising in light of the growing importanceof private equity and real assets in investors’ portfolios and the experience of several LPs inthe recent global financial crisis. It is therefore the objective of this book to narrow this gapby developing risk management guidelines drawing upon best practices.

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1.3 ORGANIZATION OF THE BOOK

This book is organized in three parts. In Part I, we discuss illiquid investments in privateequity and real assets from a market perspective. In Part II, we focus on risk measurementfor portfolios of limited partnership funds targeting these asset classes. Finally, in Part III,we discuss some techniques for managing this risk and related issues.

1.3.1 Illiquid investments as an asset class

Our discussion starts by defining long-term assets that are subject to structural illiquidity, offer-ing investors a risk premium. These assets constitute the universe of investment opportunitieswe address in this book, which have to be clearly distinguished from assets that may becometemporarily illiquid in periods of financial turmoil. In Chapter 2, we provide an estimate ofthe size of the market for illiquid investments in private equity and real assets. These assetclasses can be accessed through alternative routes, which, however, require strategy-specificrisk management approaches. In contrast, limited partnerships provide a structural investmentframework, which is largely agnostic with regard to the underlying asset class – presumablyan important reason why limited partnerships have remained the dominant route for investorsseeking exposure to private equity and real assets.

While, as we explain, the market for illiquid investments has grown rapidly over the last fewdecades, this market expansion has not been linear. Instead, there have been pronounced cyclesaround the long-term trend, which in part is explained by macroeconomic cycles and in part byasset-specific investment dynamics. Furthermore, we look at the global investor base of privateequity, which is representative of the broader universe of illiquid asset classes. While pensionfunds and insurance firms dominate the investor base in terms of the absolute amount of moneyinvested in private equity funds, endowments, foundations and family offices generally havea larger exposure to the asset class relative to the size of the portfolio they manage. As wewill discuss in more detail, relative allocations are generally a function of investors’ liabilityprofiles, which vary across different classes of investors. Moreover, asset managers are subjectto different regulations and accounting rules. However, even within specific investor classesallocations vary widely, reflecting different degrees of risk appetite.

Looking ahead, we discuss long-term trends in the asset management industry. Of particularimportance for long-term investing is the secular shift from defined benefits (DB) pensionplans to defined contributions (DC) plans. Given the transferability of claims under DC plans,investments generally require a high degree of liquidity. However, as we discuss in this chapter,this does not necessarily mean that DC plans are unable to invest in illiquid assets. Furthermore,we explore the potential role of emerging economies as suppliers of patient capital. WhileSWFs have attracted considerable attention as investors in private equity and real assets, we alsolook at pension funds and insurance firms. Their AuM grow at substantial rates as governmentsimplement important pension reforms and incomes rise. Investments are still often restrictedto domestic markets and to specific asset classes. To the extent that such restrictions are liftedand replaced by a prudent investing approach, pension funds and insurance firms in emergingeconomies could make an increasingly meaningful contribution to the global supply of long-term capital. A precondition for this to happen, however, is the introduction of a comprehensiverisk management approach that encompasses illiquid asset classes.

Portfolio diversification is at the core of “prudent investing”, a concept with far-reachinglegal consequences. As we point out in Chapter 3, the prudent investor rule, as stipulated in the

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1.3 ORGANIZATION OF THE BOOK

This book is organized in three parts. In Part I, we discuss illiquid investments in privateequity and real assets from a market perspective. In Part II, we focus on risk measurementfor portfolios of limited partnership funds targeting these asset classes. Finally, in Part III,we discuss some techniques for managing this risk and related issues.

1.3.1 Illiquid investments as an asset class

Our discussion starts by defining long-term assets that are subject to structural illiquidity, offer-ing investors a risk premium. These assets constitute the universe of investment opportunitieswe address in this book, which have to be clearly distinguished from assets that may becometemporarily illiquid in periods of financial turmoil. In Chapter 2, we provide an estimate ofthe size of the market for illiquid investments in private equity and real assets. These assetclasses can be accessed through alternative routes, which, however, require strategy-specificrisk management approaches. In contrast, limited partnerships provide a structural investmentframework, which is largely agnostic with regard to the underlying asset class – presumablyan important reason why limited partnerships have remained the dominant route for investorsseeking exposure to private equity and real assets.

While, as we explain, the market for illiquid investments has grown rapidly over the last fewdecades, this market expansion has not been linear. Instead, there have been pronounced cyclesaround the long-term trend, which in part is explained by macroeconomic cycles and in part byasset-specific investment dynamics. Furthermore, we look at the global investor base of privateequity, which is representative of the broader universe of illiquid asset classes. While pensionfunds and insurance firms dominate the investor base in terms of the absolute amount of moneyinvested in private equity funds, endowments, foundations and family offices generally havea larger exposure to the asset class relative to the size of the portfolio they manage. As wewill discuss in more detail, relative allocations are generally a function of investors’ liabilityprofiles, which vary across different classes of investors. Moreover, asset managers are subjectto different regulations and accounting rules. However, even within specific investor classesallocations vary widely, reflecting different degrees of risk appetite.

Looking ahead, we discuss long-term trends in the asset management industry. Of particularimportance for long-term investing is the secular shift from defined benefits (DB) pensionplans to defined contributions (DC) plans. Given the transferability of claims under DC plans,investments generally require a high degree of liquidity. However, as we discuss in this chapter,this does not necessarily mean that DC plans are unable to invest in illiquid assets. Furthermore,we explore the potential role of emerging economies as suppliers of patient capital. WhileSWFs have attracted considerable attention as investors in private equity and real assets, we alsolook at pension funds and insurance firms. Their AuM grow at substantial rates as governmentsimplement important pension reforms and incomes rise. Investments are still often restrictedto domestic markets and to specific asset classes. To the extent that such restrictions are liftedand replaced by a prudent investing approach, pension funds and insurance firms in emergingeconomies could make an increasingly meaningful contribution to the global supply of long-term capital. A precondition for this to happen, however, is the introduction of a comprehensiverisk management approach that encompasses illiquid asset classes.

Portfolio diversification is at the core of “prudent investing”, a concept with far-reachinglegal consequences. As we point out in Chapter 3, the prudent investor rule, as stipulated in the


Introduction 7

“Prudent Investor Act” in the United States, has to be clearly distinguished from the “prudentman” rule. Importantly, the former explicitly recognizes that diversification is a key componentof prudence, which includes the delegation of investment management to external managers.A portfolio may thus include assets which, on a stand-alone basis, might be considered toorisky from the viewpoint of the prudent man rule. Note in this context that US pension fundswere allowed to invest in private equity and venture capital funds only in 1979 when the USDepartment of Labor clarified its prudent man rule in a way that explicitly permitted fundmanagers to invest in high-risk assets.

As regulators have redefined what constitutes prudent investing, the emphasis has shiftedtowards the investment process as opposed to specific investments and allocations. As long asthe investment process is considered to be prudent, investment managers enjoy considerableflexibility to (re-)design strategies in rapidly changing market environments. Arguably, thisflexibility should reduce the risk of herding among investors who have to follow the samerules. But what exactly is a prudent investment process? In Chapter 3, we suggest a numberof criteria that are simple and transparent and can be applied across different jurisdictions.

In Chapter 4, we discuss the basic structure of limited partnerships as the dominantvehicle through which investments in many alternative asset classes are made. Understandingthis structure is critical for investors to measure their risk exposure correctly and manage itappropriately. As we argue, the high degree of illiquidity is not just a by-product of the limitedpartnership as a legal construct, but instead represents a central feature that enables the GPof a fund to harvest a premium for his LPs. This basic observation remains intact, despite theemergence of a secondary market in recent years. Although the absolute volume of transactionsin the secondary market has risen appreciably, it is still very small relative to the total amountof assets managed by private equity funds and partnerships investing in real assets.

Investors have several alternatives to achieve exposure to private equity and real assets,including: through listed vehicles; investments in the management company of private equityfirms or alternative asset managers; managed accounts; direct and co-investments. However,none of these alternative routes have seriously challenged the fund structure as the preferredchoice for investors who seek exposure to private equity and real assets. In fact, today’s limitedpartnership as a legal investment framework has precedents that can be traced back to ancientBabylon almost 5000 years ago.

While the limited partnership has a very long history, the key question for investors locking incapital for 10 years or more through such vehicles is whether they are adequately compensatedfor the illiquidity they accept. To be sure, the illiquidity risk involved in long-term investingin funds is far from trivial, as such commitments make it very difficult, if not impossible,for investors to continuously rebalance their portfolios, a key assumption in standard assetallocation models. In Chapter 5, therefore, we discuss recent attempts in the literature tomeasure risk and returns in private equity to get a better understanding of the illiquiditypremium investors may expect.

Generally, the literature finds that GPs have achieved excess returns through a combinationof strategic measures, operational measures and financial measures. This does not tell us,however, whether their LPs have actually enjoyed excess returns, given the management feesand the carry paid to the GP. While earlier studies actually raised doubts whether privateequity has outperformed public equity net-of-fees, more recent work does suggest that thereis a positive illiquidity premium to be earned.

However, it is important to note that the outperformance recent studies find is not adjusted forrisk. As we discuss in more detail, the public market equivalent (PME) – a standard measure

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to compare returns of investments in private equity funds with similar (cash flow-based)investments in a public market index – implicitly assumes beta to be equal to one, implyingthe absence of market risk. To the extent that the true beta is under- or overestimated, the truePME is over- or underestimated. Fortunately, we receive some comfort from recent academicresearch that finds changes in beta have a strongly diminishing effect on the PME: thus, evenif the true beta were 1.5 (the upper end of empirical estimates for buyout funds) instead of1, which is implicitly assumed in PME-based comparisons, there would still be considerableoutperformance of private equity. Similarly, it is found that PMEs are remarkably insensitiveto the multiple of the public market returns. In fact, even if public market returns had beentwice the S&P 500, the median PMEs would still be larger than 1 for the 1990s and 2000svintages, suggesting that systematic risk does not explain the estimated outperformance ofbuyout funds.

It remains an open question, however, whether this outperformance is enough for theilliquidity risk investors take when committing capital to private equity and similar funds.Academic research that addresses liquidity risk explicitly in extended approaches of the CapitalAsset Pricing Model (CAPM) has just begun to emerge. While this research puts the illiquiditypremium in the range of 2–4%, more work is required to say with sufficient confidence whetherthese estimates provide a reasonable range for the risk illiquid investments in funds entail.

Notwithstanding the remaining uncertainty about the size of the illiquidity premium, agrowing number of investors have begun to implement an allocation approach that seeks togenerate diversification gains on the basis of a limited number of distinct risks. One risk isilliquidity, a factor that can be accessed through private equity and real assets. This renders pri-vate equity and real assets different compared with, say, high-yield bonds, which are primarilysubject to term risk and credit risk. As we stress, however, each risk needs to be measuredand managed carefully to harvest the premiums associated with the risks in each asset class.

In the final chapter of Part I, we focus on the role of the secondary market, which hassometimes been seen as a panacea for illiquidity in primary fund investments. We cautionagainst such a view. As important as the emergence of a secondary market has been forinvestors seeking to mitigate the J-curve effect of their primary fund investments programmeand improve the risk/return characteristics of their private equity holdings, it is not a gamechanger in terms of the basic characteristics of illiquid investments. In fact, as we argue inChapter 6, it would be highly dangerous for investors to regard the secondary market as asubstitute for proper management of liquidity risk. For starters, as we emphasized before, thesecondary market has remained small relative to the overall exposure of investors to privateequity and real assets. More importantly, liquidity in the secondary market tends to dry upprecisely when sellers need it most. In the recent global financial crisis, transaction volumesfell sharply as buyers demanded huge discounts relative to the net asset value (NAV) ofthe portfolios the sellers wanted to liquidate. This experience casts doubt on the role of thesecondary market in discovering the true price of illiquid investments. Putting in place anadequate risk management system that is designed for the specific risks in illiquid asset classesis therefore a key condition for investors venturing into private equity and real assets.

1.3.2 Risk measurement and modelling

In the second part of the book, we outline the main features of proper risk management basedon current best practices. In Chapter 7, we set the scene by introducing risk as the potential

97



to compare returns of investments in private equity funds with similar (cash flow-based)investments in a public market index – implicitly assumes beta to be equal to one, implyingthe absence of market risk. To the extent that the true beta is under- or overestimated, the truePME is over- or underestimated. Fortunately, we receive some comfort from recent academicresearch that finds changes in beta have a strongly diminishing effect on the PME: thus, evenif the true beta were 1.5 (the upper end of empirical estimates for buyout funds) instead of1, which is implicitly assumed in PME-based comparisons, there would still be considerableoutperformance of private equity. Similarly, it is found that PMEs are remarkably insensitiveto the multiple of the public market returns. In fact, even if public market returns had beentwice the S&P 500, the median PMEs would still be larger than 1 for the 1990s and 2000svintages, suggesting that systematic risk does not explain the estimated outperformance ofbuyout funds.

It remains an open question, however, whether this outperformance is enough for theilliquidity risk investors take when committing capital to private equity and similar funds.Academic research that addresses liquidity risk explicitly in extended approaches of the CapitalAsset Pricing Model (CAPM) has just begun to emerge. While this research puts the illiquiditypremium in the range of 2–4%, more work is required to say with sufficient confidence whetherthese estimates provide a reasonable range for the risk illiquid investments in funds entail.

Notwithstanding the remaining uncertainty about the size of the illiquidity premium, agrowing number of investors have begun to implement an allocation approach that seeks togenerate diversification gains on the basis of a limited number of distinct risks. One risk isilliquidity, a factor that can be accessed through private equity and real assets. This renders pri-vate equity and real assets different compared with, say, high-yield bonds, which are primarilysubject to term risk and credit risk. As we stress, however, each risk needs to be measuredand managed carefully to harvest the premiums associated with the risks in each asset class.

In the final chapter of Part I, we focus on the role of the secondary market, which hassometimes been seen as a panacea for illiquidity in primary fund investments. We cautionagainst such a view. As important as the emergence of a secondary market has been forinvestors seeking to mitigate the J-curve effect of their primary fund investments programmeand improve the risk/return characteristics of their private equity holdings, it is not a gamechanger in terms of the basic characteristics of illiquid investments. In fact, as we argue inChapter 6, it would be highly dangerous for investors to regard the secondary market as asubstitute for proper management of liquidity risk. For starters, as we emphasized before, thesecondary market has remained small relative to the overall exposure of investors to privateequity and real assets. More importantly, liquidity in the secondary market tends to dry upprecisely when sellers need it most. In the recent global financial crisis, transaction volumesfell sharply as buyers demanded huge discounts relative to the net asset value (NAV) ofthe portfolios the sellers wanted to liquidate. This experience casts doubt on the role of thesecondary market in discovering the true price of illiquid investments. Putting in place anadequate risk management system that is designed for the specific risks in illiquid asset classesis therefore a key condition for investors venturing into private equity and real assets.

1.3.2 Risk measurement and modelling

In the second part of the book, we outline the main features of proper risk management basedon current best practices. In Chapter 7, we set the scene by introducing risk as the potential


Introduction 9

deviation from an expected outcome. Risk, as we emphasize, can usefully be distinguished fromuncertainty. Whereas risk generally refers to the probability of an event occurring, uncertaintyis immeasurable, given that particular events are so infrequent or unique that no probabilitydistribution can be determined. Typically perceived as a negative outcome – not least froma regulatory perspective – risk is usually calculated as the product of the probability of anevent and the expected loss if the event occurs. However, investment strategies are generallysubject to both downside and upside risks, requiring investors to navigate carefully throughthe potential losses without ignoring the opportunities that are associated with a particularallocation decision.

While risk is generally predicated on the notion of quantifiability, in practice risk managersoften face substantial challenges in measuring risk in a statistically meaningful way. Frequently,we have to accept a considerable degree of subjectivity in quantifying risks. This is not leasttrue in alternative investing where historical data remain rare and market-based valuationsare not available. Not surprisingly, therefore, risk models for such assets have remained rareand subject to considerable controversy. Given the nature of investing in private equity andreal assets, we argue that a new risk management approach is needed that embraces thelack of high-frequency market data by using all available information, including qualitativeassessments.

At the core of any risk management approach lies the definition of the types of risk that needto be managed. From a broader portfolio standpoint, risk is generally seen as market risk andtypically estimated in the CAPM framework, to help determine the desired allocation of capitalto different asset classes. However, once an allocation to these asset classes is determined,investors have to manage their asset-specific risks. First and foremost, as we explain inChapter 8, investors in limited partnership funds face the risk that the fund manager failsto return the invested capital in full (plus an expected return). Conceptually, this may beconsidered as a default, and with many practitioners viewing default risk as more relevant thanmarket risk, there have been attempts to apply credit risk models to illiquid assets. However,such attempts are fundamentally flawed as they focus only on the downside, whereas in aportfolio of funds unrealized gains may serve as a buffer, a viewpoint that has long beenaccepted by the Basel Committee in the context of banks’ equity portfolios.

As we emphasize throughout this book, the key differentiating factor between investmentsthrough limited partnership funds and investments in marketable assets is the high degree ofilliquidity of the former. As far as commitments to funds are concerned, two dimensions ofliquidity risk can be distinguished. First, investments are subject to market liquidity risk, in thesense that there might not be enough demand for purchasing assets in the secondary market.Second, investors face the risk of lacking sufficient liquidity to fund their commitments. Capitalcalls are made at short notice, requiring investors to have sufficient liquidity at any point intime to avoid defaulting on their commitments. However, hoarding cash comes at significantopportunity costs. Related to the illiquidity problem is the absence of market prices as thebasis for risk measurement. Instead, we need to base such a measurement on suitable models.Thus, as we discuss further in Chapter 8, investors are well advised to run funding tests bymonitoring key liquidity ratios or undertaking more sophisticated scenario analysis for futurecash flows. LPs also need to employ such a funding test to confirm that they are able to honourall capital calls or, alternatively, are able to undertake orderly transactions under no duress,which obviously is a critical assumption for modelling the economic substance of investmentsin limited partnership funds.

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In Chapter 9, we return to the issue of potential capital losses in fund portfolios. Specifically,we are interested in the maximum loss an investor could suffer within a given confidenceinterval – a question which can usefully be addressed in the framework of a value-at-risk(VaR) analysis.2 Applying VaR analysis to illiquid assets, for which market prices do not exist,raises a number of important conceptual and statistical issues. In addressing these issues, wediscuss two alternative approaches. The first approach is a VaR analysis based on (typicallyquarterly) changes in NAVs as reported by the funds in a portfolio. While this approachappears to be conventional and relatively easy to implement, its simplicity is deceptive and ithas important limitations. Chief among these is the fact that changes in reported NAVs do notreflect the lifecycle characteristics of limited partnerships, such as the J-curve phenomenonand the future pattern of undrawn commitments. The second, alternative approach presentedfocuses on the volatility of cash flows. This approach uses historical cash flow data over theentire lifecycle of funds. These data can be used in a Monte Carlo simulation to generatecash flow scenarios for a portfolio of funds, taking into account correlations between portfoliosegments, such as specific vintage years or strategies.

Working with cash flows is more akin to the needs of non-financial firms. While financialinstitutions employ VaR to determine their capital adequacy and measure tradable risks, realinvestments in fixed assets by non-financial firms cannot easily be liquidated. Instead, industrialcompanies tend to focus on the cash-flow-at-risk (CFaR) as a more relevant measure of theirinvestment risk exposure. Specifically, the CFaR measures the maximum deviation of actualcash flows from a given level within a given confidence interval. Contrary to VaR, which iscalculated for very short time periods, CFaR relates to longer periods, typically quarters oreven years (i.e., intervals that are also relevant for investors in limited partnership funds).Importantly, the CFaR mirrors both cash inflows and cash outflows as key determinants of thefunding test limited partners are required to meet at any given point in time.

