22.11Summary and Conclusions

This chapter addressed the practice of hedging, examininghow to use popular financial instruments like forwards, fu-tures, swaps, and options for hedging. In addition, the dis-cussion analyzed a variety of tools to estimate risk expo-sure and hedge ratios, including factor models, regression,and mean-variance mathematics.

Although the analysis focused on the elimination of risk,risk elimination is not necessarily a desirable goal, becauseit often comes at a very high price. Rather, the focus of themanager should be on the management of risk. Once a tar-get risk level for a risk exposure is identified, the managercan put the tools developed in this chapter to use. For ex-ample, a manager who estimates the firm’s exchange rateexposure to be a $12 million decrease in profits for every1percent increase in the dollar/yen exchange rate may tar-get the optimal exchange rate risk exposure at “$7 million.”In this case, the manager’s hedge is targeted to reduce the

firm’s exchange rate exposure from $12 million (per 1 per-cent increase in the dollar/yen rate) to $7 million (per 1 per-cent increase in the dollar/yen rate). This hedging would notbe different from that of a manager who found himself with$5million ($12 million $7 million) of exchange raterisk exposure and wanted to eliminate all of this exposure.

Before applying the tools of this chapter, managersneed to analyze the firm’s asset and liability picture fromthe broadest perspective possible. Even if they under-stand how to hedge, many managers may overhedge byfailing to recognize the important message of Chapter12; namely, that options are the key aspects to most proj-ects and most firms. Many firms implement a hedge oftheir estimated cash flows without recognizing that theoption to cancel, expand, downsize, or fundamentally al-ter their projects may have important implications forhedge ratios. Indeed, these options in the projects often

Grinblatt1637Titman: Financial	VI. Risk Management	22. The Practice of Hedging	© The McGraw1637Hill
Markets and Corporate			Companies, 2002
Strategy, Second Edition

Chapter 22

The Practice of Hedging

813

imply that options should be used in the hedging vehiclesnicians are. Like the running of any major aspect of a busi-as well.ness, hedging needs to be guided by artful, creative man-

In short, straightforward answers and cookbook, albeitagers who are fairly skilled in the technical aspectscomplex, formulas for almost any hedging problem can beofhedging so as not to be overly impressed by thefound in the abundant literature on hedging. They arerecommendations of the technicians. Management needsfound in this chapter, too. However, the natural inclinationto fully understand not only the motivations for hedging,to leave hedging to technicians is a foolish decision, nobut also the broader picture of what strategic considera-matter how mathematically skilled or competent such tech-tions drive the firm’s value and its risk.

Key Concepts

Result	22.1:	Futures hedges must be tailed to account	hedge ratio when hedging long-dated
		for the interest earned on the amount of	obligations with short-term forward
		cash that is exchanged as a consequence	agreements. When hedging with futures, a
		of the futures mark-to-market feature.	further tail is needed (see Result 22.1).
		Such tailed hedges require holding less of	Result 22.5:The greater the unhedgeable convenience
		the futures contract the further one is	yield risk, the lower is the hedge ratio for
		from the maturity date of the contract.	hedging a long-term obligation with a
		The magnitude of the tail relative to an	short-term forward or futures contract.
		otherwise identical forward contract hedge
			Result 22.6:If a firm’s exposure to a risk factor is
		depends on the amount of interest earned
			eliminated by acquiring bforward
		(on a dollar paid at the date of the hedge)
			contracts, then the firm also can eliminate
		to the maturity date of the futures
			that risk exposure by acquiring b
		contract.
			options, where represents the option’s
Result	22.2:	Long-dated obligations hedged with short-	forward delta.
		term forward agreements need to be tailed
			Result 22.7:The factor risk of a cash flow is eliminated
		if the underlying commodity has a
			by acquiring a portfolio of financial
		convenience yield. The degree of the tail
			instruments with factor betas exactly the
		depends on the convenience yield earned
			opposite of the cash flow factor betas.
		between the maturity date of the forward
			Result 22.8:Regression coefficients represent the
		instrument used to hedge and the date of
			hedge ratios that minimize variance given
		the long-term obligation. When hedging
			no capital expenditures constraints and no
		with futures, a greater degree of tailing is
			constraints on the use of costless financial
		needed (see Result 22.1).
			instruments for hedging. Given flexibility
Result	22.3:	The greater the sensitivity of the
			in the scale of a real investment project, a
		convenience yield to the commodity’s spot
			cost to the hedging financial instrument,
		price, the less risky is the long-dated
			and a capital expenditure constraint, the
		obligation is to buy or sell a commodity.
			techniques of mean-variance analysis for
Result	22.4:	The greater the sensitivity of the	finding the efficient portfolio or the global
		convenience yield to the price of the	minimum variance portfolio may be more
		underlying commodity, the lower is the	appropriate for finding a hedge ratio.

