Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII. Risk Management 27. Managing Risk © The McGraw−Hill Companies, 2003 CHAPTER TWENTY-SEVEN 754 MANAGING RISK Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII. Risk Management 27. Managing Risk © The McGraw−Hill Companies, 2003 MOST OF THE time we take risk as God-given. An asset or business has its beta, and that’s that. Its cash flow is exposed to unpredictable changes in raw material costs, tax rates, technology, and a long list of other variables. There’s nothing the manager can do about it. That’s not wholly true. To some extent managers can choose the risks that the business takes. We have already come across one way that they can do so. In our discussion of real options in Chapter 22 we described how companies reduce risk by building flexibility into their operations. A company that uses standardized machine tools rather than specialized equipment lowers the cost of bailing out if things go wrong. A petrochemical plant that is designed to use either oil or natural gas as a feedstock reduces the impact of an unfavorable shift in relative fuel prices. And so on. In this chapter we shall explain how companies also enter into financial contracts that insure against or hedge (i.e., offset) a variety of business hazards. But first we should give some reasons why they do so. Insurance and hedging are seldom free: At best they are zero-NPV transactions. 1 Most businesses insure or hedge to reduce risk, not to make money. Why, then, bother to reduce risk in this way? For one thing, it makes financial planning easier and reduces the odds of an embarrassing cash shortfall. A shortfall might mean only an unexpected trip to the bank, but if financing is hard to obtain on short no- tice, the company might need to cut back its capital expenditure program. In extreme cases an un- hedged setback could trigger financial distress or even bankruptcy. Banks and bondholders are aware of this possibility, and, before lending to your firm, they will often insist that it is properly insured. In some cases hedging also makes it easier to decide whether an operating manager deserves a stern lecture or a pat on the back. Suppose your confectionery division shows a 60 percent profit in- crease in a period when cocoa prices decline by 12 percent. How much of the increase is due to the change in cocoa prices and how much to good management? If cocoa prices were hedged, it’s prob- ably good management. If they were not, things have to be sorted out with hindsight by asking, What would profits have been if cocoa prices had been hedged? 2 Finally, hedging extraneous events can help focus the operating manager’s attention. It’s naive to expect the manager of the confectionery division not to worry about cocoa prices if her bottom line and bonus depend on them. That worrying time would be better spent if the prices were hedged. 3 Of course, managers are not paid to avoid all risks, but if they can reduce their exposure to risks for which there are no compensating rewards, they can afford to place larger bets when the odds are in their favor. 755 1 Hedging transactions are zero-NPV when trading is costless and markets are completely efficient. In practice the firm has to pay small trading costs at least. 2 Many large firms insure or hedge away operating divisions’ risk exposures by setting up internal, make- believe markets between each division and the treasurer’s office. Trades in the internal markets are at real (external) market prices. The object is to relieve the operating managers of risks outside their control. The treasurer makes a separate decision on whether to offset the firm’s exposure. 3 A Texas oilman who lost hundreds of millions in ill-fated deals protested, “Why should I worry? Worry is for strong minds and weak characters.” If there are any financial managers with weak minds and strong characters, we especially advise them to hedge whenever they can. 27.1 INSURANCE Most businesses buy insurance against a variety of hazards—the risk that their plant will be damaged by fire; that their ships, planes, or vehicles will be involved in acci- dents; that the firm will be held liable for environmental damage; and so on. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII. Risk Management 27. Managing Risk © The McGraw−Hill Companies, 2003 When a firm takes out insurance, it is simply transferring the risk to the insur- ance company. Insurance companies have some advantages in bearing risk. First, they may have considerable experience in insuring similar risks, so they are well placed to estimate the probability of loss and price the risk accurately. Second, they may be skilled at providing advice on measures that the firm can take to reduce the risk, and they may offer lower premiums to firms that take this advice. Third, an insurance company can pool risks by holding a large, diversified portfolio of poli- cies. The claims on any individual policy can be highly uncertain, yet the claims on a portfolio of policies may be very stable. Of course, insurance companies cannot diversify away macroeconomic risks; firms use insurance policies to reduce their specific risk, and they find other ways to avoid macro risks. Insurance companies also suffer some disadvantages in bearing risk, and these are reflected in the prices they charge. Suppose your firm owns a $1 billion offshore oil platform. A meteorologist has advised you that there is a 1-in-10,000 chance that in any year the platform will be destroyed as a result of a storm. Thus the expected loss from storm damage is $ . The risk of storm damage is almost certainly not a macroeconomic risk and can potentially be diversified away. So you might expect that an insurance company would be prepared to insure the platform against such destruction as long as the premium was sufficient to cover the expected loss. In other words, a fair premium for insuring the platform should be $100,000 a year. 4 Such a premium would make insurance a zero-NPV deal for your company. Unfortunately, no insurance com- pany would offer a policy for only $100,000. Why not? • Reason 1: Administrative costs. An insurance company, like any other business, incurs a variety of costs in arranging the insurance and handling any claims. For example, disputes about the liability for environmental damage can eat up millions of dollars in legal fees. Insurance companies need to recognize these costs when they set their premiums. • Reason 2: Adverse selection. Suppose that an insurer offers life insurance policies with “no medical needed, no questions asked.” There are no prizes for guessing who will be most tempted to buy this insurance. Our example is an extreme case of the problem of adverse selection. Unless the insurance company can distinguish between good and bad risks, the latter will always be most eager to take out insurance. Insurers increase premiums to compensate. • Reason 3: Moral hazard. Two farmers met on the road to town. “George,” said one, “I was sorry to hear about your barn burning down.” “Shh,” replied the other, “that’s tomorrow night.” The story is an example of another problem for insurers, known as moral hazard. Once a risk has been insured, the owner may be less careful to take proper precautions against damage. Insurance companies are aware of this and factor it into their pricing. When these extra costs are small, insurance may be close to a zero-NPV transac- tion. When they are large, insurance may be a costly way to protect against risk. Many insurance risks are jump risks; one day there is not a cloud on the hori- zon and the next day the hurricane hits. The risks can also be huge. For example, Hurricane Andrew, which devastated Florida, cost insurance companies $17 bil- 1 billion/10,000 ϭ $ ˇ 100,000 756 PART VIII Risk Management 4 This is imprecise. If the premium is paid at the beginning of the year and the claim is not settled until the end, then the zero-NPV premium equals the discounted value of the expected claim or $.100,000/11 ϩ r2 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII. Risk Management 27. Managing Risk © The McGraw−Hill Companies, 2003 lion; the attack on the World Trade Center is likely to involve payments of more than $35 billion. Many in the industry worry that one day a major disaster will wipe out a large proportion of the capital of the U.S. insurance industry. Therefore, insurance com- panies have been looking for ways to share these risks with investors. One solution is for the insurance company to issue catastrophe bonds (or Cat bonds). The payment on a Cat bond depends on whether a catastrophe occurs and how much is lost. 5 The first public issue of a Cat bond was made by the Swiss insurance giant, Win- terthur. As a major provider of automobile insurance, Winterthur wanted to pro- tect itself against the risk that storm damage could lead to an unusually large num- ber of claims. Therefore, when it issued its bond, the company stated that it would not pay the annual interest if ever there was a hailstorm in Switzerland which dam- aged at least 6,000 cars that it had insured. In effect, owners of the Winterthur Cat bonds coinsured the company’s risks. How British Petroleum (BP) Changed Its Insurance Strategy 6 Major public companies typically buy insurance against large potential losses and self-insure against routine ones. The idea is that large losses can trigger financial distress. On the other hand, routine losses for a corporation are predictable, so there is little point paying premiums to an insurance company and receiving back a fairly constant proportion as claims. BP Amoco has challenged this conventional wisdom. Like all oil companies, BP is exposed to a variety of potential losses. Some arise from routine events such as vehicle accidents and industrial injuries. At the other extreme, they may result from catastrophes such as a major oil spill or the loss of an offshore oil rig. In the past BP purchased considerable external insurance. 