1 RAROC, Credit and Corporate Growth David C. Shimko Harvard University and Risk Capital Mgmt, Inc. Risk Management Workshop Hebrew University November.

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RAROC, Cre

dit and

Corpora

te G

rowth

David C. Shimko

Harvard University and

Risk Capital Mgmt, Inc.

Risk Management Workshop

Hebrew University

November 10, 1999

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OUTLINE OF SEMINARS

• Part I– Theoretical foundations of RAROC as a determinant of discount

rates

• Part II– Application of VAR and RAROC to nonfinancial firms

• BREAK (required by Geneva Convention Rules)

• Part III– Paradoxes in counterparty credit risk management

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CAPM Approach Simplified

• Everyone prefers to avoid risk.• When risk reduction costs nothing, as in the case of

diversification, people diversify as much as possible.• Some risks, called systematic risks, can never be diversified,

because they affect such a large number of investments.• Whenever a risk cannot be diversified, investors must be paid a

price to bear the risk.• Consequently, any diversifiable risk has no price in the CAPM

– Capital markets are competitive (an assumption)

– Capital is never scarce at the right price (an assumption)

– Any temporary risk premium for diversifiable risk is eliminated by competition among investors

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Components of the CAPM return

• ri = rf+ i(rm - rf) + 0

Expected returnon any asset i

Risk-freereturn

Scaled covariancebetween asset riskand systematic risk

Market riskpremium

Diversifiable risk premium

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Generalizations to the basic CAPM

• Most empirical tests reject the basic form of the CAPM• Robert Merton (Nobel prize winner with Fischer Black)

developed the intertemporal CAPM in 1973– This model allows for nondiversifiable changes in investment

opportunities

– This creates a larger set of nondiversifiable risks

– Each of these risks earns its own risk premium

– There is still no compensation for diversifiable risk

• Steve Ross (future Nobel prize winner) developed the Arbitrage Pricing Theory (APT) in 1976– The APT does not explain the source of risk premia

– But the APT (in portfolio form) does rely on asset diversification and a zero risk premium for diversifiable risk

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Conclusion for CAPM and related models

• None of these models allows a risk premium for diversifiable risk• The financial models as a class differ from insurance models of

risk pricing– Select any introductory insurance textbook (e.g. Goovaerts et al)

– Typical expression of the pricing of risk for an insurance company• (on a single policy)

– ri = + k

Required reserveon a liability

Expected loss

Capital availabilityfactor

Volatility of loss

Scaled by diversifiabilityScaled by size of portfolioScaled by concentration

Are the insurance models completely wrong?

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What is risk capital, and how is it measured?

• CONCEPTS & DEFINITIONS:– Risk capital is the amount of money one is prepared to lose on a

trade, portfolio, or strategy

– Often termed value-at-risk (VAR)

– VAR is a better measure of capital than capital itself

– RAROC (risk-adjusted return on capital) is simply return on risk capital, or return on VAR

• Definition: RAROC = P&L/VAR

• COMPARISON TO THE SHARPE RATIO:– RAROC is similar to the Sharpe Ratio (invented by William Sharpe)

– RAROC can be applied more broadly than the Sharpe Ratio

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What’s a good RAROC?

95% confidence interval 99% confidence interval

SharpeRatio

1-day 30-day 1-yr 1-day 30-day 1-yr

S=0.60 2% 9% 31% 1% 7% 26%

S=1.00 3% 15% 51% 2% 12% 43%

S=2.00 5% 29% 102% 4% 25% 86%

RAROCS*

Historical performance of S&P 500

Typical hedge-fund ex-ante investment criterion

*RAROC = Sharpe x (t)/z t = VAR period in years z = # std devs in VAR

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Components of the RAROC return

• ri = rb + k

Return onany asset

Return on benchmark

Capital scarcityfactor (RAROC)

Marginal riskof asset relative tobenchmark

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Can RAROC be reconciled with the CAPM?

• Loosen one of the CAPM assumptions• What if capital is somehow constrained in a market?

– Legal constraints such as bank regulations

– Psychological constraints such as fears of emerging market investments or commodities

– Asymmetric information constraints• Corporations cannot fully/credibly communicate investment prospects• Investors restrict capital they will invest

• When capital is constrained…– The unconstrained investors are relatively over-exposed to the

constrained asset

– They demand a risk premium because of their concentrated, undiversified positions

– Competitive forces fail to eliminate the risk premium

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How is the RAROC risk premium determined?