Key Terms

basis794	cross-hedging809
basis risk794	delta hedging799
basket options802	exposures773
basket swaps796	forward delta803
cash flow at risk (CAR)777	hedge ratio774
cash flow hedging774	money market hedge782
convenience yield785	regression method775
covered option strategy799	rolling stack792

Grinblatt1639Titman: Financial	VI. Risk Management	22. The Practice of Hedging	© The McGraw1639Hill
Markets and Corporate			Companies, 2002
Strategy, Second Edition

814Part VIRisk Management

simulation method	775	tailing the hedge784
spot delta803		target beta774
spot market779		value at risk (VAR)777
swap spread797		value hedging774

Exercises

22.1.Consider, again, National Petroleum from22.3.Assume a two-factor model for next year’s profits

Example 21.3 in Chapter 21. In addition to theof ExxonMobil. The factors are one-year futures

forward contracts described in Example 21.3,prices for oil and one-year futures prices for the

National Petroleum also can buy (put) options thatUS$/€exchange rate. The relevant factor

give them the right to sell the oil in one, two, orequationis

three years at an exercise price of $20 per barrel.~

˜

Profit$1 billion$10 million F

The one-year option costs $2.00, the two-year^XONOIL

˜˜

option $3.00, and the three-year option $3.50 per$20 million F

$1XON

barrel. What should National Petroleum do to

Assume that each one-year oil futures contract

eliminate the possibility of financial distress and

purchased has the factor equation

still have money to fund new exploration in the

event that oil prices increase?C˜˜

$10,000F

OILOIL22.2.AB Cable, Wire, and Fiber plans to open up a new

Each one-year futures contract on the US$/€

factory three years from now, at which point it

exchange rate has the factor equation

plansto purchase 1 million pounds of copper.

Assume zero-coupon risk-free yields are going to˜˜

C$100,000F

$c$c

remain at a constant 5 percent (annually

compounded rate) for all investment horizons,If ExxonMobil wants to reduce its exposure to the

there is no basis risk in forwards or futures,two risk factors in half, how can it accomplish this

storage of copper is costless, markets areby buying or selling futures contracts?

frictionless, and forward spot parity holds. Copper22.4.Assume that General Motors is planning to

has a 3 percent per year (annual compounded rate)acquire an automobile company in Japan. The deal

convenience yield.will probably be consummated within a year

a.What should the relative magnitude of theprovided that approval is granted by the proper

futures and forward prices for copper be,regulatory authorities in Japan and the United

assuming the contracts are of the sameStates. The two automakers have agreed upon the

maturity? How should futures and forwardterms of the deal. GM will pay ¥100 billion once

prices change with contract maturity?the deal is consummated. Discuss the advantages

b.Assume that one-year forwards are the onlyand disadvantage of hedging the currency risk in

hedging instruments available. How manythis deal with forwards, options, and swaps.

pounds of copper in forwards should be

22.5.Assume that Schering-Plough, a drug

acquired today to maximally hedge the risk of

manufacturer, has discovered that it is cheaper to

the copper purchase three years from now?

manufacture one of its drugs in France than

How does the hedge ratio change over time?

anywhere else. All revenues from the drug will be

Provide intuition and describe the rollover

in the United States. The company estimates that

strategy at the forward maturity date.

the costs of manufacturing the drug will be €100

c.Assume that three-month futures are the only

million per year and that the factory has a life of

hedging instruments available. How many

10 years. At the end of the 10 years, a balloon

pounds of copper in futures can be acquired

payment on the mortgage from the factory is due.

today to maximally hedge the risk of the copper

Net of proceeds from salvage value, the company

purchase three years from now? How does the

will have to pay €1 billion at the end of 10 years.

hedge ratio change over time? Provide intuition

How can the currency risk of this deal be

and describe the rollover strategy at the futures

eliminated with a currency swap?

maturity date.

Grinblatt1641Titman: Financial	VI. Risk Management	22. The Practice of Hedging	© The McGraw1641Hill
Markets and Corporate			Companies, 2002
Strategy, Second Edition