This leads us to the importance of diversification within fund portfolios across differentdimensions. As we discuss in more detail, significant gains are already achieved at relativelylow levels of diversification, especially as far as investing over different vintage years isconcerned. A key conclusion from this analysis is that continuous monitoring and managementof diversification should be an integral part of a LP’s risk management. There are two importantcaveats, however. First, as the degree of diversification increases – in the extreme case, aninvestor holds the market portfolio – the potential to achieve extraordinary returns declines.Second, in periods of financial turmoil cash flow correlations tend to rise, reducing the potentialdiversification gains with respect to managing liquidity risk – as opposed to the risk of actualcapital losses we also consider in Chapter 9.

The estimation of the true VaR in portfolios of limited partnership funds is inextricablyintertwined with the question of how undrawn commitments should be treated in this frame-work. The answer the standard finance model gives is simple – undrawn commitments can beignored. According to what represents the main framework of finance theory, different invest-ments and assets can be valued in isolation. Each investment has its own net present value(NPV), which is calculated by discounting future cash flows using an appropriate discountrate. Since undrawn commitments do not represent actual cash flows, they have NPV = 0 andhence should not matter.

2 This approach is widely used in financial risk management and regulation, with maximum losses due to adverse movementsin asset prices typically determined at the 99% or 99.5% level of confidence (implying an event occurring every 100 or 200 years,respectively).

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In Chapter 9, we return to the issue of potential capital losses in fund portfolios. Specifically,we are interested in the maximum loss an investor could suffer within a given confidenceinterval – a question which can usefully be addressed in the framework of a value-at-risk(VaR) analysis.2 Applying VaR analysis to illiquid assets, for which market prices do not exist,raises a number of important conceptual and statistical issues. In addressing these issues, wediscuss two alternative approaches. The first approach is a VaR analysis based on (typicallyquarterly) changes in NAVs as reported by the funds in a portfolio. While this approachappears to be conventional and relatively easy to implement, its simplicity is deceptive and ithas important limitations. Chief among these is the fact that changes in reported NAVs do notreflect the lifecycle characteristics of limited partnerships, such as the J-curve phenomenonand the future pattern of undrawn commitments. The second, alternative approach presentedfocuses on the volatility of cash flows. This approach uses historical cash flow data over theentire lifecycle of funds. These data can be used in a Monte Carlo simulation to generatecash flow scenarios for a portfolio of funds, taking into account correlations between portfoliosegments, such as specific vintage years or strategies.

Working with cash flows is more akin to the needs of non-financial firms. While financialinstitutions employ VaR to determine their capital adequacy and measure tradable risks, realinvestments in fixed assets by non-financial firms cannot easily be liquidated. Instead, industrialcompanies tend to focus on the cash-flow-at-risk (CFaR) as a more relevant measure of theirinvestment risk exposure. Specifically, the CFaR measures the maximum deviation of actualcash flows from a given level within a given confidence interval. Contrary to VaR, which iscalculated for very short time periods, CFaR relates to longer periods, typically quarters oreven years (i.e., intervals that are also relevant for investors in limited partnership funds).Importantly, the CFaR mirrors both cash inflows and cash outflows as key determinants of thefunding test limited partners are required to meet at any given point in time.

This leads us to the importance of diversification within fund portfolios across differentdimensions. As we discuss in more detail, significant gains are already achieved at relativelylow levels of diversification, especially as far as investing over different vintage years isconcerned. A key conclusion from this analysis is that continuous monitoring and managementof diversification should be an integral part of a LP’s risk management. There are two importantcaveats, however. First, as the degree of diversification increases – in the extreme case, aninvestor holds the market portfolio – the potential to achieve extraordinary returns declines.Second, in periods of financial turmoil cash flow correlations tend to rise, reducing the potentialdiversification gains with respect to managing liquidity risk – as opposed to the risk of actualcapital losses we also consider in Chapter 9.

The estimation of the true VaR in portfolios of limited partnership funds is inextricablyintertwined with the question of how undrawn commitments should be treated in this frame-work. The answer the standard finance model gives is simple – undrawn commitments can beignored. According to what represents the main framework of finance theory, different invest-ments and assets can be valued in isolation. Each investment has its own net present value(NPV), which is calculated by discounting future cash flows using an appropriate discountrate. Since undrawn commitments do not represent actual cash flows, they have NPV = 0 andhence should not matter.

2 This approach is widely used in financial risk management and regulation, with maximum losses due to adverse movementsin asset prices typically determined at the 99% or 99.5% level of confidence (implying an event occurring every 100 or 200 years,respectively).


Introduction 11

However, undrawn commitments, which are contractually binding, obviously did matterduring the recent financial crisis. In addressing this apparent conundrum, our discussion inChapter 10 starts by asking whether overcommitments to funds actually represent leverage.In fact, we find important commonalities between overcommitments and leverage, with bothstrategies being motivated by the objective to magnify returns. To the extent that overcommit-ments are used in order to achieve higher returns, they imply higher risk – just as in the case ofleverage. Conversely, holding capital in low-yielding Treasury bills to always be in a positionto respond to capital calls lowers or even eliminates risk – at the expense of higher returns.Investors may therefore choose a commitment strategy that is consistent with a risk/returnprofile according to their utility function. However, this suggests that undrawn commitmentsdo play an important role, in contrast to the standard finance model where capital held inhighly liquid assets has no economic value as negative cash flows are assumed to be financedthrough borrowing.

The important role undrawn commitments have played in the losses some investors havesuffered during the recent financial crisis will no doubt continue to attract a substantialamount of attention from practitioners and academics alike. A key question that will needto be addressed concerns the treatment of such commitments in the standard finance model.Specifically, how can discount rates be determined in the presence of undrawn commitments?In addressing this question, the accounting view, which treats undrawn commitments as off-balance sheet items, needs to be reconciled with the economic perspective that recognizes theresources dedicated to private equity and the risk from possible overcommitment strategies.Finding a solution to this challenge looks set to rank prominently on the research agenda foryears to come. As we argue in the final part of Chapter 10, a first possible step could lie intreating undrawn capital as a loan. Intuitively, one may think of a credit line from a bank usedby the LP to fund his commitments. Alternatively, as here, it may be assumed that the GPdraws down the capital entirely at the beginning of the fund’s life and lends the money to theLP in order for them to respond to their capital calls.

Given the high degree of liquidity risk associated with investments in private equity andreal assets, cash flow modelling is a key challenge that needs to be addressed in internalmodels. Generally, two approaches can be distinguished. Non-probabilistic models use alimited number of parameters and are preferable in cases where the modeller is confrontedwith important data constraints. A well-known example is the model developed by the Yaleendowment’s investment team, whose basic structure is presented in Chapter 11. While thismodel and its numerous variants that have been developed in recent years are relatively simpleand easy to implement, they are subject to strict limitations. Importantly, non-probabilisticmodels do not provide for outcome ranges and hence are unable to capture the volatility ofcash flows. As a result, they are appropriate only in exceptional circumstances, for instance inthe case of large diversified and fully funded portfolios of fund investments.

By contrast, probabilistic models are generally more complex and pose important datachallenges. Probabilistic models use extensive cash flow libraries to project the cash flows of agiven investment portfolio, taking into account the maturity of the individual funds making upthe portfolio. Probabilistic models can usefully be subjected to scenario analysis to determinethe sensitivity of cash flows to deviations from the past. Scenarios are particularly useful tostress-test cash flow projections derived from probabilistic models in order to evaluate andquantify the impact of exogenous shocks. The experience that many investors had in therecent financial crisis leaves little doubt about the importance of cash flow modelling underalternative assumptions.

100



Risk models for funds can be constructed top-down or bottom-up. While probabilisticmodels using cash flow libraries tend to start with a top-down approach, a bottom-up analysiscan refine projections and add considerable granularity. In this analysis, a key ingredient is thedistribution waterfall as specified in the limited partnership agreement. The basic structure ofthe waterfall is presented in Chapter 12, on the basis of which we provide different examplesof cash inflows and outflows under alternative assumptions about hurdle rates and carriedinterest. While these parameters determine the profit for the LPs, they are also highly relevantfrom a risk management perspective. Realistically, however, a bottom-up analysis may be toocomplex and resource-intensive for most investors, given substantial variations between fundsin terms of the key parameters determining profit sharing between the GP and his or her LPs.

As important as quantitative risk measurement is, in illiquid asset classes risk managers oftenface important data constraints. This does not mean, however, that effective risk managementcannot be done. Rather, the risk manager has to work with the set of information that isavailable to him or her, and this includes qualitative assessments. Understandably, manyrisk managers feel uncomfortable using qualitative data, as they fear that such informationmay be inconsistent and hence result in distorted conclusions. However, this discomfortcan be mitigated, at least to some degree, by employing classification schemes for limitedpartnership funds.

As far as mutual funds are concerned, there are several external agencies that provide ratingsaiming to provide a forward-looking prognosis based on a standardized valuation. As we arguein Chapter 13, independent ratings of limited partnerships are more difficult, as there are fewobjective criteria that can be used in a standardized fashion. Furthermore, there may be toofew potential users, given the still relatively limited number of investors in private equity andreal assets, making these asset classes less scalable in terms of external ratings. However, agrowing number of LPs are using proprietary fund grading systems that, in an effort to exploitall available information, take into account qualitative assessments. Importantly, funds arebenchmarked against their peers in such grading systems. Defining the appropriate peer groupis therefore essential for the risk manager to extract information from the grading of funds andas a basis for quantifying risks, as we discuss in Chapter 14.

1.3.3 Risk management and its governance

In Part III we turn to the question of how the concepts discussed in this book can be appliedin practice. The management of securitizations of private equity funds should be seen as a casestudy where such instruments were successfully used in the market place under the scrutiny ofrating agencies. While in the risk-on/risk-off environment in the post-crisis era securitizationin general has played a less prominent role, the principle of securitizing portfolios of illiquidfunds is highly illustrative for effective risk management. As we discuss in Chapter 15, suchstructured vehicles represent a relatively simple case of asset liability management and aretherefore instructive for LPs facing comparable issues, such as pension plans and insurancecompanies. Securitizations of portfolios of limited partnership funds demonstrate how onerisk dimension can be transformed into another and how trade-offs between risk dimensionscan be managed – equity versus debt, market risk versus credit risk, illiquidity versus liquidity,liquidity risk versus capital risk.

Focusing on the investment process as a defining criterion of prudent investing could easilylead to confusion over the role of the LP’s risk manager versus the role of its complianceofficer. In Chapter 16, therefore, we clarify the two functions as distinctly different parts of an

101



Risk models for funds can be constructed top-down or bottom-up. While probabilisticmodels using cash flow libraries tend to start with a top-down approach, a bottom-up analysiscan refine projections and add considerable granularity. In this analysis, a key ingredient is thedistribution waterfall as specified in the limited partnership agreement. The basic structure ofthe waterfall is presented in Chapter 12, on the basis of which we provide different examplesof cash inflows and outflows under alternative assumptions about hurdle rates and carriedinterest. While these parameters determine the profit for the LPs, they are also highly relevantfrom a risk management perspective. Realistically, however, a bottom-up analysis may be toocomplex and resource-intensive for most investors, given substantial variations between fundsin terms of the key parameters determining profit sharing between the GP and his or her LPs.

As important as quantitative risk measurement is, in illiquid asset classes risk managers oftenface important data constraints. This does not mean, however, that effective risk managementcannot be done. Rather, the risk manager has to work with the set of information that isavailable to him or her, and this includes qualitative assessments. Understandably, manyrisk managers feel uncomfortable using qualitative data, as they fear that such informationmay be inconsistent and hence result in distorted conclusions. However, this discomfortcan be mitigated, at least to some degree, by employing classification schemes for limitedpartnership funds.

As far as mutual funds are concerned, there are several external agencies that provide ratingsaiming to provide a forward-looking prognosis based on a standardized valuation. As we arguein Chapter 13, independent ratings of limited partnerships are more difficult, as there are fewobjective criteria that can be used in a standardized fashion. Furthermore, there may be toofew potential users, given the still relatively limited number of investors in private equity andreal assets, making these asset classes less scalable in terms of external ratings. However, agrowing number of LPs are using proprietary fund grading systems that, in an effort to exploitall available information, take into account qualitative assessments. Importantly, funds arebenchmarked against their peers in such grading systems. Defining the appropriate peer groupis therefore essential for the risk manager to extract information from the grading of funds andas a basis for quantifying risks, as we discuss in Chapter 14.

1.3.3 Risk management and its governance

In Part III we turn to the question of how the concepts discussed in this book can be appliedin practice. The management of securitizations of private equity funds should be seen as a casestudy where such instruments were successfully used in the market place under the scrutiny ofrating agencies. While in the risk-on/risk-off environment in the post-crisis era securitizationin general has played a less prominent role, the principle of securitizing portfolios of illiquidfunds is highly illustrative for effective risk management. As we discuss in Chapter 15, suchstructured vehicles represent a relatively simple case of asset liability management and aretherefore instructive for LPs facing comparable issues, such as pension plans and insurancecompanies. Securitizations of portfolios of limited partnership funds demonstrate how onerisk dimension can be transformed into another and how trade-offs between risk dimensionscan be managed – equity versus debt, market risk versus credit risk, illiquidity versus liquidity,liquidity risk versus capital risk.

Focusing on the investment process as a defining criterion of prudent investing could easilylead to confusion over the role of the LP’s risk manager versus the role of its complianceofficer. In Chapter 16, therefore, we clarify the two functions as distinctly different parts of an


Introduction 13

investment firm’s risk management system. Assuring conformity with regulatory requirementsand dealing effectively with operational risk is fundamental for the long-term success of aninvestment firm. However, compliance has little, if anything, to do with the management offinancial risks in the sense of trading off risks versus rewards in asset markets, which fallssquarely into the remit of the risk manager. Put differently, compliance has to ensure thatspecific processes are followed in the way they were intended to work, but it is the role of riskmanagement to help design such processes in the first place.

Ensuring that the risk manager can fulfil his or her role effectively requires appropriategovernance structures. This raises a number of important issues. Where in the LP’s organizationshould the risk management function be anchored? To whom should the risk manager report?Who is accountable in case of failures? And how should the risk manager be remuneratedwithin the broader structure of the firm? These are only some of the thorny issues we discuss.

In addressing these and other issues, LPs should have a clear risk management policy in placethat sets the framework for coordinating and executing the firm’s activities in a risk-sensitivemanner. Conceivably, as we examine in the final chapter of this book, this framework mayconsist of a set of clearly defined rules or may be based on rather general principles. However,while a pure rules-based system may be too rigid, a principles-based framework may betoo weak or ambiguous. In practice, therefore, a combination of the two may be superior,a direction that is favoured by new regulatory initiatives, such as the European AlternativeInvestment Fund Manager (AIFM) directive. Importantly, as we point out in Chapter 17,risk management policy is a living instrument rather than a static set of checks and balances.Periodic reviews are necessary to ensure that an investment firm’s risk management policy isconsistent with the industry’s best practices. In installing a risk management framework, it isimportant to note that its effectiveness is not least a function of its organizational setting. To beeffective, the risk management function has to enjoy a high degree of independence versus thefirm’s operating units, must be equipped with adequate resources and must have access to allinformation. The firm’s reporting system is equally important. This and the general complexityof risk models imply an appropriate IT system that allows the running of large-scale stresstests and scenario analyses.

For LPs, putting in place an effective risk management policy is a prerequisite for adoptinginternal model-based approaches to risk management. In fact, regulated investors – such asbanks, insurance firms and pension funds – have a strong incentive to employ internal riskmodels, which allow them to reduce significantly their regulatory capital charges comparedwith the standard approach. For the internal model to be approved by the regulatory authorities,it has to pass a “use test”, however. This entails, inter alia, explaining the rationale of the model,the underlying assumptions, the valuation methods and the data used. However, the use testalso includes procedural questions, pertaining, for example, to the model’s function in thebroader governance system, its role as an integrated tool in decision-making processes and itsadaptation to the investor’s evolving risk profile.

A Workout in Computational FinanceAndreas Binder & Michael Aichinger 978-1-119-97191-7 • Hardback • 336 pages • August 2013 Buy Now!


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2

Binomial Trees

Binomial trees, although – as it will turn out – they are not our favorite method, are widely usedin the pricing of options.1 In this chapter, we will present the basic binomial tree algorithmand some refinements. As we want to apply binomial trees to the valuation of options in thischapter, we have to describe these options beforehand.

2.1 EQUITIES AND SOME BASIC OPTIONS

An equity (stock, share) is a specified portion of ownership of a company, giving the holderof the share some rights, e.g., to participate in the annual general meeting and in the electionsthere and to obtain a dividend as a part of the profit of the company. Throughout this book,we assume that the stock is exchange-traded, so that the actual trading price of the share canbe obtained (maybe with some time delay) by consulting the exchange’s homepage or yourReuters or Bloomberg screen. With the exception of an initial public offering or an increasein capital, a change in the share price does not change the firm’s capital or liquidity, but is – atleast in an ideal world – the investors’ consensus on the value of the share. If the universe ofinvestors thinks that the iPhone will be a cash cow, then the stock price of Apple will increase.

As experiences of the last years showed, equities can not only go up in price but also cango down significantly. In order to limit the impact of downward moves of your investment ata certain point in time, a European call option may be the instrument you desire:

European call and put options: A European call option on the underlying 𝑆𝑆 gives the holderof the option the right but not the obligation to buy one share of the equity 𝑆𝑆 at a future time𝑇𝑇 , the expiry time, for a fixed price 𝐾𝐾 , the strike price.

A European put option on the underlying 𝑆𝑆 gives the holder of the option the right but notthe obligation to sell one share of the equity 𝑆𝑆 at a future time 𝑇𝑇 , the expiry time, for a fixedprice 𝐾𝐾 , the strike price.

So, at expiry, the payoff of the European options looks as shown in Figure 2.1.Whereas European options may only be exercised at the date of expiry, American options

may be exercised at any time during their lifetimes; Bermudan options may be exercisedonly at certain but known dates. Bermudan style exercise is quite popular in the fixed incomeworld. Bonds are sometimes equipped with an early redemption right for the issuer. This earlyredemption typically may take place on coupon days.

Call and put options (on liquid underlyings) are actively traded for different strike prices andfor different expiries. Of course, a (call or put) option always has a non-negative value. Holding,e.g., a call option provides an insurance against movements of the underlying below the strikeprice. The value of the option can therefore be interpreted as the premium to be paid for thisinsurance. Calculating fair values of a wide variety of options and other derivative or structured

1 If you google for the combination of “binomial tree” and “option pricing”, you obtain 34 200 results (date of search: November24, 2010).

104


8 A Workout in Computational Finance

K S

Call value

K S

Put value

Figure 2.1 Payoff of a call and of a put option at expiry as functions of the equity price 𝑆𝑆. Both optionshave a strike price 𝐾𝐾 .

instruments, analyzing their values under different scenarios and ultimately managing theirrisks is one of the main purposes of, as the authors understand it, computational finance.

2.2 THE ONE PERIOD MODEL

Consider (at time 0) an equity that can, at the expiry 𝑇𝑇 of the option, assume only two possiblestates 𝑠𝑠1 and 𝑠𝑠2 and that the random variable 𝑆𝑆𝑇𝑇 has the distribution

𝑆𝑆𝑇𝑇 ={

𝑠𝑠1 with probability 𝑝𝑝𝑝𝑠𝑠2 with probability 1 − 𝑝𝑝𝑝 (2.1)

The payoff of the option should then, depending on the price of the underlying, have thevalue 𝑉𝑉𝑇𝑇 (𝑠𝑠1) = 𝑣𝑣1 and 𝑉𝑉𝑇𝑇 (𝑠𝑠2) = 𝑣𝑣2. Is it possible to construct a portfolio 𝑃𝑃 consisting of cash(which is assumed to pay interest at a continuous rate2 𝑟𝑟) and shares of the equity in such away that the portfolio replicates the option value independent of the outcome of the randomprocess for the equity?

