2014 Risk Management - Part 1

Financial Risk Management

Prof. Dr. Jörg Prokop

Winter Term 2014/15

Financial Risk Management 2

Course Contents

• Concept of risk management

• Mechanics of financial markets, in particular derivatives markets

• Applications and limitations of financial derivatives in riskmanagement

Preliminary Course Outline

1. What Is Risk?

2. Introduction to Derivatives

3. Mechanics of Futures Markets

4. Hedging Strategies Using Futures

5. Interest Rates

6. Determination of Forward and Futures Prices

7. Swaps

8. Properties of Options

9. Binomial Trees

10. The Black-Scholes-Merton Model

11. Conclusion



Recommended Readings

• Hull, John C. Options, Futures, and Other Derivatives, 8th ed., Pearson 2012 [OFD]

� main textbook (note: the older editions 6 or 7 will do as well)

• Hull, John C. Solutions Manual for Options, Futures, and Other Derivatives, 8th ed., Pearson 2012

• Damodaran, Strategic Risk Taking: A Framework For Risk Management, Pearson 2008 [SRT] (draft version: http://pages.stern. nyu.edu/~adamodar/New_Home_Page/valrisk/book.htm)

• Hull, John C. Fundamentals of Futures and Options Markets, 7th ed., Pearson 2011

� alternative textbook


Preliminary Schedule

Date Time Room Topic Chapter

17 Sep 14.00-17.00 BC-207 • What Is Risk?• Introduction to Derivatives

• SRT 1, 2, 4• OFD 1

18 Sep 14.00-17.00 BC-208 • Mechanics of futuresmarkets

• Hedging strategies usingfutures

• OFD 2• OFD 3

19 Sep 09.00-12.0014.00-17.00

BC-208BC-208

• Interest rates• Forward and futures prices• Swaps• Properties of Options

• OFD 4• OFD 5• OFD 7• OFD 9, 10

30 Sep 10.00-13.0014.00-17.00

BC-207BC-208

• Binomial trees• The Black-Scholes-Merton

model• Conclusion / recap session

• OFD 12• OFD 13,

14• OFD 35


Course Organization

• Assessment: – Written examination, date tba– The exam will be closed book. However, you will be

permitted a hand-written two-sided “cheat sheet” with notes and / or formulae.

• Slides & course announcements=> Moodle

• Best way to contact me: [email protected]

Financial Risk Management: What Is Risk?

Suggested Reading:• SRT, ch. 1, 2, 4• Holton, Defining Risk, Financial Analysts

Journal, 2004, Vol. 60, No. 6, pp. 19-25


Basic Principle

„There’s no such thing as a free lunch.“

(Hessen, Free Lunch, in: Eatwell/Milgate/Newman: The New Palgrave: A Dictionary of Economics, Volume II, London 1988, p. 450)

� How does that relate to Finance and Economics?


What Is Risk?

Risk

Measurable uncertainty?(e.g., Knight, 1921)

Uncertainty + exposure? (e.g., Holton, 2004)

…?


What Is Uncertainty?

� Being uncertain about a proposition means:

– that you do not know wetherit is true or false (perceiveduncertainty)

or

– that you are not aware ofthe proposition.


What Is Exposure?

� Having exposure to a proposition means:

• that you care whether it is true or false

or

• that you would carewhether it is true orfalse if you were awareof the proposition.


Taking Risk

Some situations that involve risk:• Trading natural gas,• launching a new business,• military adventures,• asking for a pay raise,• sky diving, and• romance.

Do organizations (e.g., companies) take risk? Who does?


Why Do We Care About Risk?The St. Petersburg Paradox

• Try the following:– Flip a coin. If it comes up tails, you receive one dollar.

In this case, you may flip it again. If it comes up tails again, your winnings will be doubled.

– You may continue the game to double your winnings as long as the coin does not come up heads.

– If it comes up heads, the experiment ends, and you receive your accumulated gains.

• How much would you pay to participate in this game?


Why Do We Care About Risk?The St. Petersburg Paradox

• Expected value:

• Judging only on the basis of the game‘s expected value, we would be willing to pay a very (or even infinitely) high amount of cash to participate

• However, in reality most people would pay only a few $�St. Petersburg Paradox (first published by D. Bernoulli in St.