Chapter 22

The Practice of Hedging

815

22.6.	Assume that Dell Computer, a worldwide	compounded annually. Assume that the spot price
	manufacturer and mail-order retailer of personal	of oil changes instantaneously from $20 to $21 per
	computers, has estimated the following regression	barrel.
	associated with its operations in Europe.	a.Describe the necessary number of one-year
		forwards you must hold in order to perfectly
	European profits
	t
		hedge a long position in 1 barrel of oil. Then
	$10 million
		describe any changes in the perfectly hedged
	$8 million
		position of spot oil and forwards, including any
	($€ 1-year forward exchange rate)
	t	cash that changes hands, when the spot price of
	˜
	t	oil instantaneously increases by $1.00.
		b.Repeat part a for a perfectly hedged position
	a.How should Dell Computer minimize variance
		using futures contracts.
	associated with these European operations,
		c.Repeat parts a and b, assuming that you now
	using only forward contracts on the $/€
		want to hedge a short position of 5,000 barrels
	exchange rate? Is your answer affected by
		of oil.
	whether the European operations are fixed or
	scalable in size?	22.9.Assume that EXCO has an obligation to deliver
	b.Assuming that European profits are normally	1.5 million barrels of oil in nine months at a fixed
	distributed, what is Dell’s profit at risk at the 5	price of $24 per barrel. Assume a constant
	percent significance level, assuming that the	convenience yield of 2 percent per year and a risk-
	percentage change in the $/€exchange rate is	free rate of 9 percent per annum compounded
	normally distributed and has a volatility of 10	annually.
	percent? Ignore ˜risk for this calculation.	a.How can EXCO hedge all the risk of this
		obligation in the forward market, using only
22.7.	Your U.S. based company has an opportunity to
		forwards maturing three months from now and
	break into the British market, but your CEO is
		then rolling over new 3-month forwards?
	concerned about the currency risk of such a
		b.How can EXCO hedge all the risk of this
	venture. You estimate that sales in the United
		obligation, using only 3-month futures?
	Kingdom will be £2 million (worst-case scenario)
		c.Repeat parts aand b, assuming EXCO owns
	or £5 million (best-case scenario) over the next 10
		1.5 million barrels of oil.
	months. The likelihood that each of these
	scenarios will occur is equal. Your CEO wishes to	22.10.General Motors has an obligation to deliver 2
	hedge the expected value of these sales, but is not	million barrels of oil in six months at a fixed price
	sure which hedging vehicle to use.	of $25 per barrel. European options exist to buy
	a.You are given the following information and	oil in six months at $28 per barrel. Assume the
	are assigned the task of recommending the best	six-month annualized (continuously compounded)
	method of hedging (that is, what is the highest	riskless rate is 5 percent. Because of recent unrest
	dollar amount you can lock in today).	in the Middle East, however, the volatility (that is,
		standard deviation) of the annualized percentage
	Current US$/£ spot rateUS$1.55/£
		change in the price of oil has soared to an
	Current forward rate for currency exchanged	incredible 59.44 percent (annualized).
	10 months from today US$1.60/£	Can General Motors eliminate its exposure to
	10-month US$ LIBOR is 6.5 percent	oil price risk generated by the delivery agreement
	perannum	using options, and if so, how many options will it
		have to buy or sell in order to do this? (Hint: The
	10-month £ LIBOR is 11.7 percent per
		Black-Scholes option pricing equation is valid
	annum
		here.)
	b.Is there an arbitrage opportunity here? If so,
		22.11.Disney wants to borrow €24 million for three
	how would you exploit it?
		years while Metallgesellschaft wants to borrow
22.8.	Suppose you wish to hedge your exposure to oil
		US$20 million for three years. The spot exchange
	prices by means of forwards and futures over the
		rate is currently €1.20/$. Suppose Disney and
	next year. You have the following information: the
		Metallgesellschaft can borrow Euros and dollars
	current price of oil is $20 per barrel and the risk-
		from their domestic banks at the following
	free rate of interest is 10 percent per year
		(annual) fixed interest rates.

Grinblatt1643Titman: Financial	VI. Risk Management	22. The Practice of Hedging	© The McGraw1643Hill
Markets and Corporate			Companies, 2002
Strategy, Second Edition

816Part VIRisk Management

US$€

Disney6.0%9.7%

Metallgesellschaft8.410.0

Design a currency swap agreement that will

benefit both firms and also yield a 0.4 percent

profit for the bank acting as an intermediary for

the swap.

22.12.Consider a two-factor model, where the factors are

interest rate movements and changes in the

exchange rate. Your company has a future cash

flow with factor betas of 2 on the interest rate

factor and 5 on the exchange rate factor. You

would like to eliminate your sensitivity to both of

these factors by means of financial securities, but

do not wish to use any of the company’s cash to

do this.

The following investment opportunities are

available to you.

•You can purchase 30-year government

bonds.

•You can enter into a 2-year interest rate

swap agreement.

•You can invest in a foreign index fund.

The following factor equations, with the two

factors being changes in interest rates and changes

in exchange rates, correspond to the future values

of the three investment opportunities, respectively.