At time 0, let our portfolio consist of 𝑎𝑎1 units of cash and of 𝑎𝑎2 shares. Its value 𝑃𝑃0 at time0 is then

𝑃𝑃0 = 𝑎𝑎1 + 𝑎𝑎2𝑠𝑠0𝑝 (2.2)

At time 𝑇𝑇 , the cash amount has increased to 𝑎𝑎1𝑒𝑒𝑟𝑟𝑇𝑇 , whereas the equity portion’s value haschanged to 𝑎𝑎2𝑠𝑠1 or 𝑎𝑎2𝑠𝑠2, respectively. If the portfolio should replicate the option value, theunknowns 𝑎𝑎1𝑝 𝑎𝑎2 have to satisfy

𝑣𝑣1 = 𝑎𝑎1𝑒𝑒𝑟𝑟𝑇𝑇 + 𝑎𝑎2 𝑠𝑠1𝑝


with the solutions

𝑎𝑎2 =𝑣𝑣1 − 𝑣𝑣2𝑠𝑠1 − 𝑠𝑠2

𝑝

𝑎𝑎1 = 𝑒𝑒−𝑟𝑟𝑇𝑇(𝑣𝑣1 −

(𝑣𝑣1 − 𝑣𝑣2)𝑠𝑠1𝑠𝑠1 − 𝑠𝑠2

)𝑝

2 See section 4.1.1 for compounding.

105



K S

Call value

K S

Put value

Figure 2.1 Payoff of a call and of a put option at expiry as functions of the equity price 𝑆𝑆. Both optionshave a strike price 𝐾𝐾 .

instruments, analyzing their values under different scenarios and ultimately managing theirrisks is one of the main purposes of, as the authors understand it, computational finance.

2.2 THE ONE PERIOD MODEL

Consider (at time 0) an equity that can, at the expiry 𝑇𝑇 of the option, assume only two possiblestates 𝑠𝑠1 and 𝑠𝑠2 and that the random variable 𝑆𝑆𝑇𝑇 has the distribution

𝑆𝑆𝑇𝑇 ={

𝑠𝑠1 with probability 𝑝𝑝𝑝𝑠𝑠2 with probability 1 − 𝑝𝑝𝑝 (2.1)

The payoff of the option should then, depending on the price of the underlying, have thevalue 𝑉𝑉𝑇𝑇 (𝑠𝑠1) = 𝑣𝑣1 and 𝑉𝑉𝑇𝑇 (𝑠𝑠2) = 𝑣𝑣2. Is it possible to construct a portfolio 𝑃𝑃 consisting of cash(which is assumed to pay interest at a continuous rate2 𝑟𝑟) and shares of the equity in such away that the portfolio replicates the option value independent of the outcome of the randomprocess for the equity?

At time 0, let our portfolio consist of 𝑎𝑎1 units of cash and of 𝑎𝑎2 shares. Its value 𝑃𝑃0 at time0 is then

𝑃𝑃0 = 𝑎𝑎1 + 𝑎𝑎2𝑠𝑠0𝑝 (2.2)

At time 𝑇𝑇 , the cash amount has increased to 𝑎𝑎1𝑒𝑒𝑟𝑟𝑇𝑇 , whereas the equity portion’s value haschanged to 𝑎𝑎2𝑠𝑠1 or 𝑎𝑎2𝑠𝑠2, respectively. If the portfolio should replicate the option value, theunknowns 𝑎𝑎1𝑝 𝑎𝑎2 have to satisfy



with the solutions

𝑎𝑎2 =𝑣𝑣1 − 𝑣𝑣2𝑠𝑠1 − 𝑠𝑠2

𝑝

𝑎𝑎1 = 𝑒𝑒−𝑟𝑟𝑇𝑇(𝑣𝑣1 −


)𝑝

2 See section 4.1.1 for compounding.


Binomial Trees 9

Hence, if we choose the weights 𝑎𝑎1 and 𝑎𝑎2 accordingly, 𝑃𝑃 replicates the option and thereforethe option value equals the portfolio value also at time 0. Hence, we obtain

𝑣𝑣0 = 𝑃𝑃0 = 𝑠𝑠0

(𝑣𝑣1 − 𝑣𝑣2𝑠𝑠1 − 𝑠𝑠2

)+ 𝑒𝑒−𝑟𝑟𝑟𝑟

(𝑣𝑣1 −


). (2.3)

Note that the formula for the option value does not depend on the probability 𝑝𝑝 of theoutcomes 𝑠𝑠1, 𝑠𝑠2!Wewould have obtained the same result by discounting the expected outcome(at time 𝑟𝑟 ) with the expectation value taken under a probability 𝑞𝑞 for 𝑠𝑠1 and 1 − 𝑞𝑞 for𝑠𝑠2 with

𝑞𝑞 =𝑆𝑆0𝑒𝑒𝑟𝑟𝑟𝑟 − 𝑠𝑠2𝑠𝑠1 − 𝑠𝑠2

. (2.4)

The measure implied from this change of probability is called the risk neutral measure ofthe binomial model, whereas the physical measure is the one with the probability 𝑝𝑝. For a moredetailed discussion concerning the measure theoretic foundation of risk neutral valuation, see,e.g., Delbaen and Schachermayer (2006). Note that, in the risk neutral measure, the expectedvalue of the share price grows with the risk free rate 𝑟𝑟 independent of the physical growthrate implied by 𝑠𝑠1 and 𝑠𝑠2 and their physical probabilities. In order to obtain a probability 𝑞𝑞in the interval (0, 1), it is required that the risk-free forward value 𝑆𝑆0𝑒𝑒𝑟𝑟𝑟𝑟 lies between 𝑠𝑠1 and𝑠𝑠2. If 𝑆𝑆0𝑒𝑒𝑟𝑟𝑟𝑟 were outside this interval, arbitrage (a guaranteed profit at a higher rate than therisk-free rate) would be possible.

2.3 THE MULTIPERIOD BINOMIAL MODEL

The assumption of only two possible states for the price of the equity at the expiry of theoption is not a very realistic one. But, at least in theory, it might be a reasonable assumption, ifthe time interval under consideration is sufficiently small. Therefore, we build an𝑁𝑁-level treerecursively as indicated in the following figure. Note that the random variables which choosethe up or the down branch are assumed to be independent for all time steps. This is an essentialassumption for the convergence analysis utilizing the central limit theorem.

OB

A

p

1 – p

106



Following this construction, in thismultiperiod binomial tree, each node𝑂𝑂 has two successornodes𝐴𝐴 and𝐵𝐵. The distribution (in the physicalmeasure) of reaching𝐴𝐴 or𝐵𝐵 from𝑂𝑂 is assumedto be

𝑆𝑆𝑛𝑛𝑛𝑛 ∕𝑁𝑁 =

{(1 + 𝑏𝑏(𝑁𝑁))𝑆𝑆(𝑛𝑛−1)𝑛𝑛 ∕𝑁𝑁 with probability 𝑝𝑝 (Point B)

(1 + 𝑎𝑎(𝑁𝑁))𝑆𝑆(𝑛𝑛−1)𝑛𝑛 ∕𝑁𝑁 with probability 1 − 𝑝𝑝 (Point A)(2.5)

with the up and down factors (1 + 𝑏𝑏(𝑁𝑁)) and (1 + 𝑎𝑎(𝑁𝑁)), respectively, where𝑁𝑁 is the numberof time levels used.

In order to obtain a recombining tree, in the figure we implicitly assumed that the up anddown factors are constant during the lifetime of the option. Otherwise a bushy tree with up to2𝑁𝑁 branches would be the result. If we know the option value at𝐴𝐴 and 𝐵𝐵, we can calculate thefair value of the option at node 𝑂𝑂 by a one-period binomial as shown in the previous section.The risk neutral probability we have to use is given by

𝑞𝑞 = 𝑒𝑒𝑟𝑟𝑛𝑛 ∕𝑁𝑁 − 1 − 𝑎𝑎(𝑁𝑁)𝑏𝑏(𝑁𝑁) − 𝑎𝑎(𝑁𝑁)

. (2.6)

As the option value is known for all nodes at expiry (the payoff function of the option), wecan recursively calculate the values at all nodes.

As an example, we obtain, after some manipulation (and taking into account the indepen-dence of branching also in the risk-free measure), for the fair value of a European call option(with strike price 𝐾𝐾 and an initial stock price of 𝑆𝑆0)

𝑉𝑉0(𝑁𝑁) = 𝑒𝑒−𝑟𝑟𝑛𝑛⏟⏟⏟(𝐷𝐷𝐷𝐷 )

𝑁𝑁∑𝑛𝑛=0

(𝑁𝑁𝑛𝑛

)𝑞𝑞𝑛𝑛(1 − 𝑞𝑞)𝑁𝑁−𝑛𝑛

⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟(𝑃𝑃𝐷𝐷)

((1 + 𝑏𝑏(𝑁𝑁))𝑛𝑛(1 + 𝑎𝑎(𝑁𝑁))𝑁𝑁−𝑛𝑛𝑆𝑆0 −𝐾𝐾

)+

⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟(𝑃𝑃𝑂𝑂)

(2.7)

with the interpretations (𝐷𝐷𝐷𝐷 ) discount factor, (𝑃𝑃𝐷𝐷) probability density of the binomial distri-bution in the risk-free measure and (𝑃𝑃𝑂𝑂) payoff of the contingent claim, here the call option.For any real-valued argument ℎ, we used the notation

(ℎ)+ ∶= max(ℎ, 0). (2.8)

Until now, we have not specified the dependence of 𝑎𝑎(.) and 𝑏𝑏(.) on the number of time levels𝑁𝑁 . Obviously, if the tree should not explode for𝑁𝑁 → ∞, 𝑎𝑎(𝑁𝑁) and 𝑏𝑏(𝑁𝑁)must be chosen (andtend to zero) appropriately. This leads us to the Black-Scholes model.

2.4 BLACK-SCHOLES AND TREES

In the Black-Scholes model, the time-dependent evolution of the price of an equity 𝑆𝑆 startingin 𝑆𝑆0 at time 0 is modeled by

dS𝑡𝑡 = 𝜇𝜇𝑆𝑆dt + 𝜎𝜎𝑆𝑆dW, (2.9)

with 𝑆𝑆𝑡𝑡 being the stock price at time 𝑡𝑡, dS its incremental change in the infinitesimal timeinterval (𝑡𝑡, 𝑡𝑡 + dt), 𝜎𝜎 the annualised volatility, and dW the increment of a standard Wienerprocess. The parameter 𝜇𝜇 is the expected growth rate in the physical measure.

107



Following this construction, in thismultiperiod binomial tree, each node𝑂𝑂 has two successornodes𝐴𝐴 and𝐵𝐵. The distribution (in the physicalmeasure) of reaching𝐴𝐴 or𝐵𝐵 from𝑂𝑂 is assumedto be

𝑆𝑆𝑛𝑛𝑛𝑛 ∕𝑁𝑁 =

{(1 + 𝑏𝑏(𝑁𝑁))𝑆𝑆(𝑛𝑛−1)𝑛𝑛 ∕𝑁𝑁 with probability 𝑝𝑝 (Point B)

(1 + 𝑎𝑎(𝑁𝑁))𝑆𝑆(𝑛𝑛−1)𝑛𝑛 ∕𝑁𝑁 with probability 1 − 𝑝𝑝 (Point A)(2.5)

with the up and down factors (1 + 𝑏𝑏(𝑁𝑁)) and (1 + 𝑎𝑎(𝑁𝑁)), respectively, where𝑁𝑁 is the numberof time levels used.

In order to obtain a recombining tree, in the figure we implicitly assumed that the up anddown factors are constant during the lifetime of the option. Otherwise a bushy tree with up to2𝑁𝑁 branches would be the result. If we know the option value at𝐴𝐴 and 𝐵𝐵, we can calculate thefair value of the option at node 𝑂𝑂 by a one-period binomial as shown in the previous section.The risk neutral probability we have to use is given by

𝑞𝑞 = 𝑒𝑒𝑟𝑟𝑛𝑛 ∕𝑁𝑁 − 1 − 𝑎𝑎(𝑁𝑁)𝑏𝑏(𝑁𝑁) − 𝑎𝑎(𝑁𝑁)

. (2.6)

As the option value is known for all nodes at expiry (the payoff function of the option), wecan recursively calculate the values at all nodes.

As an example, we obtain, after some manipulation (and taking into account the indepen-dence of branching also in the risk-free measure), for the fair value of a European call option(with strike price 𝐾𝐾 and an initial stock price of 𝑆𝑆0)

𝑉𝑉0(𝑁𝑁) = 𝑒𝑒−𝑟𝑟𝑛𝑛⏟⏟⏟(𝐷𝐷𝐷𝐷 )

𝑁𝑁∑𝑛𝑛=0

(𝑁𝑁𝑛𝑛

)𝑞𝑞𝑛𝑛(1 − 𝑞𝑞)𝑁𝑁−𝑛𝑛

⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟(𝑃𝑃𝐷𝐷)

((1 + 𝑏𝑏(𝑁𝑁))𝑛𝑛(1 + 𝑎𝑎(𝑁𝑁))𝑁𝑁−𝑛𝑛𝑆𝑆0 −𝐾𝐾

)+

⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟(𝑃𝑃𝑂𝑂)

(2.7)

with the interpretations (𝐷𝐷𝐷𝐷 ) discount factor, (𝑃𝑃𝐷𝐷) probability density of the binomial distri-bution in the risk-free measure and (𝑃𝑃𝑂𝑂) payoff of the contingent claim, here the call option.For any real-valued argument ℎ, we used the notation

(ℎ)+ ∶= max(ℎ, 0). (2.8)

Until now, we have not specified the dependence of 𝑎𝑎(.) and 𝑏𝑏(.) on the number of time levels𝑁𝑁 . Obviously, if the tree should not explode for𝑁𝑁 → ∞, 𝑎𝑎(𝑁𝑁) and 𝑏𝑏(𝑁𝑁)must be chosen (andtend to zero) appropriately. This leads us to the Black-Scholes model.

2.4 BLACK-SCHOLES AND TREES

In the Black-Scholes model, the time-dependent evolution of the price of an equity 𝑆𝑆 startingin 𝑆𝑆0 at time 0 is modeled by

dS𝑡𝑡 = 𝜇𝜇𝑆𝑆dt + 𝜎𝜎𝑆𝑆dW, (2.9)

with 𝑆𝑆𝑡𝑡 being the stock price at time 𝑡𝑡, dS its incremental change in the infinitesimal timeinterval (𝑡𝑡, 𝑡𝑡 + dt), 𝜎𝜎 the annualised volatility, and dW the increment of a standard Wienerprocess. The parameter 𝜇𝜇 is the expected growth rate in the physical measure.


Binomial Trees 11

The equation for valuating an option on an underlying equity following (2.9) will be derivedin Chapter 3. There, the risk neutral measure induced by the replicating portfolios will replace𝜇𝜇 by the risk-free interest rate 𝑟𝑟.

It can be shown that the random variable 𝑆𝑆𝑇𝑇 ∕𝑆𝑆0 is (in the physical measure) normallydistributed with mean (𝜇𝜇 − 𝜎𝜎2∕2)𝑇𝑇 and variance 𝜎𝜎2𝑇𝑇 . In the risk neutral measure, 𝜇𝜇 has to bereplaced by 𝑟𝑟.

If the 𝑁𝑁-level binomial tree with time step Δ𝑇𝑇 = (𝑇𝑇 ∕𝑁𝑁) should be a numerical approxi-mation for the Black-Scholes model, the parameters 𝑎𝑎(𝑁𝑁) and 𝑏𝑏(𝑁𝑁) should be chosen in sucha way that the corresponding distribution in the binomial model approaches the log-normaldistribution of the Black-Scholes model in the risk neutral measure for 𝑁𝑁 → ∞ (to be morespecific: convergence in distribution will be obtained).

There are (infinitely) many ways to choose the up/down parameters 𝑎𝑎(.) and 𝑏𝑏(.). FollowingKorn and Muller (2010), the way to choose 𝑎𝑎, 𝑏𝑏 and the physical probability 𝑝𝑝 is such thatmean and variance of the Black-Scholes return in the risk-free measure are matched. Notethat, for the valuation process in the binomial tree, the physical probability 𝑝𝑝 disappears,therefore this mingling of physical and risk-free measures is justified. Prominent examples oftree parameters are:

Cox-Ross-Rubinstein

(1 + 𝑏𝑏) = 𝑒𝑒𝜎𝜎√Δ𝑇𝑇 (1 + 𝑎𝑎) = 𝑒𝑒−𝜎𝜎

√Δ𝑇𝑇 (2.10)

Forward Tree

(1 + 𝑏𝑏) = 𝑒𝑒𝑟𝑟Δ𝑇𝑇+𝜎𝜎√Δ𝑇𝑇 (1 + 𝑎𝑎) = 𝑒𝑒𝑟𝑟Δ𝑇𝑇−𝜎𝜎

√Δ𝑇𝑇 (2.11)

Note that in the literature our “Forward Tree” is sometimes named Cox-Ross-Rubinstein.

Rendleman-Bartter

(1 + 𝑏𝑏) = 𝑒𝑒(𝑟𝑟−𝜎𝜎2∕2)Δ𝑇𝑇+𝜎𝜎

√Δ𝑇𝑇 (1 + 𝑎𝑎) = 𝑒𝑒(𝑟𝑟−𝜎𝜎

2∕2)Δ𝑇𝑇−𝜎𝜎√Δ𝑇𝑇 (2.12)

Depending on the preferred choice of the tree, there may be upper bounds for Δ𝑇𝑇 in orderto guarantee the no-arbitrage condition 𝑞𝑞 ∈ (0, 1) for 𝑞𝑞 as in (2.6). For the forward tree, thisis always fulfilled. The Cox-Ross-Rubinstein tree has to restrict Δ𝑡𝑡 for 𝑟𝑟 large and 𝜎𝜎 small,the Rendleman-Bartter tree for large 𝜎𝜎. Working out the conditions on Δ𝑇𝑇 in detail is an easyexercise and left to the reader.

The convergence in distribution of the discrete 𝑁𝑁-level trees towards the Black-Scholesmodel can be shown for all the trees mentioned above. The central limit theorem is the keytool for proving convergence (Kallenberg, 2006). It can be shown that with𝑁𝑁 → ∞ , the treevalue 𝑉𝑉0(𝑁𝑁) as in (2.7) converges to

𝑉𝑉0 = 𝑒𝑒−𝑟𝑟𝑇𝑇⏟⏟⏟(𝐷𝐷𝐷𝐷 )

∫∞

0

1𝜎𝜎𝑆𝑆

√2𝜋𝜋𝑇𝑇

𝑒𝑒−𝛼𝛼2∕2

⏟⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏟(𝑃𝑃𝐷𝐷)

(𝑆𝑆 −𝐾𝐾

)+

⏟⏞⏞⏞⏟⏞⏞⏞⏟(𝑃𝑃𝑃𝑃)

dS (2.13)

with 𝛼𝛼 = 1𝜎𝜎√𝑇𝑇(log(𝑆𝑆∕𝑆𝑆0) + (𝑟𝑟 − 𝜎𝜎2∕2)𝑇𝑇 ).

108



2.5 STRENGTHS ANDWEAKNESSES OF BINOMIAL TREES

2.5.1 Ease of Implementation

The following piece of code is an example of a forward tree realized in Mathematica. Bychanging the settings for the up and the down parameters, one can easily obtain a Cox-Ross-Rubinstein or a Rendleman-Bartter tree.