Petersburg Academy Proceedings, 1738)

∑∞

=

∞==++++=

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1 2

1...

2

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...816

14

8

12

4

11

2

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Expected Utility Theory

“The determination of the value of an item must not be based on its price, but rather on the utility it yields. The price of the item is dependent only on the thing itself and is equal for everyone; the utility, however, is dependent on the particular circumstances of the person making the estimate. Thus there is no doubt that a gain of one thousand ducats is more significant to a pauper than to a rich man though both gain the same amount.”

(Bernoulli, 1738, [cited in Econometrica 22(1), 1954, p. 24])

How can we turn this idea into a decision model?


Expected Utility Theory

• Bernoulli‘s approach: Utility functions

�Step 1: Assign a subjective utility value toevery potential outcome of the uncertain target variable

�Step 2: Calculate the expectation value of the distribution of uncertain utility values from step 1

�Expected Utility Theory

W~

( )WU

( )[ ]W~

UE

NB: The following discussion of Expected Utility Theory is partly based on Elton / Gruber / Brown / Goetzman: Modern Portfolio Theory and Investment Analysis, 6th ed., Hoboken 2003, chapter 10


• Probability distributions of three investments:

• Given utility function: U(W) = 4W - (1/10)W2

� Investment A: U(20) = 4*20 - (1/10)*202 = 40U(18) = 4*18 - (1/10)*182 = 39,6U(14) = 4*14 - (1/10)*142 = 36,4etc.

Example: Bernoulli -Principle


• Probability distributions and utility profiles:

� Expected utility: E[U(WA)] = 40*3/15+39,6*5/15... = 36,3E[U(WB)] = 39,9*1/5+30*2/5... = 26,98E[U(WC)] = 39,6*1/4+38,4*1/4... = 34,4

� Resulting preference relation:

Example: Bernoulli -Principle

BCA WWW ff


Characteristics of Utility Functions

Example: „Fair gamble“

� The investor‘s options:


Characteristics of Utility Functions

(strictly) concave

(strictly) convex

linear

Utility functions given:(1) Risk preference (e.g., U(W) = W2)(2) Risk neutrality (e.g., U(W) = W)(3) Risk aversion (e.g., U(W) = W0,5)


Risk Management

http://www.sciencecartoonsplus.com/gallery/risk/index.php


Risk Management

• Potential risk management actions:

– Reduce risk exposure

– Maintain current level of risk exposure

– Increase risk exposure

• Let’s focus on the first one:How can we reduce risk exposure?

http://www.sciencecartoonsplus.com/gallery/risk/index.php


Risk Hedging Alternatives

From Copeland/Weston/Shastri, Financial Theoryand Corporate Policy, 4th ed., 2005, p. 724 (mod.)

Natural Hedges Financial Hedges

• Borrow in the same currency thatyour asset risk is denominated in

• Engineer flexibility into operations• Diversify• Improve forecasting• Match operating costs and revenues

in the same currency• Optimize insurance policy• Share risks: joint ventures, sales

agreements

• Forwards• Futures• Options• Swaps


Risk Management

• Is the above definition „risk = uncertainty + exposure“ operational?

„If you can‘t measure it, you can‘t manage it!“(Kaplan/Norton, The Balanced Scorecard: Translating Strategy Into Action, 1996, p. 21)

� I.e., we need some adequate risk metrics


Risk vs Return

• There is a trade off between risk and expected return

• The higher the risk, the higher the expected return

• We can characterize investments by their expected return (µi) and standard deviation of returns (σi):

• The relationship between two investments’ return data can be described by their covariance (σij), or by theircorrelation coefficient (ρij):

∑=

⋅==n

jjijii rwr

1,

~]~[Eµ ( )∑=

−⋅==n

jijijii rw

1

2,

2 ~ µσσ

( ) ( )∑=

−⋅−=n

kjjkiikkij rrw

1

~~ µµσji

ijij σσ

σρ

⋅=

Systematic vs Non-Systematic Risk

• Nonsystematic risk– Results from uncontrollable or random events that are

firm-specific– Examples: labor strikes, lawsuits

• Systematic risk– Attributable to forces that affect all similar investments– Examples: war, inflation, political events