˜4 4˜

CF(per $1 million invested)

1int

˜6 2˜6˜

CFF(per $1 million invested)

2intex

˜3 3F˜F˜

C 2(per $1 million invested)

3intex

Design a proper hedge against interest rate

movements and exchange rates in this

environment.

22.13.Ford is considering building a factory to produce

its new Taurus. The factory will cost $100 million

and will produce 10,000 automobiles one year

from now, but its cost and production can be scaled

up or down. As an analyst at Ford, you run a

regression of the historical sales margin of 10,000

cars against the return of Ford’s stock. You find

that the regression coefficient is –$130 million,

that the sales margin of a Taurus one year from

now has a standard deviation of $1,000, and that

the volatility of Ford’s stock is 0.5. The risk-free

rate over the coming year will be 10 percent. You

can assume that the return on the factory is the

total sales margin from all cars produced by the

factory divided by the cost of the factory, less one.

Your task is the following:

a.To identify the minimum variance portfolio

combination of Ford stock and the factory, and

to interpret the results.

b.To identify the tangency portfolio mix of

factory and stock if the expected selling margin

of the Taurus is $22,000 and the expected

return of Ford stock is 30 percent over the next

year.

22.14.The National Basketball Association (NBA) has

hired you as a consultant to figure out what the

proper mix of Eastern and Western teams should

be. An Eastern team has a return variance of .04, a

Western team has a return variance of .09, and the

correlation between the returns of an Eastern and a

Western team is .25. Assume that all Eastern

teams are identical and all Western teams are

identical. What should the ratio of Eastern to

Western teams be if the NBAwants to minimize

return variance?

References and Additional Readings

Allen, William. The Walt Disney Company’s YenChowdhry, Bhagwan; Mark Grinblatt; and David Levine.

Financing.Harvard Case 9-287-058, HarvardInformation Aggregation, Security Design, and

Business School Publishing, 1987.Currency Swaps. UCLAworking paper, July 2001.Backus, David; Leora Klapper; and Chris Telmer.Culp, Christopher, and Merton Miller. “Metallgesellschaft

Derivatives at Banc One (1994).Case study, Newand the Economics of Synthetic Storage.” Journal of

York University, New York, 1995.Applied Corporate Finance7 (1995), pp. 6–21.

Brennan, Michael, and Nicholas Crew. “Hedging LongFama, Eugene, and Kenneth French. “Commodity Futures

Maturity Commodity Commitments with Short-DatedPrices: Some Evidence on Forecast Power,

Futures Contracts.” In Mathematics of DerivativePremiums, and the Theory of Storage.” Journal of

Securities,Michael Dempster and Stanley Pliska, eds.Business60, no. 1 (1987), pp. 55–74.

Cambridge: Cambridge University Press, 1996.

Grinblatt1645Titman: Financial	VI. Risk Management	22. The Practice of Hedging	© The McGraw1645Hill
Markets and Corporate			Companies, 2002
Strategy, Second Edition

Chapter 22

The Practice of Hedging

817

Gibson, Rajna, and Eduardo Schwartz. “Stochastic

Convenience Yield and the Pricing of Oil Contingent

Claims.” Journal of Finance45, no. 3 (1990),

pp.959–76.

Grinblatt, Mark, and Narasimhan Jegadeesh. “The

Relative Pricing of Eurodollar Futures and Forward

Contracts.” Journal of Finance51, no. 4 (September

1996), pp. 1499–1522.

Jorion, Philippe. Value at Risk.Burr Ridge, IL: Richard

D. Irwin, 1997.

Linsmeier, Thomas J., and Neil D. Pearson. Risk

Measurement: An Introduction to Value at Risk.

Working paper, University of Illinois, Urbana-

Champaign, 1996.

Margrabe, William. “The Value of an Option to Exchange

One Asset for Another.” Journal of Finance33, no. 1

(1978), pp. 177–86.

Mello, Antonio, and John Parsons. “Maturity Structure of

a Hedge Matters.” Journal of Applied Corporate

Finance8 (1995), pp. 106–20.

Neuberger, Anthony. “How Well Can You Hedge Long-

Term Exposures with Multiple Short-Term Futures

Contracts?” Review of Financial Studies12, no. 3

(1999), pp. 429–59.

Ross, Stephen. “Hedging Long-Run Commitments:

Exercises in Incomplete Market Pricing.”Economic

Notes2 (1997), pp. 385–420.

Smithson, Charles; Clifford Smith; and D. Sykes Wilford.

Managing Financial Risk.Burr Ridge, IL: Richard

D. Irwin, 1995.

Grinblatt1646Titman: Financial	VI. Risk Management	23. Interest Rate Risk	© The McGraw1646Hill
Markets and Corporate		Management	Companies, 2002
Strategy, Second Edition

CHAPTER

Interest Rate