BinomialEuropeanCall2[S_, K_, r_, sigma_, T_, n_] :=Module[{dt, forward, up, down, P, Q, Probup, Probdown, BinomTree,

value, level},

dt = T/n; forward = Exp[r*dt];

up = Exp[sigma*Sqrt[dt]]*forward;

down = Exp[-sigma*Sqrt[dt]]*forward;

Probup = (forward - down)/(up - down);

Probdown = 1 - Probup;

P = Probup*Exp[-r*dt];(* Discounting per timestep *)

Q = Probdown*Exp[-r*dt];(* Discounting per timestep *)

BinomTree =Table[Max[S*down∧node*up∧(n - node) - K, 0], node, 0, n];

(* Terminal condition of a call option *)

Do[BinomTree = Table[

{P, Q}.{BinomTree[[node]], BinomTree[[node + 1]]},

{node, 1,level]},

(* In the caes of an American option, compare here against

the exercise value: BinomTree= Max[BinomTree, exercise value]

or add knock-out conditions of barrier options here *)

{level, n, 1, -1}];

value = BinomTree[[1]];

Clear[BinomTree];

value]

The main advantage of the binomial tree method is its ease of implementation, also foroptions which may be exercised early like American or Bermudan ones. It is an explicitmethod so that no systems of equations have to be solved (see also Chapter 3 for a comparisonof explicit/implicit methods in the finite difference framework).

2.5.2 Oscillations

How fast do binomial trees converge? Figure 2.2 shows the binomial tree values of a Europeancall option (strike price 100, expiry 1 year, current equity price 100, interest rate 0.03, volatility0.35) for the different binomial trees described in the previous section. Valuation has beenperformed for𝑁𝑁 = 2 to 100.

We notice the oscillating behavior (between “even values” and “odd values”) for all of thesetree implementations; the amplitude of these oscillations is typically larger for the Cox-Ross-Rubinstein tree than for the Forward and Rendleman-Bartter trees. To obtain a guaranteedrelative accuracy of 0.05 % for this specific example (in the sense of staying below this errorlevel when you use any larger number of time levels), 𝑁𝑁 has to be chosen to be at least 437(Cox-Ross-Rubinstein), 277 (Forward tree), 255 (Rendleman-Bartter) which means that thetree has at least 30 000 nodes.

109



2.5 STRENGTHS ANDWEAKNESSES OF BINOMIAL TREES

2.5.1 Ease of Implementation

The following piece of code is an example of a forward tree realized in Mathematica. Bychanging the settings for the up and the down parameters, one can easily obtain a Cox-Ross-Rubinstein or a Rendleman-Bartter tree.

BinomialEuropeanCall2[S_, K_, r_, sigma_, T_, n_] :=Module[{dt, forward, up, down, P, Q, Probup, Probdown, BinomTree,

value, level},

dt = T/n; forward = Exp[r*dt];

up = Exp[sigma*Sqrt[dt]]*forward;

down = Exp[-sigma*Sqrt[dt]]*forward;

Probup = (forward - down)/(up - down);

Probdown = 1 - Probup;

P = Probup*Exp[-r*dt];(* Discounting per timestep *)

Q = Probdown*Exp[-r*dt];(* Discounting per timestep *)

BinomTree =Table[Max[S*down∧node*up∧(n - node) - K, 0], node, 0, n];

(* Terminal condition of a call option *)

Do[BinomTree = Table[

{P, Q}.{BinomTree[[node]], BinomTree[[node + 1]]},

{node, 1,level]},

(* In the caes of an American option, compare here against

the exercise value: BinomTree= Max[BinomTree, exercise value]

or add knock-out conditions of barrier options here *)

{level, n, 1, -1}];

value = BinomTree[[1]];

Clear[BinomTree];

value]

The main advantage of the binomial tree method is its ease of implementation, also foroptions which may be exercised early like American or Bermudan ones. It is an explicitmethod so that no systems of equations have to be solved (see also Chapter 3 for a comparisonof explicit/implicit methods in the finite difference framework).

2.5.2 Oscillations

How fast do binomial trees converge? Figure 2.2 shows the binomial tree values of a Europeancall option (strike price 100, expiry 1 year, current equity price 100, interest rate 0.03, volatility0.35) for the different binomial trees described in the previous section. Valuation has beenperformed for𝑁𝑁 = 2 to 100.

We notice the oscillating behavior (between “even values” and “odd values”) for all of thesetree implementations; the amplitude of these oscillations is typically larger for the Cox-Ross-Rubinstein tree than for the Forward and Rendleman-Bartter trees. To obtain a guaranteedrelative accuracy of 0.05 % for this specific example (in the sense of staying below this errorlevel when you use any larger number of time levels), 𝑁𝑁 has to be chosen to be at least 437(Cox-Ross-Rubinstein), 277 (Forward tree), 255 (Rendleman-Bartter) which means that thetree has at least 30 000 nodes.


Binomial Trees 13

0 20 40 60 80 10015.0

15.1

15.2

15.3

15.4

15.5

Figure 2.2 Binomial tree value as a function of the number of time steps. Blue: Cox-Ross-Rubinstein,Green: Forward Tree, Red: Rendleman-Bartter. 𝑆𝑆 = 100, 𝐾𝐾 = 100, 𝑇𝑇 = 1, 𝑟𝑟 = 0.03, 𝜎𝜎 = 0.35. Theanalytical Black-Scholes value is 15.2142.

The main reason for the oscillations is the non-smooth payoff of the call option (with itsjump in the first derivative at the strike price). Presmoothing the end condition by applying,e.g., the analytical Black-Scholes formula close to the expiry date might help. We do not carryout this procedure here, because it is feasible only when an analytical formula is available atleast in the vicinity of discontinuities.

We have seen in the previous section that Cox-Ross-Rubinstein and Rendleman-Barttertrees may violate the no-arbitrage condition for large time steps and for certain parametersettings. We give two examples in Figures 2.3 and 2.4.

0 20 40 60 80 1000

20

40

60

80

100

Figure 2.3 The Cox-Ross-Rubinstein violates the no-arbitrage condition for small volatilities and largetime steps. Here 𝑆𝑆 = 100, 𝐾𝐾 = 100, 𝑇𝑇 = 8, 𝑟𝑟 = 0.05, 𝜎𝜎 = 0.02. Even (wrong) negative option valuescould result. The forward and Rendleman-Bartter trees converge fast in this case.

110



0 20 40 60 80 1000

20

40

60

80

100

Figure 2.4 The Rendleman-Bartter tree violates the no-arbitrage condition for large volatilities andlarge time steps. Here 𝑆𝑆 = 100, 𝐾𝐾 = 100, 𝑇𝑇 = 8, 𝑟𝑟 = 0.05, 𝜎𝜎 = 1.3. Forward tree and Cox-Ross-Rubinstein exhibit oscillations, as expected.

2.5.3 Non-recombining Trees

As long as one deals with options on underlyings which either do not pay dividends (likeforeign currencies) or pay dividends proportional to the price of the equity, recombining treescan be constructed. However, if the dividend is a fixed amount of cash, then, in general, treesdo not recombine anymore but become bushy as shown in Figure 2.5.

Other sources for non-recombining trees are up/down factors that are not constant on thetree. As these factors are matched to market data for interest rates and volatilities, this occursquite frequently.

2.5.4 Exotic Options and Trees

Obviously, when there is an analytic solution available (as is the case for vanilla options inthe Black-Scholes model), it does not make too much sense to calculate their value by usingbinomial trees or any other numerical procedure. Numerical methods only begin to play a role

Figure 2.5 Bushy trees arising from discrete dividends.

111



0 20 40 60 80 1000

20

40

60

80

100

Figure 2.4 The Rendleman-Bartter tree violates the no-arbitrage condition for large volatilities andlarge time steps. Here 𝑆𝑆 = 100, 𝐾𝐾 = 100, 𝑇𝑇 = 8, 𝑟𝑟 = 0.05, 𝜎𝜎 = 1.3. Forward tree and Cox-Ross-Rubinstein exhibit oscillations, as expected.

2.5.3 Non-recombining Trees

As long as one deals with options on underlyings which either do not pay dividends (likeforeign currencies) or pay dividends proportional to the price of the equity, recombining treescan be constructed. However, if the dividend is a fixed amount of cash, then, in general, treesdo not recombine anymore but become bushy as shown in Figure 2.5.

Other sources for non-recombining trees are up/down factors that are not constant on thetree. As these factors are matched to market data for interest rates and volatilities, this occursquite frequently.

2.5.4 Exotic Options and Trees

Obviously, when there is an analytic solution available (as is the case for vanilla options inthe Black-Scholes model), it does not make too much sense to calculate their value by usingbinomial trees or any other numerical procedure. Numerical methods only begin to play a role

Figure 2.5 Bushy trees arising from discrete dividends.


Binomial Trees 15

95 100 105 110 115 120Stock price

2

4

6

8

10

Value

Figure 2.6 Up-and-out call option with barrier 𝐵𝐵 = 120 (continuously observed), strike 𝐾𝐾 = 100,7 days to expiry, 𝑟𝑟 = 0.05, 𝜎𝜎 = 0.30. The plot shows the value as a function of the current stock price.Thick black line: analytical value. Thin black curves: Forward trees with 𝑁𝑁 = 80, 110, 140, 170, 200.Note the zigzagging.

when the financial instrument does not allow an analytic solution any more (e.g., for Americanput options or more exotic instruments), or when the mathematical model describing theunderlying is not suitable for an analytic solution.

In the next example (Figure 2.6) we study an up-and-out call option. This is a call optionwith the additional feature that as soon as the underlying goes above a prescribed barrier,the option becomes worthless for the holder. Such knockout options are, depending on thebarrier level, significantly cheaper than plain vanilla options. For constant parameters 𝑟𝑟, 𝜎𝜎 anda constant barrier 𝐵𝐵, there is an analytic solution available (see, e.g., Wilmott (1998)). This isnot the case as soon as 𝑟𝑟, 𝜎𝜎 or 𝐵𝐵 are time-dependent.

2.5.5 Greeks and Binomial Trees

Numerical methods in computational finance are not only used for the valuation of derivativeor structured instruments, but also for determining the Greeks (see Chapter 3) for hedgingpurposes. We try to calculate the first derivative Delta of the option value with repect to theunderlying 𝑆𝑆 by numerical differentiation. Here we use a central difference quotient

Delta = 𝑉𝑉 (𝑆𝑆 + Δ𝑆𝑆, 𝑆𝑆) − 𝑉𝑉 (𝑆𝑆 − Δ𝑆𝑆, 𝑆𝑆)2Δ𝑆𝑆

. (2.14)

The Delta results for a barrier option obtained by the forward tree are reported in Figure 2.7.

2.5.6 Grid Adaptivity and Trees

In order to obtain a recombining tree, all branches of the tree must look the same. This meansthat in order to have small time steps or a fine discretization of the underlying in one region,one needs to use a fine grid everywhere unless sophisticated extensions are made to the tree.

112



95 100 105 110 115 120Stock price

–1.0

–0.5

0.5

1.0Delta

Figure 2.7 Up-and-out call option with barrier 𝐵𝐵 = 120 (continuously observed), strike 𝐾𝐾 = 100,7 days to expiry, 𝑟𝑟 = 0.05, 𝜎𝜎 = 0.30. The plot shows the delta value as a function of the current stockprice. Curve: analytical value. Thin line: Numerical differentiation with Δ𝑆𝑆 = 0.01 applied to a forwardtree with𝑁𝑁 = 140. Note that the calculated binomial delta is not only inaccurate but frequently has eventhe wrong sign. Instead of reducing the risk by delta hedging, it is increased.

We will see in several chapters of this book how easily grid-adaptivity can be carried out withother numerical methods, e.g. finite elements.

2.6 CONCLUSION

Binomial trees can be implemented intuitively and easily.As it turned out on the previous pages,binomial trees work fine for simple models, simple derivative constructs and if computingtime does not play a major role. For more complex instruments, the valuation may becomeinaccurate. This is even more the case for calculating Greeks by utilizing binomial trees.

113



95 100 105 110 115 120Stock price

–1.0

–0.5

0.5

1.0Delta

Figure 2.7 Up-and-out call option with barrier 𝐵𝐵 = 120 (continuously observed), strike 𝐾𝐾 = 100,7 days to expiry, 𝑟𝑟 = 0.05, 𝜎𝜎 = 0.30. The plot shows the delta value as a function of the current stockprice. Curve: analytical value. Thin line: Numerical differentiation with Δ𝑆𝑆 = 0.01 applied to a forwardtree with𝑁𝑁 = 140. Note that the calculated binomial delta is not only inaccurate but frequently has eventhe wrong sign. Instead of reducing the risk by delta hedging, it is increased.

We will see in several chapters of this book how easily grid-adaptivity can be carried out withother numerical methods, e.g. finite elements.

2.6 CONCLUSION

Binomial trees can be implemented intuitively and easily.As it turned out on the previous pages,binomial trees work fine for simple models, simple derivative constructs and if computingtime does not play a major role. For more complex instruments, the valuation may becomeinaccurate. This is even more the case for calculating Greeks by utilizing binomial trees.

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1

Private Equity as an Economic DriverAn Historical Perspective

Columbus: scientist, entrepreneur and venture capitalist

After seven years of lobbying Christopher Columbus convinced the Spanish monarchs(Ferdinand II of Aragon and Isabella I of Castile) to sponsor his trip towards the West.His ‘elevator pitch’ must have been the following: ‘I want to open a new and shorter nauticalroute to the Indies in the West, defy the elements, make you become even more powerful andrich, and laugh at the Portuguese and their blocs on the Eastern routes.’

He probably did not know at that stage that he was structuring a private equity deal (here, aventure capital operation). But indeed he was, as his project combined these elements: financedby an external investor, a high risk, a high return potential, an entrepreneurial venture, andprotection of this competitive advantage.

These elements form the common ground for all private equity deals (venture capital,growth/expansion capital, leveraged buy-out, etc.). Another element lies in the ‘private’ char-acteristics of private equity deals negotiated privately between the parties: historically, theywere made with non-listed companies.

Even though it is difficult to imagine whether, and how, Columbus did his risk-returncalculation when assessing the viability of his project, we can assume that the risks borne bythe operation were identified and that there was a plan to mitigate them – or at least sufficientlywell identified to light enough candles in church.

The risks were high, but not unlimited (thus distinguishing his venture from puregambling).

The prospect of reaching the Indies gave quite a good sense of what could have beenthe return on investment for the financial sponsors: the Spanish monarchs and the privateinvestors fromGenoa. Not only did the potential return exceed by far that which a conventionalinvestment could provide, but the new route had a potentially disruptive impact on internationalcommerce, giving the newborn unified Spanish Crown a much needed mercantile boost.

Private equity has always existed . . . just in a different form than today

This example illustrates the fact that private equity has always existed, in one form or another,throughout history. Examples of historical buy-outs are more difficult to identify, hence thefocus of this chapter on venture capital. Buy-outs transfer majority ownership in exchangefor cash and are generally friendly. Typically, buy-outs are conducted with insider knowledge.They have only recently started to become important, as they require sophisticated financialmarkets and instruments.

Historically, large buy-out operations were ‘barters’, with a strong real estate/commercialfocus. This involved mainly swapping countries or towns for other ones. The state todayknown as New York was swapped by the Dutch West Indies Company (WIC) for Surinam, a

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12 Introduction to Private Equity

plantation colony in northern South America, in 1667 (Treaty of Breda3). This turned out tobe a bad deal.

Modern private equity emerged from large macro changes (and still requires themto emerge)

The emergence of private equity as a dynamic financial tool required the interplay of (i) asupportive social, legal and tax environment, (ii) adequate human resources and (iii) sufficientcapital. Together, these three conditions developed slowly until they reached the current levelof professionalism and formalism which characterises private equity.4 The clear identificationand separation of the three conditions forming the ‘private equity ecosystem’ has been acontinuous process, which is still under way.

The purpose of this chapter is to identify the key elements distinguishing private equityfrom other categories of investment. Private equity financing in the early days of venturingwas an intricate mix of public policy, entrepreneurship and financing. The quest of Europeanmonarchs for greater wealth and power is emblematic for this mix, pooling public and privateresources in order to identify and exploit sometimes remote resources (see section 1.1).

Public policies, entrepreneurship and financing became less complex and slowly gainedautonomy. The public interest and policies were separated clearly from the King’s personalinterest and will. Once the basic legal and tax framework had been established and adapted tothe alterations in social and economic factors, the entrepreneur emerged as the central figureof the private equity ecosystem (see section 1.2).

Private equity investors developed a capability to identify them, providing capital and keyresources to help with their venture and get their share of success. By gaining this know-howand expertise, those investors contributed to further professionalisation, developing strategiesto mitigate risks and optimise returns (see Chapter 2).

1.1 POOLING INTERESTS TO IDENTIFY AND EXPLOITSOURCES OF WEALTH

The fundamental objective of any rational investor is to increase his wealth.5 Private equityoffers investors the opportunity to finance the development of private companies and benefitfrom their eventual success. Historically, the raison d’etre of those companies has beento identify and control resources, thereby developing the wealth of venture promoters byappropriation.

3 In 1626, PeterMinuit, thenDirectorGeneral of theWIC, acquired the island ofManhattan from the Indians and began constructingFort New Amsterdam. In 1664, owing to commercial rivalry between the Dutch and the English, an English fleet sent by James, Dukeof York, attacked the New Netherlands colonies. Being greatly outnumbered, Director General Peter Stuyvesant surrendered NewAmsterdam, which was then renamed in honour of James. The loss of New Amsterdam led to the Second Anglo-Dutch War of1665–1667. This conflict ended with the Treaty of Breda, under which the Dutch gave up their claim in exchange for Surinam.

4 Lerner (2009), states: ‘often, in their eagerness to get the “fun stuff” of handing out the money, public leaders neglect theimportance of setting the table, or creating a favorable environment’ (p. 12): universities and government laboratories, adapted tax andlegal policies, education (see section 4.1 for further developments) and a favourable exit environment.

5 Selectively, some investors may add secondary items on their agenda, which can vary from gaining a foothold in the market/in agiven company (corporate investors), to monitoring technical progress, achieving social recognition and other specific issues. However,viable investment programmes usually put financial returns at the top of their list (at least in order to achieve self-sustainability withina certain period of time).

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Private Equity as an Economic Driver 13

Private equity operations require a sponsor

The main financial sponsor might have been a political leader, who would legally and finan-cially ease the preparation and the execution of the venture for the benefit of the Crown andhimself. The control of resources and the conquest of land motivated the launch of explorationventures (a). Companies were created to support political efforts,6 thereby guaranteeing thedemand for their product in exchange for their participation in a public effort to build infras-tructures, create a new market and more generally encourage commerce and the generationof wealth. They could leverage public action (b). Apparently, conflicts of interest did not ringany bells at that time.

Private equity operations are symbiotic with public initiatives

Often, private investors were complementing this public initiative, convinced by the pitchmade by a person combining technical competence and know-how, with a vision and genuinemarketing talent. This person would be identified nowadays as an entrepreneur – or theprecursor of televangelists, when the marketing presentation becomes a seven-year sermon, inthe case of Columbus.

1.1.1 Identify, Control and Exploit Resources

The quest to master time and space has given birth to pioneering public and private initiatives,bearing a substantial risk but also a potentially high reward. This reward was usually associatedwith the geographical discovery of new resources (land control) and/or effectiveness (newroutes to the Indies, for example), allowing a better rotation of assets and improving thereturns.

High risk, high return potential

Columbus’s project supported a substantially higher risk than the equivalent and usual routesto the East. This project was deemed to be possible thanks to progress in navigation andmapping, and some other technical and engineering discoveries. In that respect, Columbus’sexpedition was emblematic of the technological trend, as well as being political, religious andscientific; all of which he mastered so as to present his project.

The risks taken by Columbus were of two different kinds:

(i) Initial validation of theoretical assumptions, with substantial risks linked to the transitionfrom a theoretical framework to an operational process.7 Columbus’s prediction of thediameter of the Earth (3700 km instead of 40 000 km) proved wrong, but his venturewas successful in the sense that he reached an unknown new continent. This kind ofoutcome (refocusing the ‘research and development (R&D) effort’ towards a differentoutcome) occurs from time to time in companies financed by venture capital even today.Hopefully, not all venture-backed companies have a CEO who under-evaluates the effortto be produced by a factor of 10.

6 As a result, still today, public ‘programs geared toward going to nascent entrepreneurs may instead end up boosting cronies ofthe nation’s rulers or legislators’ (Lerner, 2009, p. 11).