Portfolio Selection: Combining Risky Investments(Markowitz, Journal of Finance 1952)


can be eliminated through diversification

cannot be eliminated through diversification


Expected Returns: The Capital Asset Pricing Model(Sharpe, 1964 / Lintner, 1965 / Mossin, 1966)

1.0 β

RF

µM

)( FMjFj RµR −+= βµ

μ

Required returnon investment j

= Risk-free rate +Beta for

investment j

×

Marketreturn

−Risk-free

rate


Alpha

• Alpha = extra return on a portfolio in excess of that predicted by CAPM

so that

)( FMPFP RR −+= µβµ

)( FMPFP RR −−−= µβµα


Key Assumptions Underlying the CAPM

• Investors are risk averse

• Investors care only about an investment’s risk (σ) and expected return (µ) � Implies either normally distributed returns or quadratic utility function

• Unsystematic risks of different assets are independent

• Investors focus on returns over one period

• All investors can borrow or lend at the same risk-free rate

• Tax does not influence investment decisions

• All investors make the same estimates of µ’s, σ’s and ρ’s.

Critique Regarding the µ-σ Framework

• Quadratic utility function:– Implies negative marginal utility for certain (high) ranges

of wealth– Implies increasing absolute risk aversion– Implies that investors are equally averse to good and to

bad outcomes of the same absolute amount

• Normal distribution of returns:– Skewness?– Kurtosis?– Jumps?



Digression: Arbitrage Pricing Theory(Ross , Journal of Economic Theory, 1976, pp. 341-360)

• Assumptions:– Returns depend on several factors– Arbitrage-free markets (law of one price)

• Expected return is linearly dependent on the realization of the factors

• Each factor is a separate source of systematic risk

• Unsystematic risk is the proportion of total risk that is unrelated to all the factors

IlilIiIiii µβµβµβαµ ⋅++⋅+⋅+= ...2211

Digression: The Carhart (1997) Model

• In the Carhart (1997) model, there are four factors representing the market risk premium, high minus low B/M, small minus big, and momentum arbitrage portfolios respectively.

• The Fama-French (1993) three factor model is simply the four factor model without the momentum factor.

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Financial Risk Management


Approaches to Risk Reduction

• Risk aggregation �Aims to get rid of non-systematic risks with

diversification

• Risk decomposition�Tackles risks one by one

• In practice companies use both approaches

Reducing Risk With Diversification

Financial Risk Management 35Damodaran, Applied Corporate Finance, 3rd ed., 2010, p. 68

Recap Questions

1. What is the St. Petersburg Paradox?

2. In decision theory, what is considered a „fair gamble“? How does an investor‘s risk preference relate to her willingness to participate in a fair gamble?

3. What is the difference between systematic and nonsystematic risk? Which is more important to an equity investor? Which can lead to the bankruptcy of a corporation?

4. Explain the CAPM formula. How would you estimate the respective variables in practice?

5. A company’s operational risk includes the risk of a very large loss due to employee fraud. Do you think this particular risk should be handled by risk decomposition or risk aggregation?


Financial Risk Management: Introduction to Derivatives

Suggested Reading:• OFD 2012, ch. 1


Size of OTC and Exchange-Traded Derivatives Markets

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100,000

200,000

300,000

400,000

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1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

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Size of OTC and exchange-traded derivatives markets

Over-the-counter Exchange-traded

German GDP 2011: about 3,335 billion US$

Study on Derivatives Usage by Non-Financial Firms (2000/01)


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. 38,

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Ways Derivatives are Used

• To hedge risks

• To speculate (take a view on the future direction of the market)

• To lock in an arbitrage profit

• To change the nature of a liability

• To change the nature of an investment without incurring the costs of selling one portfolio and buying another


Forward Price

• The forward price for a contract is the delivery price that would be applicable to the contract if it were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero)

• The forward price may be different for contracts of different maturities


Terminology

• The party that has agreed to buy has what is termed a long position

• The party that has agreed to sell has what is termed a short position


Example

• On July 20, 2007 the treasurer of a corporation enters into a long forward contract to buy £1 million in six months at an exchange rate of 2.0489

• This obligates the corporation to pay $2,048,900 for £1 million on January 20, 2008

• What are the possible outcomes?