• Assume investors will invest in a passive benchmark– (This is a recursive process; the benchmark investors may also

earn a premium for diversifiable risk)

• Also assume that capital available to take nonbenchmark risks is further constrained

• Then investors will diversify nonbenchmark risks to the degree possible…– But they will not be able to diversify fully

– Hence they demand a risk premium for these risks

– Competition cannot eliminate this risk premium

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Implications for corporate investment

• Every project has benchmark and non-benchmark risks– Determine scaled benchmark return

• Is RAROC appropriate?– Compare firm’s investment opportunities to its asset base

– Examine competitor financial strength

– Assess market’s appetite for risks associated with the project

– Identify external investment constraints, legal, psychic or structural

• If yes– Determine appropriate RAROC

– Assess volatility due to non-diversifiable non-benchmark risks

• If no– Use CAPM-style approach

• But please note– The CAPM is a special case (or limiting case) of the RAROC

approach

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Introduction

• What is “enterprise-wide risk management”?– A computer system that tracks and measures business risks for

management reporting

– A conceptual framework for risk-based decision-making across the firm

• Some large users of EWRM– Bankers Trust

– Enron

– Microsoft

• Different applications, common goals– A price for risk

– A way to trade off one risk against another

– Comparisons between different risk-mitigation alternatives

– Achieving the proper balance between risk and return

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An example of risk-based decision-making

• The basic NPV rule (accept all trades with positive NPV) often leads to underperformance– Positive NPV is neither necessary nor sufficient condition for the

acceptance of a project or activity

– Scarce resources must be properly deployed• People• Market Coverage• Risk capital

Use of resource

Cum

ulat

ive

pro

fita

bili

ty

Is the firm using risk capital

INEFFICIENTLY?orEFFICIENTLY?

Maximum NPV

Max resource

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Optimizing with scarce resources: A mathematical view

• Problem: Maximize expected NPV over time (Objective)– Subject to a constraint on resource use (Resource use

Available)

• Equivalent to– Maximize [Objective minus Multiplier x (Unused resource level)]

• s.t. Multiplier x Unused resource = 0

– Interpretation of the (LaGrange) multiplier• Value of relaxing the constraint• “Shadow price” of the scarce resource

• Interpretation in management– Multiplier = Optimal transfer price

• Apply NPV rule with transfer price• Noncash charge to projects• Insures projects are adopted optimally

– Does it matter if your scarce asset is labor or risk capital?

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Opening Pandora’s box

• What is the right RAROC for a nonfinancial firm?• Does this change the way we look at capital?• Can RAROC ever have an effect on shareholder value?

• A CASE STUDY IN ENERGY

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Determining the right RAROC for a firm

• Constructive approach– Closed form is hopeless

– Simulate different acceptance rules

– Requires knowledge of stochastic and dynamic opportunity set of investments available to the firm over time

• Comparison to peers– Pure plays (in and outside the industry)

– Integrated energy firms

• An internal “risk capital market”– Business units trade risk capital with each other

– RAROC is the clearing price

• We chose the “comparison to peers” approach

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A sample of 1998 energy peer RAROCs

Company

Annualized 99% VaR

Trading Gains ($MM)

RAROCEnron 93%Duke 53%Williams 75%Reliant 53%Utilicorp/Aquila 55%KN Energy 92%DTE Energy 22%Sempra -19%PG&E -4%

1998 RAROC

÷

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Risk-Return Relationship

Relationship Between Risk and Trading Gains in 1998

$0

0

Annual Value at Risk, 99% Conf ($MM)

An

nu

al T

rad

ing

Gai

ns

($M

M)

Enron

DukeWilliams

ReliantAquilla

KN Energy

DTE

SempraPG&E

Increasing RAROC

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Separating capital and risk capital charges: Example

OLD WAY OF THINKING NEW WAY OF THINKING

$100 in S&P $100 in S&P

Expected return on S&P = 12%

Expected return on T-bills = 6%

“Worst case” loss (1 yr) = 25%

$100 risk-free cash investment (6%)

$25 risk capital (24% RAROC)

Expected cash return = $12 Expected cash return = $12

$6 $6

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Real Example: How Enron evaluates a tolling deal

Frequency Chart

Certainty is 79.16% from 0 to +Infinity

.000

.006

.013

.019

.025

0

31.25

62.5

93.75

125

-150,000 0 150,000 300,000 450,000

5,000 Trials 63 Outliers

Forecast: NPV @ 10.6%

Expected NPV $105,000“Worst case” loss $90,000

Cash $380,000 IRR 16.5%

RAROC 52.3%Risk Capital $90,000

INVESTMENT YIELDNot bad

Yowza!

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How can RAROC lead Enron to better decisions?