7 Today, this would qualify as a transition from ‘research and development’ mode to ‘go to market’ mode.

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(ii) Execution of the four successive trips, with the presence of favourable winds and currents,the correct calculation of the time spent at sea with embarked supplies, navigation hazards(storms), morale of the crew and other operational aspects. Operational risks are generallyfinanced by later stage venture capital and expansion investors.8

For all of the above reasons, Columbus’s project was innovative in many respects. It wasguided by ambition and a vision. It was designed to test concretely the validity of a certainnumber of theories, which would be of great reward if Columbus touched Indian ground afterjourneying to the West.

The high return potential was related to Columbus’s calculations, according to which thenew nautical route could save a substantial amount of time (and risk) to reach the Indiesdespite the Portuguese land bloc. The return potential would be earned not from the initial tripitself, but from opening a new route for future trips to gather expensive goods (mainly silk andspices) and bring them back to Europe.

Another key element was that this new nautical route would have paved the way to devel-oping a certain number of other new ventures using the route to gain other valuable goods.Columbus’s success would not have been a one-time pay-off but the source of recurring andlong-term income.

A long-term investment, protected by a favourable legal environment

The time horizon of the trip was calculated inmonths, which represents a long-term investment,and the pay-off would have been calculated in years. This represents another element thatqualifies Columbus’s trip to the West as a private equity project.Protection by the Spanish monarchs of this advantage, by giving a legal right to the private

sponsors of the project to the use of this new route (the historical equivalent of the current‘barriers to entry’ in a given market), was a crucial element of the evaluation of the return oninvestments. Columbus was promoted to the status of ‘Admiral of the Seas’ by the Spanishmonarchs, and then to Governor once he succeeded in his venture. This meant that he just hadto sit and wait for the profits to come, after making this initial breakthrough.

As an additional incentive, Columbus would have received a share of all the profits madevia this nautical route. More specifically, Columbus asked, aside from the titles and an officialcharge, for a 10% share of the profits realised through the exploitation of the route to the West.He had option rights to acquire one eighth of the shares of any commercial venture willingto use the nautical route that he had opened. This kind of financial incentive (percentage onprofits realised and the equivalent of stock options; in private equity this incentive is calledcarried interest) is often used to reward the management of a company, should it reach a certainnumber of targets.

In that respect, the dispute about the reward to be granted by the monarchs of Spain toColumbus after his journeys, as well as the difficulty of providing a quick and easy returnfor the Genoese investors (as there was little gold to capture on the Caribbean Islands), isanother point comparable with typical private equity operations, an outcome different fromthat originally planned. Some disputes held in recent years between creators and managers of

8 This is an early illustration of a phenomenon which would become Johnson’s ‘10/10 Rule’ (Johnson, 2010): a decade to build anew platform, and a decade to find a mass audience (or exploitation).

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internet start-ups and their financial backers prove that this still happens today – and, just likeback then, before the courts.

Pooling of resources

This pooling of the energies and resources of an entrepreneur (Columbus); of Genoese privateinvestors (representing 50% of the pool of money) and of the Spanish monarchs as a sponsorsyndicate for the project, is another criterion for its qualification as a private equity project. Itscommercial purpose, even if not exclusive in this example, is another.

Still not a template for modern venture capital

Columbus’s venture, however, stands out as different from a typical private equity investment.He benefited from political and legal support which would not be sustainable in an open andfair trade market today – or at least not so openly provided.

The Italian investors were ‘hands off’ in the project. However, Columbus convinced themand enrolled the providers of the three ships in his venture. This implies that even if therewas no equivalent of a ‘lead investor’ and ‘investment managers’ (see Chapter 2) to look afterColumbus’s project, the monitoring was done according to historical standards, that is to say:on site, day-to-day and probably with vigorous debates about the option of continuing andtaking the risk of wreckage; or returning and saving both fleet and crew.

1.1.2 Leverage Public Policies and a Favourable Business Environment

Even if Columbus’s project was driven by religious and commercial purposes, the politi-cal ambitions of the Spanish monarchs were the key factor triggering public commitment.9

Governmental, and more generally public, support is instrumental in contributing to the emer-gence of private equity ventures by funding fundamental research, financing key infrastruc-tures and creating a favourable environment for the development of ventures. However, privateequity projects which qualify as such and which have served public policies are limited innumber – and public programmes alone are not sufficient.10

1.1.2.1 The Separation of Public and Private Financing as a Key Element of theEmergence of an Autonomous Private Equity Sector

This stems from the fact that with the separation of the King as a public body and the King asa private person, projects were no longer financed by public subsidies and the specific conver-gence of interest which had allowed Columbus to set up his project slowly became a rarity.

The increased control of the use of public money, a greater focus on fair trade and thewill to let market forces act as far as possible in favour of private and public interests haveplayed a significant role in the limitation of the state’s direct intervention in private equityprojects. This, however, does not mean that this role has totally disappeared: it has evolved

9 Interestingly, as noted by Lerner (2009): ‘the critical early investments have not been made by domestic institutions but ratherby sophisticated international investors’ (p. 12).

10 ‘Far too often, government officials have encouraged funding in industries or geographic regions where private interest simplydid not exist’ (Lerner, 2009, p. 13).

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towards the establishment of an appropriate legal and tax framework, as well as more complexintervention, mixing public contracts and the active management of public money. Lerner(2009) confirms that ‘policymakers face [today] the challenge of having to consider manydifferent policies. It is often unclear how proposed changes will interact with each other. Thereis no clear “instruction manual” that explains which changes will have the desired effects.’

1.1.2.2 The Transformation of Public Intervention: Setting up a Legaland Tax Framework

With progress in commerce, transportation and techniques, entrepreneurs could reach a highernumber of clients, as well as producing in quantity and more capital intensive goods. To followthis trend, and finance the investments needed, the entrepreneur often had to seek outsidefinancing, and thus set up a formal company, with agreements, contracts and partnerships withthird parties.

To enforce these conventions, a legal and tax framework has to be in place and respected.One of the most ancient examples of a legal framework is known as the Code of Hammurabi,King of Babylonia (1792–1750 BC, see Gompers & Lerner, 2006). This set of 285 laws wasdisplayed in public places to be seen by all, so that it could be known and thus enforced. ThisCode liberated the commercial potential of the Babylonian civilisation, notably paving theway for the creation of partnerships – and hence later of private equity partnerships. Untilthen, most companies were initiated and run by families. Financial support at that time oftencame from personal or family wealth, and/or from guilds that helped their members set uptheir venture after being admitted as a member.

With partnerships, Mesopotamian families could pool the necessary capital to fund a givenventure, spreading the risk. However, these ventures were not financed by equity investment.Capital infusion mostly took the form of loans, which were sometimes secured by the pledgeof a man’s entire estate, with his wife and children considered as being a part of it. If hedefaulted on payments, his family would be sold into slavery to pay his debts (Brown, 1995).Lending to support risky ventures with significant collaterals was still current practice asrecently as the 16th century, as described by Shakespeare in The Merchant of Venice (wherethe borrower-venturer puts a portion of his heart as a collateral to the lender).

In that respect, the Code of Hammurabi initiated the distinction between the entrepreneurand the financier, with the distinction between equity and debt, the creation of collateral forthe debt and the privileges attached to loans (such as priority of reimbursement in the case ofliquidation of the company).

1.1.2.3 The Transformation of Public Intervention: Infrastructure Financing

However, this legal and tax support may not have been sufficient for the emergence of privateequity. Besides law, other public actions are usually geared to helping entrepreneurs, directlyor indirectly, and create favourable conditions that nurture the creation of companies. However,as mentioned by Lerner (2009), ‘for each effective government intervention, there have beendozens, even hundreds, of failures, where substantial public expenditures bore no fruit’. As aresult, direct help, because of its cost to the public budget and the distortion in competitionthat it introduces, tends to be confined and to give way to a more indirect mode of intervention.This indirect mode of intervention had already been identified and used by Hammurabi, who,

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aside from being a military leader, invested in infrastructures in order to foster the prosperityof his empire.

During his reign, he personally supervised navigation and irrigation plans, stored grainagainst famine and lent money at no interest to stimulate commerce. Broad wealth distribu-tion and better education improved standards of living and stimulated extra momentum in allbranches of knowledge, including astronomy, medicine, mathematics, physics and philosophy(Durant, 1954). In that respect, the liberation of private energy and the symbiotic relationshipbetween public and private investments greatly rewarded the King for his action. This interac-tion with the private sector might be a test for modern programmes: if the public initiative doesnot act as a catalyst or indirect support, then the programme might simply not be relevant.

Indeed, public initiatives and private equity financing are still acting in an intricate way inmany respects, but the relations between these two spheres have evolved towards autonomy ofthe private equity sector and a ‘hands off’ approach in public intervention. As a result, publicintervention is creating the backdrop for private equity, paving the way for a more subtleinteraction, combining contracting, incentives and soft regulations.

1.2 CHAMPIONING ENTREPRENEURSHIP

However, this favourable legal and tax environment is useless if the social acceptance of riskand innovation is low. The figure of the entrepreneur, as the individual willing to take the initialrisk of creating and developing a venture, is therefore central in the private equity landscape.

Without him, private equity does not have any reason to exist (see section 1.2.1). However,private equity needs very specific entrepreneurs and companies to finance. The role of theentrepreneur is to support the creation of value (for example by converting product/serviceinnovation into business successes), and therefore generate a financial return (see section 1.2.2).Entrepreneurship acts as a transformer of disparate elements in a venture, making it blossomand become an attractive fruit. As ametaphor, private equity could be described as an ecosystemin itself (see section 1.2.3).

1.2.1 No Private Equity without Entrepreneurs

The figure of the entrepreneur is at the centre of the private equity universe. He is the one whocan transform inputs into something bigger than the sum of the elements taken separately,which are time, capital, work, ideas and other elements. What distinguishes the entrepreneurfrom other workers is his ability to innovate (at large), to take risks and to create and managea company. However, not all entrepreneurs are able to manage a company successfully.

What makes private equity attractive is the reasonable and proven prospect of getting asubstantially higher reward than on the financial markets (i.e., listed stocks or bonds, oftenthe result of privately negotiated transactions and not efficient and transparent markets). Thisreward is the counterpart of a risk that would not be borne by the rest of the financial system(banks, individuals and other sources of capital). Thus, private equity-backed entrepreneursare in fact a small portion of the pool of entrepreneurs that are active in any given country.

Company creation and disruptive innovation

The chief image of the entrepreneur is the ‘company creator’. This individual is guided by avision, often supported by an innovation. The emblematic entrepreneur financed by venture

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capital investors is building a company willing to capitalise on a ‘disruptive innovation’,which could radically change a market or create a new branch of a given industry. James Watt(1736–1819) is probably the incarnation of this category.

This Scottish mathematician and engineer improved the steam engine, set to replace waterand muscle power as the primary source of power in use in industry (Burstall, 1965). Althoughcreated in 1689 to pump water from mines, steam power existed for almost a century andseveral cycles of improvement before the steam engine made a breakthrough. In 1774, JamesWatt introduced his disruptive ‘Watt steam engine’ which could be used not just in miningbut in many industrial settings. Using the steam engine meant that a factory could be locatedanywhere, not just close to water. Offering a dramatic increase in fuel efficiency (75% lessconsumption), the newdesignwas retrofitted to almost all existing steam engines in the country.

Serial entrepreneurs: a cultural or universal phenomenon?

Another figure which has emerged over time is the ‘serial entrepreneur’, an emblematic figurein the US which has still to appear in Europe. This is probably related to the different culturalcontexts and the social fluidity on the two continents. Thomas Edison (1847–1931) inventedand developed many important devices such as the light bulb, the phonograph and the stockticker. He patented the first machine to produce motion pictures and planned the first electricitydistribution system to carry electricity to houses (Bunch & Hellemans, 2004). ‘The Wizard ofMenlo Park’ was one of the first inventors to apply the principles of mass production to theprocess of invention. One of the most prolific inventors, Edison held more than 1000 patentsat a certain stage.

In 1878, Edison convinced several investors such as John Pierpont Morgan, Lord Rothschildand William Vanderbilt to invest USD 300 000 in the creation of the Edison Electric Light(EEL) Co., and to fund his experiments with electric lighting in return for a share in the patentsderived from his research. JP Morgan continued to support the growing company by acquiringshares and backing the company’s merger with EEL’s main competitor, the Thomson-HoustonElectrical Company. This merger resulted in the creation of General Electric (Frederick Lewis,1949).

Gompers, Kovner, Lerner and Scharfstein (2010) state that there is a persistence of per-formance in entrepreneurship. An entrepreneur who has already been ‘successful’ (an IPOor a take-over of his company has happened) has a 30% chance of succeeding (21% for anemerging entrepreneur and 22% for an entrepreneur who tried and failed).

They hence develop specific skills, which are critical. This is important, because some ofthese entrepreneurs will retire once their success is fulfilled (which is a net loss for theeconomy), and others will become business angels (see Chapter 4) and will hence provideexperience and expertise to other entrepreneurs (some sort of ‘entrepreneurial spill-over’).

These repeat entrepreneurs have also developed a reputation, associated with success. Thatmight be crucial as suppliers, clients and recruits would then be willing to do business withthese successful entrepreneurs. Once again, this reputation might be ‘portable’ to start-upswhich are financially supported by a successful entrepreneur turned business angel.

Nursing ideas (laboratories) and nursing companies (incubators and EIR programmes)

Not every entrepreneur is able to come up with an idea ready to be produced. Inventors anddevelopers are sometimes hatched in a laboratory and can develop their ideas before spinning

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off, but most are developing new products and technologies in their garages or other morecasual places. To help them support their efforts, some funds have developed ‘incubators’ or‘entrepreneurs-in-residence programmes’. These programmes offered by venture capital fundsprovide facilities, support and money to entrepreneurs with interesting ideas. Once the ideahas matured, the investors can take an early lead on the development of the company and geta greater share in the company in exchange for past efforts.

One of the most famous ‘entrepreneurs in residence’ (EIR) was probably Leonardo daVinci (1452–1519). As well as being an inventor, he was also a sculptor, architect, engineer,philosopher, musician, poet and painter. These activities generated substantial investmentopportunities, either for mercantile or for patronage purposes. Da Vinci met ‘investors’ whoaspired to both, such as Ludovico Sforza, Duke of Milan, in 1482. Da Vinci wrote a letter tothe Duke in which he stated that he could build portable bridges; that he knew the techniquesof bombardment and the engineering of cannon; that he could build ships as well as armouredvehicles, catapults and other war machines. He served as principal engineer in the Duke’snumerous military enterprises and was also active as an architect (Encarta Encyclopaedia).He spent seventeen years in Milan, leaving after the Duke’s fall in 1499.

Under the Duke’s administration, Leonardo designed weapons, buildings and machinery.From 1485 to 1490, Leonardo produced studies on multiple subjects, including nature, flyingmachines, geometry, mechanics, municipal construction, canals and architecture (designingeverything from churches to fortresses). His studies from this period contain designs foradvanced weapons, including a tank and other war vehicles, various combat devices andsubmarines.

These examples are provided by way of illustration, to show the continuity with the figuresof entrepreneurship currently backed by venture capital throughout history. Da Vinci wasprobablymore interested by research than entrepreneurship, but the ‘entrepreneur in residence’model that is active in the SiliconValley today finds its roots in the Italian financial and politicalsupport of exceptional men who were able to make breakthrough discoveries.11

Interestingly, the model of entrepreneur in residence was developed in Europe throughoutthe Middle Ages and the Renaissance, but did not manage to survive after the EuropeanRevolutions.

The ‘incubator’ model (the most famous examples being Idealab, CMGI, Internet CapitalGroup and Softbank) failed. It re-emerged under the form of ‘business accelerators’ such as YCombinator and TechStars in the US. Somehow, these incubators or business accelerators tendto emerge as early signs of venture capital bubbles. The number of incubators grew from fifteenin 1999 to 350 in 2000 (Singer, 2000, The Economist, 2000), while business accelerators grewfrom four in 2007 to more than 100 in 2011 (Vascellaro, 2011) confirming this impression.The National Business Incubation Association12 declares 1900 members in more than sixtycountries (75% are in the US).

The main criticism addressed to incubators and business accelerators is that they fall intothe same trap as venture capital funds in the US (see Chapter 4 and the ‘broken’ Americanventure capital model): they do not work on major breakthroughs, instead aiming at ‘flavour ofthe month’ start-ups (Internet business-to-consumer start-ups in 2000, applications for mobile

11 Indeed, according to Johnson (2010), location contributes to the success of an entrepreneur: ‘the average resident of a metropoliswith a population of five million people was almost three times more creative than the average resident of a town of a hundredthousand.’ Big cities make their residents more innovative than residents of smaller ones.

12 www.nbia.org.

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phones in 2012) with a quick return. They spend little on the ventures, sprinkling money andmaking a lot of investments hoping for the best to come out of this pool.

It was only in the US that entrepreneurs in residence programmes managed to gain a hold.This is linked to the fact that most of these entrepreneurs in residence are serial entrepreneurs,which are still a rarity in the rest of the world.

The difficulty for the entrepreneur is to communicate his innovation, spread the word ofhis vision and thus convince his partners (employees, managers, financial backers, bankers,clients, providers . . .) that he is able to lead the company to the next stage and transform hisyoung venture into a business success.

1.2.2 Convert Ventures into Business Successes

Normally, there is innovation in companies financed by private equity, either in the product orin the service it delivers (innovation by destination); or else in the processes it has engineered(innovation by processing); in the way it contributes to structure its market (strategy innova-tion); or in the way it is managed (financial and management innovation). In order to be able todeliver a consistent and high level of returns, a private equity firm has to focus on value creationand develop specific expertise which is applied to a certain type of innovation (Guerrera &Politi, 2006). However, value creation is not only related to innovation. Value creation can begenerated in leveraged buy-outs by boosting companies through top line growth, operationalimprovements or some other area of company improvement. Innovation financing provides uswith a template illustrating the logic behind private equity.

Technological or managerial innovation: a basis for private equity

In the process of mastering space and time, entrepreneurs have discovered breakthroughtechnologies and invented newways of communication. The infant equivalent of private equitywas instrumental in financing the development and the deployment of these new technologies.An example of this public action helping to convert innovation into business success lies in thesupport provided to Galileo Galilei (1564–1642) by the Medici family, and especially Cosimode Medici.

Galileo’s achievements included demonstrating that the velocities of falling bodies are notproportional to their weight; showing that the path of a projectile is a parabola; buildingthe first astronomical telescope; coming up with the ideas behind Newton’s laws of motion;and confirming the Copernican theory of the solar system. Galileo translated his scientificknowledge into various technologies. In 1598, Galileo developed a ‘Geometric and MilitaryCompass’ suitable for use by gunners and surveyors. For gunners, it offered, in addition to anew and safer way of elevating cannons accurately, a way of computing quickly the charge ofgunpowder for cannonballs of different sizes and materials. In about 1606, Galileo designed athermometer, using the expansion and contraction of air in a bulb to move water in an attachedtube.

In 1609, Galileo capitalised on the invention of the telescope, a patent for which was deniedto a Flemish designer, Paolo Sarpi, a friend of Galileo, and lobbied the Venetian governmentagainst purchasing the instrument from foreigners, since Galileo could at the very least matchsuch an invention. By then, Galileo had improved upon the principle of the telescope. TheVenetian government subsequently doubled his earnings, even though Galileo felt that theoriginal conditions were not honoured (Kusukawa & MacLean, 2006).

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However, public intervention itself does not provide the support necessary to create anddevelop a company and follow it through every step of its life. This is where private equity’sintervention is fundamental. Galileo and da Vinci could have greatly benefited from theirinventions, if they could have created companies to exploit them. Columbus’s wealth wasbuilt on his project to go West, which was probably as risky and theoretical in its reach asthe discoveries and inventions of the two Italian geniuses. What distinguishes them fromColumbus is the fact that they were treated as civil servants, receiving a salary and someadditional resources for their work. Columbus’s travels were financed as to 50% by Genoeseinvestors willing to benefit from the new nautical route.