Profit from aLong Forward Position

Profit

Price of Underlyingat Maturity, ST

K


Profit from a Short Forward Position

Profit

Price of Underlyingat Maturity, ST

K


Futures Contracts

• Agreement to buy or sell an asset for a certain price at a certain time

• Similar to forward contract

• Whereas a forward contract is traded OTC, a futures contract is traded on an exchange


Examples of Futures Contracts

• Agreement to:

– Buy 100 oz. of gold @ US$900/oz. in December (NYMEX)

– Sell £62,500 @ 2.0500 US$/£ in March (CME)

– Sell 1,000 bbl. of oil @ US$120/bbl. in April (NYMEX)


1. Gold: An Arbitrage Opportunity?

• Suppose that:– The spot price of gold is US$900– The 1-year forward price of gold is US$1,020– The 1-year US$ interest rate is 5% per annum

• Is there an arbitrage opportunity?


2. Gold: Another Arbitrage Opportunity?

• Suppose that:– The spot price of gold is US$900– The 1-year forward price of gold is US$900– The 1-year US$ interest rate is 5% per annum



The Forward Price of Gold

If the spot price of gold is S and the forward price for a contract deliverable in T years is F, then

F = S (1+r )T

where r is the 1-year (domestic currency) risk-free rate of interest.

In our examples, S = 900, T = 1, and r =0.05 so thatF = 900(1+0.05) = 945


1. Oil: An Arbitrage Opportunity?

• Suppose that:– The spot price of oil is US$95– The quoted 1-year futures price of oil is US$125– The 1-year US$ interest rate is 5% per annum– The storage costs of oil are 2% per annum



2. Oil: Another Arbitrage Opportunity?

• Suppose that:– The spot price of oil is US$95– The quoted 1-year futures price of oil is US$80– The 1-year US$ interest rate is 5% per annum– The storage costs of oil are 2% per annum



Options

• A call option is an option to buy a certain asset by a certain date for a certain price (the strike price)

• A put option is an option to sell a certain asset by a certain date for a certain price (the strike price)


American vs European Options

• An American option can be exercised at any time during its life

• A European option can be exercised only at maturity

CBOE Intel Option Prices, Sept 12, 2006 (Stock Price: 19.56)

• American Options• Contract size: 100 shares


Strike Price

Oct Call

Jan Call

Apr Call

Oct Put

Jan Put

Apr Put

15.00 4.650 4.950 5.150 0.025 0.150 0.275

17.50 2.300 2.775 3.150 0.125 0.475 0.725

20.00 0.575 1.175 1.650 0.875 1.375 1.700

22.50 0.075 0.375 0.725 2.950 3.100 3.300

25.00 0.025 0.125 0.275 5.450 5.450 5.450

Net Profit of a Call Strategy at Maturity(Strike $20)


-500

0

500

1000

1500

2000

0 5 10 15 20 25 30 35 40

Pro

fit

($)

Stock price ($)

Net Profit of a Put Strategy at Maturity(Strike $17.5)


-500

0

500

1000

1500

2000

0 5 10 15 20 25 30 35 40

Pro

fit

($)

Stock price ($)


Options vs Futures/Forwards

• A futures/forward contract gives the holder the obligation to buy or sell at a certain price

• An option gives the holder the right to buy or sell at a certain price


Types of Traders

• Hedgers

• Speculators

• Arbitrageurs

N.B.:Some of the largest trading losses in derivatives have occurred because individuals who had a mandate to be hedgers or arbitrageurs switched to being speculators (see for example Barings Bank, Business Snapshot 1.2, OFD p. 15)


Hedging Examples

• A US company will pay £10 million for imports from Britain in 3 months and decides to hedge using a long position in a forward contract

• An investor owns 1,000 Microsoft shares currently worth $28 per share. A two-month put with a strike price of $27.50 costs $1. The investor decides to hedge by buying 10 contracts


Value of Microsoft Shares With and Without Hedging


Speculation Example

• An investor with $2,000 to invest feels that a stock price will increase over the next 2 months. The current stock price is $20 and the price of a 2-month call option with a strike of $22.50 is $1

• What are the alternative strategies?


Arbitrage Example

• A stock price is quoted as £100 in London and $200 in New York

• The current exchange rate is 2.0300 $/£

• What is the arbitrage opportunity?