7 During the 1980s it paid out an average of $115 million a year in insurance premiums and recovered $25 million a year in claims. BP then took a hard look at its insurance strategy. It decided to allow local man- agers to insure against routine risks, for in those cases insurance companies have an advantage in assessing and pricing risk and compete vigorously against one an- other. However, it decided not to insure against most losses above $10 million. For these larger, more specialized risks BP felt that insurance companies had less abil- ity to assess risk and were less well placed to advise on safety measures. As a re- sult, BP concluded, insurance against large risks was not competitively priced. How much extra risk did BP assume by its decision not to insure against major losses? BP estimated that large losses of above $500 million could be expected to occur once in 30 years. But BP is a huge company with equity worth about $180 bil- lion. So even a $500 million loss, which could throw most companies into bank- ruptcy, would translate after tax into a fall of less than 1 percent in the value of CHAPTER 27 Managing Risk 757 5 For a discussion of Cat bonds and other techniques to spread insurance risk, see N. A. Doherty, “Fi- nancial Innovation in the Management of Catastrophe Risk,” Journal of Applied Corporate Finance 10 (Fall 1997), pp. 84–95; and K. Froot, “The Market for Catastrophe Risk: A Clinical Examination,” Journal of Fi- nancial Economics 60 (2001), pp. 529–571. 6 Our description of BP’s insurance strategy draws heavily on N. A. Doherty and C. W. Smith, Jr., “Cor- porate Insurance Strategy: The Case of British Petroleum,” Journal of Applied Corporate Finance 6 (Fall 1993), pp. 4–15. 7 However, with one or two exceptions insurance has not been available for the very largest losses of $500 million or more. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII. Risk Management 27. Managing Risk © The McGraw−Hill Companies, 2003 BP’s equity. BP concluded that this was a risk worth taking. In other words, it con- cluded that for large, low-probability risks the stock market was a more efficient risk-absorber than the insurance industry. BP Amoco is not the only company that has looked at the package of risks that it faces and the way that these risks should be managed. Here is how The Economist summarized risk management in Duke Energy: 8 Duke’s risk managers are currently designing a model that examines different types of risk together: movements in exchange rates, changes in raw material prices, downtime caused by distribution failures, and so on. This is supposed to produce an “aggregate loss distribution,” which estimates the likelihood that several events could happen at once and sink the company. With this better understanding of the company’s aggregate risk, Duke’s managers can make a more informed decision about how much of this potential loss should be absorbed by shareholders, how much hedged in the financial markets, and how much transferred to insurers. 758 PART VIII Risk Management 8 “Meet the Riskmongers,” The Economist, July 18, 1998, p. 93. 9 “Side bet” conjures up an image of wicked speculators. Derivatives attract their share of speculators, some of whom may be wicked, but they are also used by sober and prudent businesspeople to reduce risk. 10 We oversimplify. For example, the miller won’t reduce risk if bread prices vary in proportion to the postharvest wheat price. In this case the miller is in the hazardous position of having fixed her cost but not her selling price. This point is discussed in A. C. Shapiro and S. Titman, “An Integrated Approach to Corporate Risk Management,” Midland Corporate Finance Journal 3 (Summer 1985), pp. 41–56. 27.2 HEDGING WITH FUTURES Hedging involves taking on one risk to offset another. We will explain shortly how to set up a hedge, but first we will give some examples and describe some tools that are specially designed for hedging. These are futures, forwards, and swaps. To- gether with options, they are known as derivative instruments or derivatives because their value depends on the value of another asset. You can think of them as side bets on the value of the underlying asset. 