The necessity of entrepreneurial talent and enlightened financial support

Converting a disruptive innovation into a commercial success therefore requires not only anentrepreneurial talent, but also some additional competences and resources that only privateequity investors can provide. This is not only capital, but also an ability to help tailor a companyproject to a viable reach and ambitious goals. The expertise of the private equity investor isthus often used in the shadow of the entrepreneur himself. An illustration of this comes fromthe partnership between Matthew Boulton and James Watt. The innovations of Watt wouldhave never seen daylight without the ever-cheery Boulton, who funded the venture and took ashare of the patent rights, even if Watt almost gave up on the project several times.

The responsibilities were clearly distributed: Watt was the inventor and Boulton providedthe management experience and the capital. This is one of the first examples of a successfulventure by a duo combining entrepreneurship and innovation on one side, and finance andoperational management on the other. The separation of the entrepreneur and the investmentmanager is a key landmark in the emergence of the private equity sector as such and this is whatwas missing from Columbus’s project, to transform it into a complete commercial success.

The entrepreneurial and financial relationship: a fruitful tension

The impact of this separation is not theoretical: it changes the way an idea can be convertedinto a commercial success dramatically. Offering a very high increase in fuel efficiency forwhat was a minor design change, Watt’s new design for the steammachine was soon retrofittedto almost all of the steam engines in the country. Watt’s design used about 75% less fuel thanthe most established steam engine at that time: the Newcomen engine. Since the changes werefairly limited, Boulton andWatt licensed the idea to existing Newcomen engine owners, takinga share of the cost of fuel they saved.

Ten years after Boulton and Watt entered formally into partnership (and after Boultoninvested GBP 40 000, taking all the financial risks on his own), the venture began to producethe expected returns. In 1800, the two partners retired from business, now extremely wealthy,and handed it over to their sons, Matthew Robinson Boulton and James Watt junior. Thisconfiguration, even though illustrating the separation between investors and entrepreneurs,would be considered unusual now. First, because the investor did not cash out from thecompany but rather adopted a long-term approach and was willing to stay in the company aslong as possible (this approach is actually close to the approach of family offices, managingfortunes and businesses in an inter-generational perspective). This implies a perfect alignmentof interests between the entrepreneur and the investor, which may not be the case nowadays,as investors usually sell their stake in companies after three to five years. Closed end funds are

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usually created for 10 years, and they must manage to invest and divest from the companieswithin this timeframe (this will be developed and explained later in this book).

The fact that the company that Boulton and Watt created broke even after 10 years wouldnot disqualify the company from being financed by private equity investors. Investors wouldprobably sell their stake prior to that, either by listing the company (which is what happensfor biotechnology companies) or by selling it to competitors, who will be able to generateeconomies of scale and benefit from the growth prospects of the company. What is unusual,however, is that the entrepreneur and the investor managed to focus on this venture withoutmaking a living out of it for a long time. The rule of risk diversification and the necessityto generate returns early would not allow an investor to invest 100% of his time on a givenportfolio company, nor wait for such a long time before getting a return.

This is probably because Boulton was investing his own money and that private equityinvestors today invest as professionals (‘general partners’) the money they have collected fromthird parties (‘limited partners’). This is another source of possible misalignment of interests.The pressure from limited partners to generate stable and consistent returns above a certainthreshold stems from the fact that these limited partners have to deliver a certain return to theirshareholders (corporations), or to be able to cash in at least under a certain time constraint,with a given risk-return profile (banks, insurers).

This pressure is then transmitted along the investment value chain to the fund and itsmanagers. These managers have to deal with these constraints and thus exert pressure on themanagers of companies to deliver the expected returns within a given timeframe. This pressureshould, however, not be perceived as negative.

As seen with the historical examples, the fact that Columbus and Watt had some investorson their side also helped them to get results and stay focused on the outcome. The delicateequilibrium to be maintained between innovation and the strategy to go to market with thisinnovation is probably the key differentiator between aborted companies and successful butmeteoric successes on the one hand; and long-standing and growing companies on the other.

The investor must not only have genuine know-how and talent to support the entrepreneurs,but also challenge them and guide them towards the market. Even though big corporationshave financial and technical know-how, very few have the expertise to nurture innovation andbring it to the market. This means that private equity has its own specificities which are notonly difficult to replicate, but also to copycat outside of a given ecosystem.

1.2.3 Entrepreneurship and Private Equity Form a Specific Ecosystem

The separation of the roles of entrepreneurs and investors, associated with the emergenceof partnerships, has paved the way towards a better collaboration between the financial andthe entrepreneurial worlds. Not every partnership was built under the same conditions as thetemplate-like Watt-Boulton relationship. Most of the time, partnerships have to be establishedbetween entrepreneurs and investors who did not know each other prior to the contact leadingto a potential investment from the investor in the projected venture of the entrepreneur.

Entrepreneurial and financial frictions: the exit scenario

Aside from these conditions, the existence of exit strategies from a given investment is crucialfor professional investors. If an investor chooses to back an entrepreneur, he usually does itwith a certain roadmap in mind. Entrepreneurs can afford to spend all the time necessary to

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lead a venture to succeed, their own expectations and the money available being the only limit.This means that, theoretically, an entrepreneur with a company generating positive incomecould continue to run it for a very long time (possibly until his retirement).

Investors have a given timeframe to make an investment and get the return from it, as theiractivity is usually to generate profits and redistribute them. In that respect, the presence ofan active private equity sector is determined by the existence of exit scenarios, that is to sayopportunities to sell investments to third parties. These exit scenarios are usually:

∙ A listing on the stock exchange, offering to the private equity investor the opportunityto sell his stake on the market. This stock exchange must exist, offering certain liquidityand attractive listing conditions, including adapted regulations. This exit route remains anexception as the majority of exits are trade sales (36 exits for venture capitalists in Q3 2012in the US according to Demos, 2012).

∙ A profitable trade sale to another company or private equity group, offering the privateequity investor the opportunity to sell his stake to a third party. For some sectors, this exitscenario may prove to be difficult, given the concentration of the number of players (anti-trust regulations) or the nature of the sector (banks and insurers are sometimes barred fromtake-over by foreign players, and must comply with specific regulations preventing certainoperations). Trade sale is the main exit route in private equity (72% of exits for venturecapitalists in Q3 2012, according to Demos, 2012).

∙ A sale to the management, which is rare as this means that the management must structurea private equity operation with its own capital (otherwise, this operation would fall withinthe trade sale scenario). This, however, could happen in the event that a venture-backedcompany becomes profitable. As it is debt free, the management could try to structure amanagement buy-out (MBO) to acquire the stake of the investors in the company, if no otherexit scenario is offered.

∙ A sale to another financial investor, which is rather frequent in the case of secondaryleveraged buy-outs, and increasingly from venture capitalists to LBO investors (Demos,2012): 18 of such acquisitions alone happened in Q3 2012 in the US;

∙ End of activity, bankruptcy or sale of remaining assets. This exit is more common in venturecapital than in other segments of the private equity market. It is compensated by the factthat successes are also more rewarding in absolute terms.

The stock exchange: useful indicator, overbearing influence

One of the first historical examples of a professional exit from a private equity-like operation isthe introduction of the company created initially by Thomas Edison. In 1896, General Electricwas one of the original 12 companies listed on the newly-formedDow Jones Industrial Average,and is the only one remaining from that time today. This listing allowed its investors to exitfrom their investments and realise a profit. However, this exit route is an exception as most ofthe exits in private equity are trade sales with longer holding periods for companies.

The rise of private equity as a financial tool for funding companies has been enabled by thegrowth of the stock exchange. Private equity could find not only an exit path for financing onthe stock exchange, but also a source of opportunities such as corporate spin-offs, or delistingcompanies, and even taking parts of public companies.

As we will see (Chapter 4), the influence of the stock exchange can also be overwhelming.As it is a major source of information to establish the value of private companies, and as

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it is also an important (even if numerically minor) source of exits, private equity tends toadopt some of the behaviours specific to the stock exchange. This results in overvaluations,over-confidence, booms and busts as we will see later in this book.

Private equity has also influenced the way business is done. More specifically it contributedto create a true entrepreneurial ecosystem, with booms and busts, and a process of ‘creativedestruction’. This process bears a certain risk and it is the role of professional private equityinvestors to manage this risk, mitigate it and generate a return which is commensurate withthis risk. Chapter 2 will explore this question in more detail.

1.3 CONCLUSION: AN ATTEMPT AT DEFINITION

So far, Chapter 1 has identified the main elements which are necessary for the emergence of aprivate equity sector. In that respect, an investment in private equity could be defined as:

1.3.1 A Negotiated Investment in Equity or Quasi-Equity

Shareholders’ equity is the sum of the capital brought into the company by the shareholdersand the undistributed profit left in the company (retained profits). Investment in capital maytake the form of capital increases (venture capital, expansion capital), replacement (leveragedbuy-out) and even reconstitution (turn-around capital) of the company’s capital.

To address the increasing complexity of deal structuring and funding requirements, bettermaster the risks inherent in their investments and calibrate the anticipated returns, privateequity investors innovate constantly. The underlying trend is to negotiate counterparts for theirinvestments with company managers, such as:

1.3.1.1 Preferred Returns and/or an Increased Control over Decisions

The risk that is taken by professional investors, as compared to other shareholders, increaseswith the average amount invested in a given business. Professional investors have thereforeasked for preferential rights associated with their shares. These rights are negotiated in share-holders’ agreements and grant investors such rights as additional voting rights attached to theirshares, priority dividends and even preferential and guaranteed profit, to match a predefinedmultiple of their initial investment in the event that the business is sold.

1.3.1.2 Additional Cover for the Risks Entailed by the Investment

Furthermore, some investors prefer to reduce the relative risk of their investment, even if itmeans reducing their potential added value. This is how investment in quasi-equity emerged,with less risk than an investment in pure equity: bonds or debts repaid in fine, sometimesassociated with options to convert them into the company’s shares under certain conditions.

This particular kind of debt is riskier than ordinary debt, since it is subordinated to thepriority payment of other bank loans. The payment of subordinated debt depends thereforeon the complete success of the deal. This justifies a higher interest rate and the creditors’participation in the possible success of the business. The mezzanine debt, usually undertakenin leveraged buy-outs, illustrates this: it is a debt repaid after other debts, so-called ‘junior’ and‘senior’, or even ‘second lien’. This debt benefits from options to be converted into capital.

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Venture lending is the equivalent of mezzanine debt for venture capital and growth capitaldeals. It is quite common in the United States but still rare in Europe.

1.3.2 A Fixed Maximum Term

Irrespective of which type of instrument is used (listed or unlisted shares, mezzanine, etc.),a private equity investment is usually held for four to seven years. At the early stage of itsinvestment in a given business, the private equity investor must evaluate when and how it willliquidate this investment. As we shall see in Chapter 4, this is due to a contractual requirement:funds are created for 10 (and maximum 12) years.

1.3.3 Implying Specific Risks

These investments bear specific risks as they target businesses in special situations – such ascreation or restructuring, for example. This is the intrinsic risk of each of the segments ofthis asset class. Furthermore, they are subject to the cyclical nature of private equity as anemerging asset class, and to the general business cycles.

1.3.4 With High Expected Returns

As compensation for the risk borne by private equity investors, return expectations are higherthan those from comparable investments in listed securities. Private equity investments theo-retically offer a premium compared to listed securities returns. The long-term immobilisationimplied by private equity investment is a specific risk remunerated by an ‘illiquidity premium’.

1.3.5 Undertaken on Behalf of Qualified Investors

Given the lifetime of a private equity fund (usually 10 years), the risk borne by this type ofdeal, the relative illiquidity of investments, and the need to diversify investment among severalfunds to apply a sound investment policy, the great majority of limited partnerships (LPs)are subscribed by institutional investors, that is to say pension funds, insurance companies,banks or even endowments in the United States. According to the European Private Equityand Venture Capital Association (EVCA, 2012), in 2011 banks represented 15.3% of theEUR 39.7 billion (down from 8.1% of the EUR 79.8 billion in 2008) collected by privateequity funds in Europe, ranking after pension funds (18.7% down from 25.2%), funds offunds (14.4% down from 14.5%), sovereign wealth funds (10.5%) and governmental agencies(8.1%). Figure 1.1 shows the breakdown of private equity subscribers in Europe.

1.3.6 To Support Entrepreneurs

There is no private equity without entrepreneurs. As confirmed by Monitor Group13 (2010),entrepreneurship is first and foremost a local phenomenon. Accordingly, private equity ismostly a local activity.

13 http://www.compete.monitor.com/App_Themes/MRCCorpSite_v1/DownloadFiles/NED_report_final.pdf.

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Figure 1.1 Breakdown of investors in Europe in 2011 according to their nature (in % of amount)Source: EVCA, 2012.

Monitor Group notably states that public policies address with varying success the chal-lenge of supporting entrepreneurship. Actions range from cutting the administrative burden, tosetting up incubators or improving access to venture capital. Nevertheless, a few more topicsremain neglected, such as: promoting the entrepreneurial spirit (values, attitudes, motivation),developing skills, setting up a fully functional financing framework (seed investing and busi-ness angels, as well as initial public offering), as well as taxes. The impact varies strongly asshown by Figure 1.2.

Entrepreneurship is one of the most powerful supports for economic growth and prosperityin a global modern economy. Few factors have asmuch impact on the emergence of innovation,job creation and the contribution to a dynamic and competitive economy as entrepreneurship.The ‘creative destruction’ described by Joseph Schumpeter is fuelled by waves of innovationdriven by entrepreneurs.

Entrepreneurship is the creation and the management of new companies, often throughthe discovery of new opportunities or market needs on existing markets. Entrepreneurshipleading to fast growth, transforming whole economies and industries, is specific. It is based oninnovation, that is to say the successful commercialisation of products and services based onnew ideas. It is driven by individuals gifted with specific competences, characteristics andcapacities, as illustrated by Figure 1.3.

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Figure 1.3 Relation between policies (and their impact) and the Monitor entrepreneurial indexSource:Monitor Group (2010).

According to Monitor Group, for a given amount invested, the entrepreneur producesinnovations of better quality and with a higher efficiency than large companies as illustratedby Figures 1.4 and 1.5. Four models of entrepreneurship have been identified by the consultinggroup:

1. The ‘classical’ model, illustrated by Silicon Valley: in this high tech entrepreneurshipmodel, the intellectual property developed by university or governmental laboratories iscommercialised thanks to the help of venture capital investors. This system has worked forBoston and the Route 128 in the US, and Cambridge in the UK. In general, this model iseffective when connected to research of world-class level. The presence of a close financialcentre is necessary, as well as a culture of cooperation between the academic and theprofessional sectors (which is difficult to achieve). Due to the success of this model, manyinitiatives have been undertaken to replicate it, often without success (Lerner, 2009).

2. The ‘anchor firm’ model: ventures emerge from a company either through spin-offs orthe departure of experimented employees, who have identified a business opportunity anddecide to pursue it independently. The relationship between the new venture and the anchorfirm is more symbiotic than competitive, as the latter often acts as the first client (more than

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Figure 1.4 SMEs introducing product or process innovations (as % of SMEs)Source: TrendChart-ERAWATCH database, Pro-Inno Europe (2012).

a source of financing). This is why this model usually gives birth to a cluster of companies.More than creating companies against the former employer, entrepreneurs collaboratewith it. This applies to more traditional locations such as the north-west of Saudi Arabia,Vancouver (Canada) or the triangle of research in North Carolina (USA). This is the modelwhich is the easiest to replicate, notably in developed countries.

3. The ‘event driven’model: amajor industrial or economical event drives a significant numberof unemployed individuals to launch their own company or to leave the sector. Due to asudden influx of qualified people, the launch of new companies becomes possible, such asin the case of San Diego (USA) at the end of the ColdWar, Washington DC (USA) or SouthKorea after the crisis of 1997. Israel could also qualify under this model after its foundationand the arrival of a million individuals after the fall of the USSR.

4. The ‘local hero’ model: a local entrepreneur, who started from scratch, has succeeded andgained international exposure, hence creating vocations among other entrepreneurs. Thiswas the case for Medtronics (which invented the first personal pacemaker) andMinneapolis(USA), Microsoft in Washington (USA) and Wipro in Bangalore (India).

Figure 1.5 SMEs introducing marketing or organisation innovations (as % of SMEs)Source: TrendChart-ERAWATCH database, Pro-Inno Europe (2012).

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Figure 1.6 Simplified categorisation of financial assetsSource: CalSTRS, Author.

The models can be combined and are rarely identified as ‘pure models’. HP, Apple, Googleand Intel are anchor companies in the Silicon Valley.

Alternative investments are ‘characterized by expectations of enhanced return opportunities,diversification, and lower levels of liquidity’ (Mercer Management Consulting, 2012). Beingpart of the ‘alternative investments segment’ (see Figure 1.6), a private equity investmentis ‘a negotiated investment in equity or quasi-equity with a fixed maximum term, bearingspecific risks, and generating hopefully high returns on behalf of qualified investors to supportentrepreneurs’: this definition is an attempt to pin down a sector in constant evolution.According to Mercer Management Consulting (2012), private equity’s purpose is to ‘improvereturns relative to public equity markets [and] access new sources of alpha’ (i.e., performance).

Private equity hence differentiates itself from hedge funds (speculative funds using financialleverage targeting liquid assets and applying to them specific strategies, often using optionsand financial derivatives) and ‘exotic assets’ (sometimes called ‘alternative alternatives’, seeBlessing (2011)) such as timberland, commodities and real assets, collectables and asset-basedlending (see section 4.3).

This definition provides the opportunity to discuss some of the socio-economic conse-quences which have emerged with the rise of the private equity sector. For example, in theUnited States serial entrepreneurs appeared because of the fixedmaximum term of investmentsand high expected returns. Slowly, entrepreneurs have begun to specialise in certain roles suchas the creation, development, internationalisation, restructuring or turn-around of companies.This list is not exhaustive.

Chapter 2 will take a closer look at the structuring of the private equity sector, the emergenceof its key elements and its dynamics. This will be done through an analysis of recent history.

REFERENCES

Books and Booklets

Blessing, S. (2011) Alternative alternatives (John Wiley & Sons, Chichester, United Kingdom), p. 242.Brown, D. (1995)Mesopotamia: the Mighty Kings (Lost Civilizations) (Time-Life Books, New York, USA), p. 168.

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Bunch, B. and Hellemans, A. (2004) ‘Thomas Edison’ in History of Science and Technology (Houghton MifflinHarcourt, Boston, USA), p. 784.

Burstall, A. (1965) A History of Mechanical Engineering (The MIT Press, Cambridge, USA), p. 456.Durant, W. (1954) The Story of Civilization, Vol. 1 – Our Oriental Heritage (Simon & Schuster, New York, USA).Frederick Lewis, A. (1949) The Great Pierpont Morgan (Harper and Row, New York, USA), p. 306.Gompers, P. and Lerner, J. (2006) The Venture Capital Cycle (The MIT Press, Cambridge, USA, 2nd ed), p. 581.Johnson, S. (2010) Where good ideas come from, The Natural History of Innovation (Riverhead Books, New York,USA), p. 326.

Lerner, J. (2009) Boulevard of Broken Dreams, Why Public Efforts to Boost Entrepreneurship and Venture CapitalHave Failed – and What to Do about It (Princeton University Press, Princeton, USA), p. 229.

Kusukawa, S. and MacLean, I. (2006) Transmitting Knowledge: words, images, and instruments in early modernEurope (Oxford University Press, Oxford, United Kingdom), p. 274.

Mercer Management Consulting (2012) The Roles of Alternative Investments, p. 18.

Newsletters and Newspapers

Demos, T., ‘Venture Capital – Another Breeding ground for private equity’, Deal Journal, The Wall Street Journal,18 October 2012.