• Pricing strategy– RAROC criterion provides more pricing flexibility in a competitive

market (in this case)

• Hedging strategy– Under a RAROC criterion,

• hedges may sacrifice NPV...• but increase returns by reducing dependence on risk capital

– Under traditional capital budgeting, hedges are never worthwhile unless they have positive NPV

– Traders will be rewarded for putting on efficient futures hedges and offsetting OTC deals --- this increases RAROC

• Comparables– With a RAROC criterion, the tolling deal can be compared on equal

footing to any trade or asset deal

– Example: How would the the tolling deal have compared with purchasing a gas-fired power plant?

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RAROC answers the question: “Should I hedge?”

Value-at-risk (all sources)

Exp

ecte

d P

rofi

tabi

lity

Unhedged deal

Hedge market risk

Hedge credit risk

Insure all risks

NPV RuleRAROC Rule

0

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Prepay deal

• Typical industry view: “No hedge, no deal”• Prepay valued as debt substitution• May crowd out balance sheet to the extent ratings agencies

impute operational risk• Otherwise, no additional capital costs required

• How could RAROC help on a prepay?– Deciding whether to hedge and how to hedge

• Prepays may be a more efficient means to obtain long-term exposures

– Deciding when to purchase others’ prepay contracts• Integrating credit and market risk• Major competitive advantage: Linking financing to sellers

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Main reasons banks and energy firms use RAROC

• Proper RAROC analysis prevents wasting risk capital on low-value (but positive NPV) deals

• VAR is the best (sometimes only) way to measure capital• RAROC can be applied consistently across trading and asset

businesses to ensure optimal capital allocation• RAROC can be applied within a trading business to grow

profitable activities at the expense of less profitable ones• Risk control allows firms to leverage more of their core expertise

in origination, marketing, and market development• Investors evaluate banks’ & energy company performance

relative to peers partly on RAROC analysis

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How does Microsoft’s risk analysis differ from others’?

• Bankers Trust and Enron have similar risks– Market risk

– Liquidity risk

– Credit risk

• For Microsoft, other risks are more important– Competitive risks

– Operational risks

– Legal risks

• Should Microsoft use RAROC?• In EWRM, all risks are treated equally to the extent they risk the

same amount of capital– A common language for risk and risk measurement leads to better

decision-making• Pricing, project origination and performance measurement

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Two uses of RAROC

• As a ratio:– RAROC ranks relative

performance– Trading desk makes $50 MM

and risks $80 MM for a RAROC of 62.5%

– Asset business makes $30 MM on a $100 MM investment that can be sold for $60 MM in the worst case; RAROC = 75%

• Banks tend to find this implementation easier

• As a measure of value-added– NPV = Usual NPV minus risk

charges– Risk charges = Corporate

RAROC x VAR– Suppose corporate RAROC =

40%– Trading desk adds – $50 - 40% of $80 = $18 MM– Asset business adds – $30 - 40% of $40 = $14 MM

• Risk-adjusted NPV or Risk-adjusted EVA

• Energy firms tend to find this implementation easier

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What do firms need to do to establish EWRM?

• LAY THE FOUNDATIONS...– Analytical risk assessment systems are needed

– High quality analytic staff

• AND ERECT THE STRUCTURE– Integrated VAR framework for all trades, financing and asset deals

• Market risk (paper/physical)• Credit risk• Operational risk and competitive risk

– VAR-based risk reporting (usu. daily frequency)

– VAR-based trading limits and capital allocation

– Establishing a culture of efficient risk-taking• Exposure at all levels of management• Risk-based decision-making

– RAROC-based performance measurement and compensation

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A successful organizational structure

• Chief Risk Officer independent of business– Head of risk management committee

– Report to CEO (in some cases, the Board of Directors)

– Responsible for• Capital allocation/budgeting of risk capital

– Trading and non-trading businesses• Establishment of benchmarks• Integrity of risk systems• Performance measurement• Risk and performance reporting

• CRO’s office contains the following functions (large org.)– Head of compliance

– Head of risk operations

– Head of research/analytics

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Recommended next steps for EWRM implementers

• This presentation discussed the whats and whys• Next examine the hows carefully

– Measuring VAR in the trading books and asset businesses

– Reporting

– Applying asset allocation to risk limits

– Applying RAROC consistently to project evaluation

– Establishing benchmarks by business

– Ensuring systems efforts are consistent with long-term organizational goals

• Expose decision-makers at all levels to RAROC and risk-aware decision-making

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Example: Pricing options into swap contracts

• Assumptions (using an electric power example)– Fixed price power contract with no options is worth $25/MWh