9 We start with the oldest actively traded derivative instruments, futures con- tracts. Futures were originally developed for agricultural and other commodities. For example, suppose that a wheat farmer expects to have 100,000 bushels of wheat to sell next September. If he is worried that the price may decline in the interim, he can hedge by selling 100,000 bushels of September wheat futures. In this case he agrees to deliver 100,000 bushels of wheat in September at a price that is set today. Do not confuse this futures contract with an option, in which the holder has a choice whether to make delivery; the farmer’s futures contract is a firm promise to deliver wheat. A miller is in the opposite position. She needs to buy wheat after the harvest. If she would like to fix the price of this wheat ahead of time, she can do so by buying wheat futures. In other words, she agrees to take delivery of wheat in the future at a price that is fixed today. The miller also does not have an option; if she holds the contract to maturity, she is obliged to take delivery. Both the farmer and the miller have less risk than before. 10 The farmer has hedged risk by selling wheat futures; this is termed a short hedge. The miller has hedged risk by buying wheat futures; this is known as a long hedge. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII. Risk Management 27. Managing Risk © The McGraw−Hill Companies, 2003 The price of wheat for immediate delivery is known as the spot price. When the farmer sells wheat futures, the price that he agrees to take for his wheat may be very different from the spot price. But as the date for delivery approaches, a futures contract becomes more and more like a spot contract and the price of the future snuggles up to the spot price. The farmer may decide to wait until his futures contract matures and then de- liver wheat to the buyer. In practice such delivery is very rare, for it is more con- venient for the farmer to buy back the wheat futures just before maturity. 11 If he is properly hedged, any loss on his wheat crop will be exactly offset by the profit on his sale and subsequent repurchase of wheat futures. Commodity and Financial Futures Futures contracts are bought and sold on organized futures exchanges. Table 27.1 lists the principal commodity futures contracts and the exchanges on which they are traded. Notice that our farmer and miller are not the only businesses that can hedge CHAPTER 27 Managing Risk 759 Future Exchange Future Exchange Barley WPG Orange juice NYBOT Corn CBT, MCE Sugar LIFFE, NYBOT Oats CBT Wheat CBT, KC, MCE, MPLS Aluminum LME Copper COMEX, LME Gold COMEX Soybeans CBT, MCE Lead LME Soybean meal CBT Nickel LME Soybean oil CBT Silver COMEX Tin LME Live cattle CME Zinc LME Lean hogs CME Crude oil IPE, NYMEX Cocoa LIFFE, NYBOT Gas oil IPE Coffee LIFFE, NYBOT Heating oil NYMEX Cotton NYBOT Natural gas IPE, NYMEX Lumber CME Unleaded gasoline NYMEX TABLE 27.1 Some commodity futures and the principal exchanges on which they are traded. Key to abbreviations: CBT Chicago Board of Trade LME London Metal Exchange CME Chicago Mercantile Exchange MCE MidAmerica Commodity Exchange COMEX Commodity Exchange Division of NYMEX MPLS Minneapolis Grain Exchange IPE International Petroleum Exchange of London NYBOT New York Board of Trade KC Kansas City Board of Trade NYMEX New York Mercantile Exchange LIFFE London International Financial WPG Winnipeg Commodity Exchange Futures and Options Exchange 11 In the case of some of the financial futures described below, you cannot deliver the asset. At maturity the buyer simply receives (or pays) the difference between the spot price and the price at which he or she agreed to purchase the asset. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII. Risk Management 27. Managing Risk © The McGraw−Hill Companies, 2003 risk with commodity futures. The lumber company and the builder can hedge against changes in lumber prices, the copper producer and the cable manufacturer can hedge against changes in copper prices, the oil producer and the trucker can hedge against changes in gasoline prices, and so on. 12 For many firms the wide fluctuations in interest rates and exchange rates have become at least as important a source of risk as changes in commodity prices. Financial futures are similar to commodity futures, but instead of plac- ing an order to buy or sell a commodity at a future date, you place an order to buy or sell a financial asset at a future date. Table 27.2 lists some important fi- nancial futures. It is far from complete. You can trade futures on the Thailand stock market index, the South African rand, Finnish government bonds, and many other financial assets. Financial futures have been a remarkably successful innovation. They were in- vented in 1972; within a few years, trading in financial futures significantly ex- ceeded trading in commodity futures. 