Guerrera, F. and Politi, J., ‘Flipping is a flop for investors’, Financial Times, 19 September 2006.Singer, T., ‘Inside an Internet Incubator’, Inc. Magazine, 1 July 2000.The Economist, ‘Hatching a new plan’, 10 August 2000.The Economist, ‘Filling the bank shaped hole’, 15 December 2012d.Vascellaro, J., ‘Some fear a glut in tech “incubators”’, The Wall Street Journal, 1 December 2011.

Papers and Studies

EVCA, Annual Survey of Pan-European Private Equity and Venture Capital Activity, EVCA Yearbook 2012,p. 348.

Gompers, P., Kovner, A., Lerner, J. and Scharfstein, D. (2010), Performance persistence in entrepreneurship, Journalof Financial Economics, No 96, pp. 18–32.

Monitor Group, Paths to Prosperity, 2010, p. 88.


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The Economics of Commodity MarketsJulien Chevallier & Florian Ielpo 978-1-119-96791-0 • Hardback • 360 pages • July 2013 Buy Now!


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1

Individual Dynamics: From Trendsto Risks

Starting with the asset-by-asset investigation of commodity returns, the salient features underour assessment will be first the nature and persistence of returns on commodities, moving nextto the analysis of higher order moments – that is volatility, asymmetry and extreme events.

One of the first attempts to try to bring together cross-asset conclusions regarding commodi-ties can be found in Kat and Oomen (2007a). Investigating between 22 and 29 commoditiesover the period 1965–2005 (when such data is available), they reach the following empiricalconclusions:

1. First of all – and consistent with the results of Erb and Campbell (2006) – individualcommodities do not provide investors with a risk premium on average. This conclusion hasto be differentiated from the basket of commodities case: Gorton and Rouwenhorst (2005a)show how such a risk premium is associated to a basket of equally-weighted commoditiesby using the Commodity Research Bureau dataset covering the 1959–2005 period andincluding 36 commodities.

2. The persistence in commodities is found to be important: a positive or a negative shockto commodity prices usually has long-lasting effects, unlike equities and bonds. This is anessential feature for trend-following investment strategies.

3. The volatility of commodities is not found to be excessive when compared to the volatilityof equities over the period under consideration.

4. They also find a limited asymmetry of returns in their dataset: the skewness of commodityreturns is usually found to be close to zero.

5. Finally, one of the key properties of commodities is the frequency at which extreme eventsoccur. Kurtosis being a natural way to measure such a tail event activity, they find excesskurtosis for most of the market under the scope of their investigation.

This list of empirical features seems, however, to be somewhat specific to the periodcovered by each dataset. More recently and by using various kinds of continuous time modelsencompassing time-varying volatility and jumps in the returns and volatility dynamics, Brooksand Prokopczuk (2011) studied in a more quantitative way the law of motion of commodities’returns. Their empirical findings show that jumps are an essential building block of theunderlying data-generating process of such markets. The frequency of appearance and the sizeof the jumps in returns are found to be very different from one market to another. Finally, thecorrelation between returns and their volatility is found to a have a sign that is specific to eachmarket: for example, a large negative return in the crude oil price should trigger a surge in itsvolatility that is larger than in the case of a similar but positive return. Such a pattern does nothold in the case of gold, silver and soybean, following Brooks and Prokopczuk (2011). Thisgoes against the fifth conclusion from Kat and Oomen (2007a; 2007b), but the period coveredby both studies is quite different.

138


4 The Economics of Commodity Markets

Two additional aspects should be mentioned here.

1. First, as for any financialmarket, commoditymarkets are affected by time-varying volatility.This stylized fact has been investigated in many research articles such as Serletis (1994),Ng and Pirrong (1996), Haigh and Holt (2002), Pindyck (2004), Sadorsky (2006), Alizadehet al. (2008) and Wang et al. (2008). Most of them use various specifications close tothe Generalized Autoregressive Conditional Heteroskedastic (GARCH) model initiallypresented in Engle (1982) and Bollerslev (1986). Bernard et al. (2008) present resultsregarding the aluminum market. Whereas these contributions were based on discrete timemodels, continuous time finance also focused on the addition of stochastic volatility to thebasic model by Schwartz (1997), as presented in Geman and Nguyen (2005) and Trolle andSchwartz (2009).

2. Second, the tail and jump issues that seem to be so important in the literature drovemany attempts to build models combining time-varying volatility, persistence through theconvenience yield and jumps. Deaton and Laroque (1992) found empirical evidence thatagricultural prices are agitated by jumps, while Duffie et al. (1995) also reported fat tailsfound in the dynamics of returns on commodities. Pindyck (2001) finds jumps both in thecommodity prices and in the inventory levels. This triggered numerous theoretical contri-butions based on the continuous time finance models proposed in Brennan and Schwartz(1985), Gibson and Schwartz (1990), Schwartz (1997) and Schwartz and Smith (2000).An application to agricultural markets can be found in Sorensen (2002), and to natural gasin Manoliu and Tompaidis (2002). Hilliard and Reis (1998) wrote one of the first articlesadding jumps to the model by Schwartz (1997). Deng (1999) brings jumps, mean-reversionand stochastic volatility together. Casassus and Collin-Dufresne (2005) also include explic-itly discontinuous jumps in their model. Liu and Tang (2011) relate the convenience yieldwith its volatility. Dempster et al. (2010) propose a continuous time model that encom-passes both short- and long-term jumps, highlighting how these aspects are important tothe pricing of options on commodity futures.

We now turn to the analysis of descriptive statistics computed over a set of 22 commoditiesand of four sub-indexes from theGoldman Sachs Commodity Index (GSCI) universe. Table 1.1presents the annualized returns over 1995–2012, as well as the volatilities, skewness, kurtosis,minimum and maximum returns, and the estimated autoregresssive parameters of an AR(1).We compare the results obtained for commodities to those obtained for other asset classessuch as equities, currencies and interest rates over the same period. The main conclusionsfrom Table 1.1 are:

– As explained in Kat and Oomen (2007a), the realized return and the volatility profile ofcommodities are very similar to what equities are capable of. The average return on thefour GSCI sub-indexes ranges from−1.8% for agriculture to 9.6% for precious metals. Thisis very similar to the range of −4.1% (Nikkei) to 16.6% (Bovespa) found in our equitysample. The returns on commodities have been positive over the 1995–2012 period for mostof the commodities, as well as for the sub-periods considered in the table. This is, however,not true for the agricultural products over the 1995–2003 period: during this period, thereturn on sugar was −10.4% for example. Positive returns have also been delivered by thevarious equity indices presented in the table, but for the Eurostoxx 50 case from 2003 to2012. There is an ongoing debate about the existence of a risk premium in commoditiesthat would be similar to what can be found in equities: for a large majority of them at least,

139


Table1.1

Descriptiv

estatisticson

commodity,stock,currenciesandrates

Ann.R

eturns

(%)

Volatility

(%)

Extremes

(%)

Total

1995–2003

2004–2012

Total

1995–2003

2004–2012

Skew

ness

Kurtosis

Min.

Max.

AR

Com

modities

Gold

0.089

−0.002

0.188

0.168

0.13

0.199

0.067

7.352

−0.072

0.102

−0.017

Silver

0.112

0.005

0.232

0.301

0.215

0.368

−1.119

10.509

−0.204

0.132

−0.022

Platinum

0.079

0.063

0.095

0.224

0.21

0.237

−0.379

5.498

−0.097

0.1

0.042*

Aluminum

0.002

−0.04

0.046

0.206

0.153

0.248

−0.325

2.753

−0.082

0.059

−0.026

Copper

0.061

−0.06

0.198

0.268

0.185

0.331

−0.213

4.536

−0.104

0.119

−0.044*

Nickel

0.04

0.005

0.077

0.363

0.285

0.428

−0.186

3.903

−0.181

0.131

0.009

Zinc

0.033

−0.041

0.114

0.288

0.176

0.367

−0.3

3.517

−0.121

0.091

−0.025

Lead

0.069

−0.037

0.186

0.312

0.187

0.4

−0.262

3.961

−0.128

0.127

0.055*

WTI

0.109

0.061

0.16

0.358

0.346

0.37

−0.094

4.475

−0.165

0.219

−0.008

Brent

0.122

0.054

0.196

0.341

0.334

0.347

−0.144

3.19

−0.144

0.129

−0.042*

Gasoil

0.117

0.051

0.188

0.32

0.318

0.322

−0.165

2.661

−0.157

0.112

0.004

NaturalGas

0.018

0.129

−0.082

0.548

0.566

0.529

0.388

5.717

−0.222

0.346

−0.016

Heatin

gOil

0.113

0.05

0.179

0.347

0.344

0.349

−0.246

2.335

−0.14

0.103

−0.031*

Corn

0.061

0.005

0.119

0.287

0.245

0.324

−0.71

15.701

−0.284

0.092

0.036*

Wheat

0.03

−0.007

0.067

0.314

0.256

0.362

0.21

2.269

−0.1

0.11

0.002

Coffee

0.004

−0.095

0.114

0.386

0.444

0.318

0.075

4.984

−0.15

0.212

−0.011

Sugar

0.018

−0.104

0.158

0.35

0.326

0.372

−0.236

3.549

−0.154

0.143

−0.002

Cocoa

0.032

0.03

0.034

0.311

0.298

0.324

−0.065

2.407

−0.1

0.107

−0.001

Cotton

0.001

−0.029

0.032

0.297

0.274

0.319

−1.362

26.364

−0.34

0.09

0.028

Soybean

0.059

0.006

0.114

0.249

0.208

0.284

−0.42

3.17

−0.099

0.065

−0.009

Rice

0.05

0.015

0.085

0.278

0.284

0.273

0.279

19.437

−0.219

0.255

0.047*

GSC

IAgri.

−0.018

−0.042

0.006

0.197

0.146

0.237

−0.119

2.696

−0.075

0.072

0.024

GSC

IEnergy

0.079

0.151

0.012

0.319

0.307

0.331

−0.223

2.197

−0.144

0.098

−0.019

GSC

IInd.

Metals

0.049

−0.031

0.136

0.226

0.147

0.284

−0.28

3.154

−0.09

0.076

−0.041*

GSC

IPrec.M

etals

0.096

0.016

0.183

0.178

0.13

0.216

−0.143

6.363

−0.082

0.088

0.013

Equities

Dow

Jones

0.074

0.109

0.04

0.191

0.186

0.196

−0.154

7.394

−0.082

0.105

−0.062*

S&P500

0.066

0.095

0.038

0.203

0.191

0.214

−0.233

7.578

−0.095

0.11

−0.07*

Nasdaq

0.085

0.108

0.062

0.27

0.304

0.232

−0.054

4.729

−0.102

0.133

−0.021

CanadianTSX

0.064

0.07

0.059

0.182

0.165

0.199

−0.704

8.949

−0.098

0.094

0.003

MexicoIPC

0.177

0.148

0.206

0.255

0.285

0.222

0.052

6.181

−0.143

0.122

0.092*

BrazilB

OVESP

A0.166

0.158

0.174

0.364

0.419

0.301

0.458

12.751

−0.172

0.288

0.03

EuroStoxx

0.033

0.084

−0.016

0.236

0.239

0.233

−0.052

4.553

−0.082

0.104

−0.009

FTSE

0.037

0.037

0.037

0.195

0.19

0.2

−0.155

5.69

−0.093

0.094

−0.022

CAC40

0.031

0.062

0.001

0.238

0.242

0.235

−0.016

4.422

−0.095

0.106

−0.013

(continued)

140


Table1.1

(Continued)

Ann.R

eturns

(%)

Volatility

(%)

Extremes

(%)

Total

1995–2003

2004–2012

Total

1995–2003

2004–2012

Skew

ness

Kurtosis

Min.

Max.

AR

DAX

0.07

0.064

0.077

0.248

0.266

0.229

−0.12

4.126

−0.089

0.108

−0.009

IBEX

0.048

0.097

0.001

0.237

0.237

0.238

−0.023

5.139

−0.096

0.135

0.022

MIB

−0.035

0.039

−0.105

0.251

0.239

0.262

−0.096

4.278

−0.086

0.109

0.005

AEX

0.029

0.069

−0.01

0.238

0.25

0.226

−0.132

5.594

−0.096

0.1

0OMX

0.078

0.09

0.066

0.252

0.262

0.242

0.083

3.33

−0.085

0.11

−0.009

SMI

0.05

0.085

0.016

0.199

0.209

0.188

−0.081

5.478

−0.081

0.108

0.033*

NIK

KEI

−0.041

−0.072

−0.009

0.246

0.241

0.252

−0.272

5.669

−0.121

0.132

−0.037*

HANGSE

NG

0.059

0.039

0.079

0.279

0.289

0.267

0.093

9.271

−0.147

0.172

0ASX

0.051

0.065

0.037

0.16

0.131

0.184

−0.484

6.115

−0.087

0.057

−0.029

Currencies

Euro

0.004

−0.009

0.016

0.099

0.096

0.102

0.128

1.822

−0.026

0.039

0.005

CanadianDollar

−0.02

−0.001

−0.038

0.084

0.056

0.105

−0.162

5.984

−0.058

0.028

0Japanese

Yen

−0.013

0.018

−0.043

0.111

0.117

0.105

−0.479

4.692

−0.063

0.034

−0.003

AustralianDollar

0.017

−0.021

0.056

0.127

0.101

0.148

−0.68

12.189

−0.087

0.069

−0.018

HongKongDollar

00.001

−0.001

0.005

0.003

0.006

−2.711

44.815

−0.006

0.003

−0.051*

SingaporeDollar

0.078

0.146

0.014

0.359

0.356

0.362

−0.889

12.402

−0.301

0.133

0.009

New

Zealand

Dollar

0.014

−0.012

0.041

0.129

0.104

0.15

−0.3

5.343

−0.063

0.065

0.018

BritishPo

und

0.002

0.001

0.003

0.09

0.077

0.101

−0.068

4.26

−0.035

0.052

0.014

SwissFranc

−0.021

0.007

−0.049

0.113

0.11

0.116

0.224

8.122

−0.054

0.091

−0.028

SwedishKrona

−0.006

0.014

−0.025

0.119

0.1

0.135

−0.242

3.583

−0.065

0.031

−0.023

NorwegianKrone

−0.01

0.012

−0.031

0.12

0.097

0.14

−0.234

11.1

−0.094

0.082

−0.025

Indian

Rupee

0.03

0.048

0.014

0.056

0.041

0.067

0.274

10.529

−0.03

0.034

0.061*

Vietnam

eseDong

0.037

0.037

0.038

0.04

0.041

0.039

9.875

228.613

−0.04

0.065

−0.117*

BrazilianReal

0.048

0.158

−0.049

0.158

0.149

0.166

0.671

18.853

−0.119

0.114

0.01

Mexican

Peso

0.057

0.098

0.019

0.143

0.169

0.11

−0.926

99.598

−0.207

0.137

−0.143*

PolishZloty

0.016

0.059

−0.026

0.133

0.096

0.162

0.159

5.154

−0.069

0.048

0.027

Rates

US2

−0.43

−0.663

−0.197

0.545

0.308

0.706

−0.025

10.397

−0.301

0.303

−0.078*

US5

−0.406

−0.506

−0.305

0.387

0.241

0.491

−0.163

7.377

−0.23

0.146

−0.055*

US10

−0.342

−0.389

−0.294

0.263

0.191

0.319

−0.224

6.533

−0.171

0.105

−0.025

US30

−0.275

−0.307

−0.244

0.195

0.142

0.237

−0.255

6.212

−0.114

0.08

−0.006

German

2−0.372

−0.468

−0.274

0.531

0.2

0.724

−0.577

31.917

−0.409

0.409

−0.025

German

5−0.389

−0.457

−0.32

0.32

0.181

0.414

−0.364

12.079

−0.197

0.164

0.031*

German

10−0.345

−0.398

−0.293

0.203

0.136

0.254

−0.072

8.856

−0.136

0.113

0.045*

German

30−0.325

−0.35

−0.299

0.161

0.117

0.196

0.015

4.995

−0.076

0.064

0.084*

141


Individual Dynamics: From Trends to Risks 7

we find a positive annualized return over the three types of periods considered here. Onthis debate, see Kat and Oomen (2007a), Gorton and Rouwenhorst (2005b) and Erb andCampbell (2006).1

– Commodities are supposed to exhibit a volatility that is larger than those of the usual equityindex. On this point, our figures agree with those fromKat and Oomen (2007a) – and despitethe inclusion of the 2008 crisis in our sample we do not find that commodities’ volatilityis higher than equities’. On average, annualized commodity volatility ranges around 30%.Three singular cases must, however, be distingished from the others: coffee (38.6% ofannualized volatility), sugar (35%) and heating oil (54.8%). Beyond these cases, the rest ofthe figures look very similar to stock indices for emerging or developed equities.

– The skewness figures presented in Table 1.1 should help the reader gain some intuitionabout the potential asymmetries in the distributions of returns on commodities. Two con-clusions arise from those figures. First, the sign of the skewness depends on the type ofcommodity considered: while in the case of gold (0.067) and wheat it is positive (0.21), theskewness associated with cotton is large and negative (−1.362). Equity indexes converselyare primarily affected by negative skewness, but for a couple of emerging markets such asBrazil and China. For example, the S&P 500 has a negative skewness over 1995–2012 thatis equal to −0.233. A similar case can be made out of the interest rate figures: the skewnessobtained from the variations of the 5-year rate is equal to −0.577. When considering theresults obtained from the foreign exchange rates, we obtain a picture that is very close towhat is obtained from the commodity dataset: the skewness can take various signs. Forexample the Australian Dollar vs. the US Dollar has a skewness equal to −0.479, whereasthe Euro vs. US Dollar has a skewness equal to 0.128. The US Dollar vs. the Polish Zlotyhas a skewness equal to 0.159, whereas the US Dollar vs. the Mexican Peso has a skewnessequal to −0.926. In this respect, the commodities – considered as an asset class – appearcloser to the currencies than to any other asset classes presented here. A second conclusionfrom this table is related to the scale of the skewness value: despite a few extreme values,the absolute value obtained from the commodities looks very similar to what is obtainedfrom any other asset class. In this respect, the asymmetry of commodities is very close interms of magnitude to the rest of the financial markets. The main difference here is that thesign of the asymmetry looks asset-specific.

– Turning to the kurtosis analysis, two conclusions again should be drawn from the table.First, when considering individual commodities, we find large kurtosis. This is in line withthe previously quoted articles such as Kat and Oomen (2007a) emphasizing that the maindifference between commodities and the rest of the asset classes lies in the extreme eventsfound in the variations of the prices of raw materials. Their kurtosis ranges between 2.269for coffee and 26.364 for cotton. On average each of these kurtose are higher than 3, thethreshold to be reached for the empirical distribution to depart from the thin tails obtainedfrom a Gaussian distribution. The magnitude of these kurtose is broadly speaking in linewith the figures obtained on the equity side, yet with a higher degree of heterogeneity. Inthis respect, it is again closer to the currency markets for which we obtain high variationsin kurtosis from one currency to the other. The magnitude of the kurtosis obtained with thebasket of currencies considered here is, however, much higher than the one obtained from

1 Finding a positive return for most of the commodities over the period considered here is not proof that commodity holdersreceive a risk premium for being long of such markets. Part II of this book will cast light on the possible macroeconomic fundamentalsexplaining positive or negative performances of such markets.

142



the commodity dataset. The second conclusion from the kurtosis computations is reachedwhen comparing the results obtained from individual commodities and from the basketsof GSCI indices: the kurtosis associated to the latter is, on average, lower than the onecomputed from part of its components. For example, the WTI has a kurtosis equal to 4.475whereas the GSCI Energy sub-index has a kurtosis equal to 2.197. A similar pattern isobtained from the GSCI Agricultural sub-index: its kurtosis is equal to 2.696 when cottonhas a kurtosis equal to 26.364, and rice a kurtosis equal to 19.437. This has to be related toone of the key stylized facts about commodities: the weak correlation between them, evenamongst a given commodity sector. We will discuss figures around this issue later.