Accounting for Derivatives

• Ideally hedging profits (losses) should be recognized at the same time as the losses (profits) on the item being hedged

• Ideally profits and losses from speculation should be recognized on a mark-to-market basis

• Roughly speaking, this is what the accounting treatment of futures under U.S. GAAP and IFRS (and many other accounting frameworks) attempts to achieve

• EU: IAS 39 (financial instruments: recognition and measurement), to be superseded by IFRS 9 (issued Nov 2009, but not yet endorsed)


Derivatives: The IFRS Perspective (here: IAS 39.9)

A derivative is a financial instrument or other contract within the scope of this standard (see paragraphs 2-7) with all three of the following characteristics:(a) its value changes in response to the change in a specified interest

rate, financial instrument price, commodity price, foreign exchange rate, index of prices or rates, credit rating or credit index, or other variable, provided in the case of a non-financial variable that the variable is not specific to a party to the contract (sometimes called the‘underlying’);

(b) it requires no initial net investment or an initial net investment that is smaller than would be required for other types of contracts that would be expected to have a similar response to changes in market factors; and

(c) it is settled at a future date.


How to Account for Derivatives (IAS 39.9)

A financial asset or financial liability at fair value through profit or loss is a financial asset or financial liability that meets either of the following conditions.(a) It is classified as held for trading. A financial asset or financial liability

is classified as held for trading if it is:(i) acquired or incurred principally for the purpose of selling or

repurchasing it in the near term;(ii) part of a portfolio of identified financial instruments that are

managed together and for which there is evidence of a recent actual pattern of short-term profit-taking; or

(iii) a derivative (except for a derivative that is a financial guarantee contract or a designated and effective hedging instrument).

(b) (b) Upon initial recognition it is designated by the entity as at fair value through profit or loss.


Hedge Accounting (IAS 39)

• Hedge accounting recognises the offsetting effects on profit or loss of changes in the fair values of the hedging instrument and the hedged item. (IAS 39.85)

• Definitions (IAS 39.9): – A hedging instrument is a designated derivative […] whose fair

value or cash flows are expected to offset changes in the fair value or cash flows of a designated hedged item […].

– A hedged item is an asset, liability, firm commitment, highly probable forecast transaction or net investment in a foreign operation that (a) exposes the entity to risk of changes in fair value or future cash flows and (b) is designated as being hedged […].

– Hedge effectiveness is the degree to which changes in the fair value or cash flows of the hedged item that are attributable to a hedged risk are offset by changes in the fair value or cash flows of the hedging instrument […].


Embedded Derivatives (IAS 39.10 & 11)

39.10: An embedded derivative is a component of a hybrid (combined) instrument that also includes a non-derivative host contract — with the effect that some of the cash flows of the combined instrument vary in a way similar to a standalone derivative. […]

39.11: An embedded derivative shall be separated from the host contract and accounted for as a derivative under this standard if, and only if:(a) the economic characteristics and risks of the embedded derivative are

not closely related to the economic characteristics and risks of the host contract (see Appendix A paragraphs AG30 and AG33);

(b) a separate instrument with the same terms as the embedded derivative would meet the definition of a derivative; and

(c) the hybrid (combined) instrument is not measured at fair value with changes in fair value recognised in profit or loss (i.e. a derivative that is embedded in a financial asset or financial liability at fair value through profit or loss is not separated). […]



Recap Questions

1. Explain carefully the difference between hedging, speculation, and arbitrage.

2. Explain carefully the difference between selling a call option and buying a put option.

3. A trader enters into a short cotton futures contract when the futures price is 50 cents per pound. The contract is for the delivery of 50,000 pounds. How much does the trader gain or lose if the cotton price at the end of the contract is (a) 48.20 cents per pound and (b) 51.30 cents per pound?

4. What is the difference between the over-the-counter market an the exchange-traded market? What are the bid and offer quotes of a market maker in the over-the-counter market?


Recap Questions

6. Suppose that a June put option to sell a share for $60 costs $4 and is held until June. Under what circumstances will the seller of the option (i.e., the party with the short position) make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a short position in the option depends on the stock price at maturity of the option.

7. Describe the profit from the following portfolio: a long forward contract on an asset and a long European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up.

8. What are the main ideas underlying the accounting treatment of derivatives according to IAS 39? What does the term “hedge accounting” mean in this context?

2014 Risk Management - Part 1

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