760 PART VIII Risk Management 12 By the time you read this, the list of futures contracts will almost certainly be out of date. Unsuccess- ful contracts are regularly dropped, and at any time the exchanges may be seeking approval for liter- ally dozens of new contracts. Future Exchange Future Exchange U.S. Treasury bonds CBT Dow Jones Industrial Average CBT U.S. Treasury notes CBT S&P 500 Index CME U.S. agency notes CBT European equity index (Dow Jones Eurex German government bonds (bunds) Eurex Euro Stoxx) Japanese government bonds (JGBs) Simex, TSE French equity index (CAC) MATIF British government bonds (gilts) LIFFE German equity index (DAX) Eurex Japanese equity index (Nikkei) CME, OSE, U.S. Treasury bills CME Simex UK equity index (FTSE) LIFFE LIBOR CME Individual stocks LIFFE Eurodollar deposits CME Euro CME Euroyen deposits CME, Simex, TIFFE Japanese yen CME TABLE 27.2 Some financial futures and the principal exchanges on which they are traded. Key to abbreviations: CBT Chicago Board of Trade CME Chicago Mercantile Exchange LIFFE London International Financial Futures and Options Exchange MATIF Marché à Terme d’Instruments Financiers OSE Osaka Securities Exchange SIMEX Singapore International Monetary Exchange TIFFE Tokyo International Financial Futures Exchange TSE Tokyo Stock Exchange Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII. Risk Management 27. Managing Risk © The McGraw−Hill Companies, 2003 The Mechanics of Futures Trading When you buy or sell a futures contract, the price is fixed today but payment is not made until later. You will, however, be asked to put up margin in the form of either cash or Treasury bills to demonstrate that you have the money to honor your side of the bargain. As long as you earn interest on the margined securities, there is no cost to you. In addition, futures contracts are marked to market. This means that each day any profits or losses on the contract are calculated; you pay the exchange any losses and receive any profits. For example, suppose that our farmer agreed to deliver 100,000 bushels of wheat at $2.80 a bushel. The next day the price of wheat futures declines to $2.75 a bushel. The farmer now has a profit on his sale of . The exchange’s clearinghouse therefore pays this $5,000 to the farmer. You can think of the farmer as closing out his position every day and then opening up a new position. Thus after the first day the farmer has realized a profit of $5,000 on his trade and now has an obligation to deliver wheat for $2.75 a bushel. The $.05 that the farmer has already been paid plus the $2.75 that remains to be paid equals the $2.80 selling price at which the farmer originally agreed to deliver wheat. Of course, our miller is in the opposite position. The fall in the futures price leaves her with a loss of $.05 a bushel. She must, therefore, pay over this loss to the exchange’s clearinghouse. In effect the miller closes out her initial purchase at a $.05 loss and opens a new contract to take delivery at $2.75 a bushel. 13 Spot and Futures Prices—Financial Futures If you want to buy a security, you have a choice. You can buy it for immediate de- livery at the spot price. Alternatively, you can place an order for later delivery; in this case you buy at the futures price. When you buy a financial future, you end up with exactly the same security that you would have if you bought in the spot mar- ket. However, there are two differences. First, you don’t pay for the security up front, and so you can earn interest on its purchase price. Second, you miss out on any dividend or interest that is paid in the interim. This tells us something about the relationship between the spot and futures prices: 14 Here is the t-period risk-free interest rate. An example will show how and why this formula works. Example: Stock Index Futures Suppose six-month stock index futures trade at 1,205 when the index is 1,190. The six-month interest rate is 4 percent, and the av- erage dividend yield of stocks in the index is 1.6 percent per year. Are these num- bers consistent? r f Futures price 11 ϩ r f 2 t ϭ spot price Ϫ PV q dividends or interest payments forgone r $ˇ .05 ϭ $ˇ 5,000 100,000 ϫ CHAPTER 27 Managing Risk 761 13 Notice that neither the farmer nor the miller need be concerned about whether the other party will honor his or her side of the bargain. The futures exchange guarantees the contract and protects itself by settling up profits and losses each day. 14 This relationship is strictly true only if the contract is not marked to market. Otherwise the value of the future depends on the path of interest rates up to the delivery date. In practice this qualification is usually unimportant. See J. C. Cox, J. E. Ingersoll, and S. A. Ross, “The Relationship between Forward and Futures Prices,” Journal of Financial Economics 9 (1981), pp. 321–346. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII. Risk Management 27. Managing Risk © The McGraw−Hill Companies, 2003 Suppose you buy the futures contract and set aside the money to exercise it. At a 4 percent annual rate, you’ll earn about 2 percent interest over the next six months. Thus you invest What do you get in return? Everything you would have gotten by buying the in- dex now at the spot price, except for the dividends paid over the next six months. If we assume, for simplicity, that a half-year’s dividends are paid in month six (rather than evenly over six months), your payoff is You get what you pay for. Spot and Futures Prices—Commodities The difference between buying commodities today and buying commodity futures is more complicated. First, because payment is again delayed, the buyer of the future earns interest on her money. Second, she does not need to store the commodities and, therefore, saves warehouse costs, wastage, and so on. On the other hand, the futures contract gives no convenience yield, which is the value of being able to get your hands on the real thing. The manager of a supermarket can’t burn heating oil futures if there’s a sudden cold snap, and he can’t stock the shelves with orange juice futures if he runs out of inventory at 1 P . M . on a Saturday. All this means that for commodities, No one would be willing to hold the futures contract at a higher futures price or to hold the commodity at a lower futures price. 15 It’s interesting to compare the formulas for futures prices of commodities to the formulas for securities. PV(convenience yield) plays the same role as PV(dividends or interest payments forgone). But financial assets cost nothing to store, so PV(stor- age costs) does not appear in the formula for financial futures. You can’t observe PV(convenience yield) or PV(storage) separately, but you can infer the difference between them by comparing the spot price to the discounted futures price. This difference—that is, convenience yield less storage cost—is called net convenience yield. Here is an example using quotes for August 2001. At that time the spot price of coffee was about 51 cents per pound. The futures price for March 2002 was 58.7 cents. Of course, if you bought and held the futures, you would not pay until March. The present value of this outlay is 57.4 cents, using a one-year interest rate of 4 percent. So PV(net convenience yield) is negative at 6.4 cents a pound: ϭ 51 Ϫ 57.4 ϭϪ6.4 cents PV1net convenience yield2ϭ spot price Ϫ futures price 1 ϩ r f Futures price 11 ϩ r f 2 t ϭ spot price ϩ PVa storage costs bϪPV a convenience yield b Spot price Ϫ PV1dividends2ϭ 1,190 Ϫ 1,190 1.0082 1.02 ϭ 1,181 Futures price 11 ϩ r f 2 t ϭ 1,205 1.02 ϭ 1,181 762 PART VIII Risk Management 15 Our formula could overstate the futures price if no one is willing to hold the commodity, that is, if in- ventories fall to zero or some absolute minimum. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII. Risk Management 27. Managing Risk © The McGraw−Hill Companies, 2003 Sometimes the net convenience yield is expressed as a percentage of the spot price, in this case as , or percent. Coffee in 2001 was in ample supply and evidently roasters had no worries that they would run short in the months ahead. Figure 27.1 plots percentage net convenience yields for crude oil and gas oil (used for heating). Notice how much the spread between the spot and futures price for gas oil bounces around. When there are shortages or fears of an inter- ruption of supply, traders may be prepared to pay 2 or more percent per week for the convenience of having oil in the tanks rather than the promise of future delivery. 16 There is one further complication that we should note. There are some com- modities that cannot be stored at all. You can’t store electricity, for example. As a result, electricity supplied in, say, six-months’ time is effectively a different com- modity from electricity available now, and there is no simple link between today’s price and that of a futures contract to buy or sell at the end of six months. Of course, Ϫ12.5Ϫ6.4/51 ϭϪ.125 CHAPTER 27 Managing Risk 763 16 For evidence that the net convenience yield is related to the level of inventories, see M. J. Brennan, “The Price of Convenience and the Valuation of Commodity Contingent Claims,” in D. Lund and B. Øksendal (eds.), Stochastic Models and Option Values, North-Holland Publishing Company, Amsterdam, 1991. Gas oil Crude oil 0 0.5 1 1.5 2 2.5 3 01/02/85 06/19/85 12/04/85 05/21/86 11/05/86 04/22/87 10/07/87 03/23/88 09/07/88 02/22/89 08/09/89 01/24/90 12/26/90 06/12/91 11/27/91 05/13/92 10/28/92 04/14/93 09/29/93 03/16/94 08/31/94 02/15/95 08/02/95 01/17/96 07/03/96 12/18/96 06/04/97 11/19/97 05/06/98 10/21/98 04/07/99 09/22/99 03/08/00 08/23/00 07/11/90 Weekly net convenience yields, percent FIGURE 27.1 Weekly percentage net convenience yield (convenience yield less storage costs) for two commodities. Source: R. S. Pindyck, “The Present Value Model of Rational Commodity Pricing,” Economic Journal 103 (May 1993), pp. 511–530. We thank Professor Pindyck for updating the data. [...]