– A last point must be mentioned when analyzing the basics of returns on commodities:following Kat and Oomen (2007a) and a very prolific literature that we will detail later,commodities are known to be affected by a high degree of persistence. In other words, com-modities are known to exhibit sharp trends that were one of the reasons for the developmentof the well known trend-following industry that tries to benefit from trends in financial mar-kets. A first way to gauge these persistent trends is to estimate a regression of the followingtype:

𝑟𝑟𝑖𝑖𝑡𝑡 = 𝜙𝜙0 + 𝜙𝜙1𝑟𝑟𝑖𝑖𝑡𝑡−1 + 𝜖𝜖𝑖𝑖𝑡𝑡 , (1.1)

where 𝑟𝑟𝑖𝑖𝑡𝑡 is the daily logarithmic return on the commodity 𝑖𝑖, 𝜖𝜖𝑖𝑖𝑡𝑡 is a random disturbancewith an expectation equal to 0 and standard deviation equal to 𝜎𝜎𝑖𝑖. 𝜙𝜙0 and 𝜙𝜙1 are real-valuedparameters that can be estimated by Ordinary Least Squares (OLS).2 The last column ofTable 1.1 presents such estimates along with an asterisk for each parameter significantlydifferent from zero. Out of the 22 estimates, only eight are different from zero. To observepersistent trends, we need to have 𝜙𝜙𝑖𝑖

1 positive: this is only the case for platinum, lead, cornand rice. These numbers are obtained by using daily returns that are thus less persistent thanweekly or monthly returns. Still, when comparing these results to those obtained in the caseof other assets, we have trouble finding sharply different conclusions. In the case of equity,we find two significant and positive parameters (Mexico IPC and SMI) and three negativeand statistically significant ones (Dow Jones, S&P 500 and Nikkei) out of the 18 indicesconsidered here. A similar picture is obtained in the currency case. The case of interestrates is a bit different: for these series, we have five out of eight series that yield significantestimates. From these preliminary estimates, we fail to find a picture as striking as the onepresented by Kat and Oomen (2007a): over the past 15 years, there is limited evidence of ahigher persistence in commodities than in other asset classes.

This preliminary analysis casts light on the key aspects we are going to focus on in thecoming pages: the nature and the number of trends in commodity markets, the origin of theasymmetry in returns on commodities and finally the jump activity in commodities. Theseseem to be the aspects for which our preliminary analysis pointed out differences betweencommodities and the usual asset classes. The next section deals with the complex relationshipsbetween returns on commodities and the term structure of futures. This question has been thecenter of much of the academic attention over the past 30 years. We revisit this problem, as itis one of the keys to forecasting returns on raw materials. We move then to an extensive trendanalysis in commodities, of the asymmetry in returns, and finally of the tail activity observedover the past 20 years.

2 We refer any reader interested in these time series models to Box et al. (2008).

143



1.1 BACKWARDATION, CONTANGO AND COMMODITYRISK PREMIUM

Beyond the themes that will be analyzed in the coming pages, a large part of the academicliterature has been devoted to the understanding of the existence of a slope in commodityfutures. Basically, futures are financial contracts that entitle the buyer (respectively the seller)to buy (sell) a given amount of a certain asset at a price that is set in advance for a givenmaturity. Unlike options, which allow holders to exercise or not the contract, futures involve acommitment to deliver or to buy the underlying asset. These futures contracts are actively usedby commodity traders – and their clients – either to hedge future flows or to speculate over thefuture stance of a given market. In the case of equities, this slope is solely driven by the risk-free rate through arbitrage arguments. The case of commodities is unclear: commodity futuresare bought both by producers and buyers of such products to hedge their natural exposureto market fluctuations. For example, when an oil-producing company wants to hedge – i.e.wipe out the risk in its balance sheet that is purely related to the fluctuation of oil prices: itsexposure – it can decide to sell futures six months in advance in order to know exactly atwhat price it will be able to sell its planned production in the future. On the other side of themarket, a company that needs to secure the price of its buying of raw products can decideto buy such futures. Depending on the balance of hedgers – buyers and sellers – the slopeof the term structure of futures would be upward or downward. When this slope is upward,market participants say that the market is in a contangoed position. Conversely, when the termstructure of future prices is downward sloping, the market is said to be in backwardation.

Although this problem is of little relevance for investing in commodities,3 it still mattersfrom a financial economics point of view. What is more, when the trading of commoditiesinvolves the actual delivery of the underlying asset, this term structure of commodities impliessome sort of a ‘risk premium’; that is, the fact that it is possible to buy, for example, a givenamount of raw product for a future price that will be below the actual spot price on the dayof the settlement of such futures. Several theories have tried to explain the existence of sucha slope. Keynes (1930) developed a theory of ‘normal backwardation’: in a world where risk-averse commodity-producing companies are the main market participants, their need to hedgeprice risk should drive future prices lower. By doing so, the future price of commodities shouldbe structurally lower than their spot prices, and such markets should be regularly backwarded.A side effect of this theory is that by buying futures and selling the spot asset, an investorwould be able to generate a profit: this potential profit is usually regarded as a ‘commodityrisk premium’. However, as shown in Table 1.2, such an average pattern simply does not exist:different commodities have different slopes, and through time a given commodity can either bebackwarded or contangoed. This table presents the results obtained when computing 𝑠𝑠(𝑡𝑡𝑡 𝑡𝑡 )𝑖𝑖the future curve’s slope for asset 𝑖𝑖:

𝑠𝑠(𝑡𝑡𝑡 𝑡𝑡 )𝑖𝑖 = 𝐹𝐹 (𝑡𝑡𝑡 𝑡𝑡 )𝑖𝑖

𝑆𝑆(𝑡𝑡)𝑖𝑖− 1𝑡 (1.2)

where 𝑆𝑆(𝑡𝑡)𝑖𝑖 is the spot price at time 𝑡𝑡 for commodity 𝑖𝑖 and 𝐹𝐹 (𝑡𝑡𝑡 𝑡𝑡 )𝑖𝑖 the corresponding futurewith a residual maturity equal to 𝑡𝑡 − 𝑡𝑡. We use three different generic futures contracts,

3 When a private or an institutional investor wishes to have an exposure to the commodity universe through futures, this regularlyrequires rolling the position from a future with a maturity that turned out to be short to a longer dated future. As pointed out in Gortonand Rouwenhorst (2005a), this rolling procedure of futures has, by construction, no impact on the performance of an investment incommodities provided that the net amount of this investment remains unchanged.

144



Table 1.2 Average difference between the 3, 6 and 9 month futures and the spot price of commoditiesexpressed as percentages of the spot price

All sample 1995–2003 2003–2012

3M 6M 9M 3M 6M 9M 3M 6M 9Mslope slope slope slope slope slope slope slope slope

Aluminum 0.37* 0.66* 0.84* 0.32* 0.58* 0.68* 0.41* 0.74* 1*Brent −0.08* −0.23* −0.44* −0.67* −1.36* −2.03* 0.52* 0.89* 1.15*Cocoa 1.2* 2.27* 3.28* 1.56* 2.95* 4.37* 0.84* 1.58* 2.2*Coffee 1.5* 2.97* 4.36* 0.68* 1.65* 2.69* 2.31* 4.3* 6.04*Copper −0.09* −0.21* −0.36* 0 −0.09* −0.19* −0.18* −0.33* −0.53*Corn 2.32* 4* 5.16* 1.8* 3.39* 4.59* 2.84* 4.61* 5.73*Cotton 1.82* 3.19* 5.14* 1.98* 3.42* 4.57* 1.67* 2.95* 5.7*Gasoil 0.05* 0.11* 0.18* −0.18* −0.33* −0.47* 0.28* 0.55* 0.82*Gold 0.25* 0.24* 0.42* 0.29* 0.7* 0.65* 0.2* −0.22 0.19*Heating Oil 0.19* 0.29* 0.33* −0.24* −0.42* −0.61* 0.61* 1.01* 1.27*Natural Gas 1.93* 3.32* 4.37* 0.56* 0.79* 0.96* 3.29* 5.85* 7.78*Nickel −0.12* −0.29* −0.61* −0.08* −0.17* −0.5* −0.16* −0.4* −0.72*Rice 2.05* 3.8* 5.23* 2.34* 4.55* 6.45* 1.77* 3.05* 4.01*Silver 0.26* −0.05 1.1* 0.32* 0.66* 1.21* 0.2* −0.76* 1*Soybean 0.2* 0.09 −0.16 0.11* 1.00E-02 −0.1 0.29* 0.17* −0.22Sugar −0.21* −0.67* −0.95* −1.49* −2.54* −2.89* 1.06* 1.2* 1*Wheat 2.62* 4.14* 5.36* 2.14* 3.5* 4.67* 3.1* 4.77* 6.04*WTI −0.06 −0.22* −0.42* −0.83* −1.6* −2.31* 0.71* 1.17* 1.47*

Note: An asterisk indicates that the average is statistically different from zeros at a 5% risk level.

ranging from 3 to 9 months by periods of three months. This provides us with a dataset ofslopes expressed in terms of percentage increases over the spot price for three maturities:3, 6 and 9 months. By doing so, we can bring some statistics not only around the 3 monthslope as is generally the case, but also check whether the sign of the slope is consistentacross maturities.

This table confirms previous results: commodities are both affected by backwardation andcontango. For example, aluminum exhibits on average an upward sloping future curve: every3 months of maturity increase leads on average to a future price higher by 0.3% over the periodconsidered here (1995–2012). Conversely, Brent is typically a commodity for which the futureslope is negative: 3 months of additional maturity lead to a future price lower by 0.1 to 0.2%.Out of the 18 commodities reported here, only 5 of them have been backwarded on averageover the period. Consistent with that, Kolb (1992) investigated 29 commodity futures, findingthat there is no ‘normal backwardation’. Bodie and Rosansky (1980) ended up with a similarconclusion. What is more, over the full period, the sign of the slope is consistent across thethree selected maturities. One of the only exceptions is silver over the 2003–2012 period: its6-month slope is significantly negative (−0.76%) whereas its 9-month slope is significantlypositive (1%). Finally, the sign of the futures slope can change depending on the period: forexample, heating oil has a positive slope over the 1995–2003 period, and a negative one overthe subsequent period. This holds across all maturities of the futures on heating oil consideredhere. A similar case can be made with sugar.

A natural way out of this conundrum is to assume that commodity producers are not theonly hedgers intervening in such markets. Cootner (1960) and Deaves and Krinsky (1995)

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have formulated the ‘hedging pressure hypothesis’: depending on whether hedgers are netlong or net short, this slope of the term structure can either be negative or positive. Forexample, Bessembinder (1992) found that over the 1967–1989 period, the return on futureswas influenced by the net position of hedgers. With this theory, there is a commodity riskpremium, and its sign depends on the net hedging pressures: when producers are dominant,the risk premium is positive, as buying futures and selling the spot asset should deliver apositive return to the holder. Conversely, when commodity consumers are the main hedgers,the risk premium should be negative overall. The evidence presented in Table 1.2 is somewhatmore consistent with the conclusions of this theory, as it makes it possible to have both upwardand backward sloping futures curves.

Finally, a third theory attempts to explain the existence of such a slope. The ‘theory ofstorage’ links the level and cost of commodity inventories to the shape of the futures curve.We owe this theory to Kaldor (1939) and Brennan (1991): it tries to explain why inventoriesare observed in periods of downward-sloping futures curves, as such a pattern implies a futurespot price that should be lower than the current level and therefore a lower nominal value of theinventories held. Holding inventories helps in handling the varying demand: disruptions on theproduction chain would have a limited impact on the ability to meet the global demand. Thisstock buffer improves somewhat the comfort of the commodity producer, hence generatinga ‘convenience yield’. However, by doing so, the producer has now to face a market risk,linked to the fluctuations of the market price of its commodity. Such a risk is higher whenstorage is low: for such a case, the convenience yield should be very important and the termstructure of futures downward sloping so as to provide the inventories holder with a positiverisk premium. Conversely, when inventories are high and the convenience yield is thereforelow, the term structure of futures should be upward sloping, merely reflecting the interest ratespaid when borrowing cash to build the storage space and the actual cost of storage. Gortonet al. (2012) provide an empirical assessment of the impact of inventories over 31 commodityfutures curves: as they point out, accessing such a dataset is difficult, especially over extendedperiods such as theirs.4 They conclude that inventories have a strong explanatory power overthe ‘basis’ of many commodities; that is, the difference between the first future and the spotprice of each commodity. Inventories seem to robustly predict the sign and magnitude ofrisk premium in commodities, whereas the net position of traders – that measures where thehedging pressure is – has limited – if any – explanatory power. This long-standing debate is,however, still in discussion: here, the length and depth of datasets matters.

Beyond the potential explanations of such a phenomenon, there is one interesting questionto be raised and answered here: a large part of the literature expects that the risk premiumearned from holding commodities can be explained by the slope of these futures curves. Let𝑟𝑟𝑖𝑖(𝑡𝑡𝑡𝑡𝑡+ℎ) be the return realized over the 𝑡𝑡 to 𝑡𝑡 + ℎ period by holding asset 𝑖𝑖. Table 1.3 displaysthe following correlations:

cor(𝑟𝑟𝑖𝑖(𝑡𝑡𝑡𝑡𝑡+ℎ)𝑡 𝑠𝑠(𝑡𝑡𝑡 𝑡𝑡 )𝑖𝑖). (1.3)

In the case of Table 1.3, ℎ is equal to 3 months.5 When there should be a relation between theterm structure of futures and the expected returns on a given commodity, this relation should

4 They study commodity risk premium over the 1969–2006 period, therefore limiting the impact of shorter datasets on theestimation results.

5 The results presented here are, however, weakly dependent over the choice of this period. With this 3-month period, we simplyput a larger emphasis on the stylized fact we are trying to measure.

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Table 1.3 Correlation between rolling 6-month returns and the 3 to 9 monthslopes

3M slope 6M slope 9M slope

Aluminum 0 −0.03 −0.01Brent 0.04* 0.05* 0.05*Cocoa 0.03* 0 −0.01Coffee 0.09* 0.1* 0.09*Copper 0.05* 0.05* 0.05*Corn 0.32* 0.28* 0.18*Cotton 0.23* 0.27* 0.76*Gasoil 0.12* 0.13* 0.14*Gold −0.18* 0.04* 0.03*Heating Oil 0.14* 0.16* 0.19*Natural Gas 0.28* 0.38* 0.4*Nickel 0.06* 0.05* 0.02Rice 0.45* 0.42* 0.36*Silver −0.02 0.01 0.23*Soybean 0.34* 0.38* 0.36*Sugar 0.29* 0.44* 0.36*Wheat 0.14* 0.12* 0.09*WTI 0.1* 0.09* 0.09*

be negative: a negative slope implies a positive return on average obtained from buying thefuture and selling the spot asset. From Table 1.3, we get the impression that this correlation is,however, more positive than negative. We obtain a negative correlation only in four cases, andonly one of them is significantly different from zero. For the rest of the cases, this correlation issignificantly positive, implying that a positive slope forecasts a positive return on commodities.What is more, the scale of this correlation ranges between 0 and 0.2 for most of the cases,which is rather low for a correlation. There are, however, four commodities for which thiscorrelation is higher: corn, cotton, soybean and sugar. Beyond them, the correlation remainsweak but significant. Hence, the commodity risk premium is poorly explained by the termstructure of futures, and the sign of the relationship goes against the theory that the riskpremium is negatively correlated to the slope of futures.

Cochrane and Piazzesi (2005) found that the term structure of futures has a forecasting powerover the realized future variation of the underlying interest rates. By regressing those realizedvariations over a basket of futures with various time to maturities, they found ‘tent-shaped’coefficients across futures’maturities. Combining these futures through these coefficients, theyobtained a new factor that explains one third of one-year ahead excess returns. Their findinghas been confirmed in Kessler and Scherer (2009) and Sekkel (2011) for non-US markets.One way to reconcile the relationship between the slope of the term structure of futures andthe realized performance of the spot asset is to run a regression similar to Cochrane andPiazzesi (2005). Within this approach, the slope is assumed to contain elements that forecastfuture returns. The slope would therefore be driven in part by financial market participants’expectations. By using previous notation, we run the following regression:

𝑟𝑟𝑖𝑖(𝑡𝑡𝑡𝑡𝑡+ℎ) = 𝛼𝛼𝑖𝑖0 +3∑

𝑗𝑗=1𝛽𝛽𝑖𝑖𝑗𝑗𝑠𝑠(𝑡𝑡𝑡 𝑡𝑡𝑗𝑗)

𝑖𝑖 + 𝜖𝜖(𝑡𝑡)𝑖𝑖𝑡 (1.4)

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with 𝜖𝜖(𝑡𝑡)𝑖𝑖 being a centered disturbance with volatility 𝜎𝜎𝜖𝜖 and 𝑇𝑇𝑗𝑗 for 𝑗𝑗 = 1, 2, 3 being thevarious maturities for the slopes considered here. Here, we consider various ℎ, from 1 week to6 months. Given the overlapping nature of our sample, the asymptotic volatility for the OLSestimates of the previous regression has to be modified. Following Cochrane and Piazzesi(2005), we rely on a Newey–West approach to the robust estimation of those volatilities.Results are presented in Table 1.4 along with R2. Figures 1.1, 1.2, 1.3 and 1.4 chart the 𝛽𝛽𝑗𝑗across futures maturities obtained with the 3-month returns, when both the realized returnson the spot asset and the slopes of the future curve have been scaled to make the parameterscomparable across commodities. Our results confirm that of Cochrane and Piazzesi (2005)in terms of interest rate futures: in the case of agriculture and energy, we find tent-shaped 𝛽𝛽𝑖𝑖𝑗𝑗across maturities.6 Most of the estimated parameters are found to be significantly differentfrom zero at a 5% risk level. In the 3-month case, those regressions come with an R2 that isgreater than 0.1 for 6 of the 18 cases considered here, confirming that the slope of the futurescurve contains information that can explain the commodity risk premium. From these results,it appears that the relation between the commodity risk premium is more complicated than theprevious theories predicted. Interestingly, despite the non-financial aspect of such assets, westill find properties that are consistent with what is usually found for the standard assets. Bycomparing the results obtained for various ℎ, we cast light on the dependency of our resultsupon the period over which the returns are computed. From the analysis of Table 1.4, whenincreasing the period over which the returns are computed, we obtain a growing explanatorypower of this simple regression. For example, in the case of cotton, the 𝑅𝑅2 associated withthis regression is equal to 0.06 in the 1 week returns case, and to 0.663 in the 6-month case.Hence, following these regressions, the slope of the term structure of commodity futures canincorporate information that helps predict the commodity risk premium. Figures 1.1, 1.2, 1.3and 1.4 clearly display tent-shaped parameters across maturities. The forecasting power ofthis regression does not seem to be as important as the one obtained in the bond market case.However, for some of the markets investigated here, we obtain an 𝑅𝑅2 that can reach 0.6, as inthe case of cotton. However, the variability of this 𝑅𝑅2 is higher than in the bond case. Suchresults tend to show that the term structure of futures is a variable of interest to investors, as itexpresses at least partly participants’ expectations – as for other purely financial assets.

1.2 UNDERSTANDING COMMODITIES’ MOMENTA

This section will focus on the measurement of trends in commodities. Trends are one of thebackbones of the quantitative fund management industry: ‘trend followers’ are funds whosemain strategy is to invest in assets with positive trends. These trend-following strategiesall started under the label of Commodity Trading Advisors (CTAs), investing primarily incommodities. The name has remained, but the scope of investment possibilities has increased,extending to futures and options written on any type of asset. Still, commodities may have beenthe birthplace of the trend-following industry.When reading themain conclusions appearing inKat and Oomen (2007a; 2007b) regarding the persistence of trends, the consistency betweenthese trend-following methods and the persistence found in commodities definitely makessense. The objective of this section is to assess the nature of these trends in commoditiesthrough their measurement.

6 Unlike Cochrane and Piazzesi (2005) who use forward rates from 2 to 10 years, here we can only rely on the most liquidshort-term contracts.

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