– Independent modeling suggests option is worth $1/MWh

– Value-at-risk on the fixed price contract is $15/MWh

– Value-at-risk on the fixed price contract with swings is $18/MWh

– Required return on risk capital of 20% (30-day VaR)

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Incorporating VaR into swap bid/offer

• Case I: Bid/offer for a single undiversified trade– Fixed price firm: 25±15(0.20) = {22,28}

– With option: 25+1±18(0.20) = {22.4,29.6}

• Case II: Warehousing period of one week– Fixed price firm: 25±15(0.20)0.25 = {23.5,26.5}

– With option: 25+1±18(0.20)0.25 = {24.2,27.8}

• Case III: Small trade, fully diversified– Fixed price firm: {25,25}

– With option: {26,26}

• GENERAL STATEMENTS:– Swap bid offer must contain not only option values, but charges for

marginal risk.

– Concentrations of unidirectional options require higher risk charges.

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What does this mean for credit?

• Credit risk must be computed and charged against risk capital• Same rules apply

– Single nondiversified exposure gets high charge

– Diversified credit exposures minimize credit charges if credit risks are independent

• Credit risk does not diversify market risk– Risks are multiplicative, i.e. contract in the money together with

counterparty default

• So what is a swap really?– The agreement to exchange cash flows subject to...

– Each counterparty’s right to default on this obligation along with their collective obligations

– Option may not be exercised “optimally” in the narrow sense

• What is collateral really?– The striking price of the default option

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Putting it all together

• Credit risk is a combination of two embedded options• The embedded option increases value-at-risk to both parties to

the swap• Joint collateral holdings reduce credit risk by making the default

options more out-of-the-money• Hence, good collateral management at sufficiently high levels

can hedge most of the credit risk• …And thereby reduce the necessary capital charges for credit

risk

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You could build a great model...

• Bid = Q

• –(C+u)C(XC)

• +SP(XS)

a• –k IV(XS,XC)

• – IXS

• NOTES:– Subscript C indicates counterparty, S indicates self– Probability of counterparty default is based on a credit rating plus an

uncertainty premium u– The call and put options decrease in value as collateral X increases

• Price of default-free contract

• – Probability of counterparty default x price of call option

• + Probability of own default x price of put option

• – Admin costs per unit

• – Charges for incremental risk capital

• – Charges for incremental collateral

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But it would be wrong.

• Credit risk ultimately is extremely difficult to model.– Not because of the analytic complexity of credit risks, fat tails,

correlations and aggregation

– But because of structural inefficiencies in the “balance sheet” credit methods

• INEFFICIENCY #1– Everyone pays his counterparty’s cost of credit

• INEFFICIENCY #2– One can never know one’s counterparty’s nondisclosed risks

• Market risks (LTCM)• Credit risks (The US Power Industry)

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What’s wrong with paying the other guy’s credit costs?

• Trade subsidization– Higher quality credits effectively pay for lower quality credits to

trade with them

• Incentive for all to seek higher credit quality counterparty

• HOW TO AVOID PAYING THESE COSTS– A. Price swaps to reflect counterparty credit quality

– B. Don’t trade

– C. Don’t charge traders for credit risk

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Can’t we estimate nondisclosed risks?

• That would be very difficult.– Risks change constantly

– Risks sometimes change, unknown to counterparty

• Incentives– A counterparty of equal credit rating should only trade with you if he

believes his hidden risks are greater than you realize

– You realize this

– You resist trading with those who would trade with you

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Where does this leave us?

• There are serious shortcomings of even the most sophisticated practices– Inability to determine hidden credit exposures of counterparties

• The best credit manager and the best credit analytics cannot solve these problems

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A humble suggestion

• Post collateral to cover all counterparty obligations to all other counterparties– In this system, everyone pays their own credit costs

• Do you think collateral is expensive?– It is under the current system

• Why is collateral so inefficient?– Lack of uniform collateral collection

– Unnecessary transfer costs between custody banks

– Limits to rehypothecation of collateral• Eligibility• Permission of issuing institution• Letters of Credit and Third Party Guarantees

– Inability to post collateral on a hedged or diversified basis

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Introducing the CoVar project at Bankers Trust

• First application in the energy industry• Solves four major collateral problems

– Lack of uniform collateral collection• Centralized reconciliation and messaging

– Unnecessary transfer costs between custody banks• Keeps collateral at participant’s custody bank until default

– Limits to rehypothecation of collateral• Standardizes eligible collateral• Retains and reassigns LCs and TPGs by book entry

– Inability to post collateral on a hedged or diversified basis• CoVar’s secret

• Collateral solutions imply credit solutions• For more information

– www.COVAR.com