... ϭ We can also calculate the duration of Potterton’s new liabilities The duration of the 1-year debt is 1 year, and the duration of the 6-year debt is 4.6 years The duration of the package of 1- and 6-year debt is a weighted average of the durations of the individual issues: Duration of liability ϭ 11.91/9.942 ϫ duration of 1-year debt ϩ18.03/9.942 ϫ duration of 6-year debt ϭ 1.192 ϫ 12 ϩ 1.808 ϫ 4.62... event of X’s default 769 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition © The McGraw−Hill Companies, 2003 27 Managing Risk PART VIII Risk Management FIGURE 27. 2 Hypothetical plot of past changes in the price of the farmer’s wheat against changes in the price of Kansas City wheat futures A 1 percent change in the futures price implies, on average, an 8 percent change in the price of the... all profits or losses are settled when the contract matures Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII Risk Management © The McGraw−Hill Companies, 2003 27 Managing Risk CHAPTER 27 Managing Risk Forward interest rate ϭ 11 ϩ 2-year spot rate2 2 Ϫ1 1 ϩ 1-year spot rate 11.122 2 Ϫ 1 ϭ 1404, or 14.04% ϭ 1.10 In our example you manufactured a forward loan by borrowing short-term... find a package of loans that had a present value of $9.94 million and a duration of 3.9 years Call the proportion of the proceeds raised by the six-year loan x and the proportion raised by the one-year loan 11 Ϫ x2 Then Duration of ϭ 1x ϫ duration of 6-year loan2 ϩ 3 11 Ϫ x2 package ϫ duration of 1-year loan4 3.9 years ϭ 1x ϫ 4.6 years2 ϩ 3 11 Ϫ x2 ϫ 1 year4 x ϭ 808 Since the package of loans must... million of the six-year loan An important feature of this hedge is that it is dynamic As interest rates change and time passes, the duration of Potterton’s asset may no longer be the same as that of its liability Thus, to remain hedged against interest rate changes, Potterton must be prepared to keep adjusting the duration of its debt ˇ 771 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition. .. Edition VIII Risk Management © The McGraw−Hill Companies, 2003 27 Managing Risk CHAPTER 27 Managing Risk Potterton proposes to finance the deal by issuing a package of $1.91 million of one-year debt and $8.03 million of six-year debt, each with a 12 percent coupon Think of its new asset (the stream of rental income) and the new liability (the issue of debt) as a package Does Potterton stand to gain or lose... to the interest rate on the fixed leg of the swap Rates are generally quoted against LIBOR, though dealers will also be prepared to quote rates against other shortterm debt Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII Risk Management © The McGraw−Hill Companies, 2003 27 Managing Risk CHAPTER 27 Managing Risk example, if the yield on five-year Treasury notes is 5.25 percent,... 1/␦ options 31 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII Risk Management © The McGraw−Hill Companies, 2003 27 Managing Risk CHAPTER 27 Managing Risk Option deltas change as the stock price changes and time passes Therefore, optionbased hedges need to be adjusted frequently Options can be used to hedge commodities too The miller could offset changes in the cost of future wheat... on the price guarantees Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII Risk Management © The McGraw−Hill Companies, 2003 27 Managing Risk CHAPTER 27 Managing Risk and oil trading company, Metallgesellschaft, took a $1 billion bath on its positions in oil futures Metallgesellschaft had plenty of company The Japanese company, Showa Shell, reported a loss of $1.5 billion on positions... QUESTIONS Visit us at www.mhhe.com/bm7e Period 1 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 780 VIII Risk Management © The McGraw−Hill Companies, 2003 27 Managing Risk PART VIII Risk Management 10 If you buy a nine-month T-bill future, you undertake to buy a three-month bill in nine months’ time Suppose that Treasury bills and notes currently offer the following yields: Months to Maturity . Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII. Risk Management 27. Managing Risk © The McGraw−Hill Companies, 2003 CHAPTER TWENTY-SEVEN 754 MANAGING RISK Brealey−Meyers:. the value of B: Expected change in value of A ϭ a ϩ ␦ a change in value of B b .8 ϫ 100,000 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition VIII. Risk Management 27. Managing. duration of the 1-year debt is 1 year, and the duration of the 6-year debt is 4.6 years. The dura- tion of the package of 1- and 6-year debt is a weighted average of the durations of the individual