Part Eight: Risk Management

Managing Risk

Life is punctuated by unforeseen and unforeseeable shocks. Wars, banking and currency crises, political upheavals, pandemics, and natural catastrophes such as earthquakes and floods can all cause severe economic disruption. For example, if you want to make your hair stand on end, look at Table 26.1, which lists some of the greatest macroeconomic disasters in the past 100 years.¹

Major catastrophes such as those in Table 26.1 are, fortunately, rare. However, most companies are hit from time to time by potentially ruinous shocks. Good managers try to ensure that their companies are not overwhelmed by them. They check that their company has reserve borrowing power to tide them over difficult periods, they maintain sufficient liquid assets to protect the firm from a possible banking or currency crisis, and they ensure that the firm is not overly dependent on a single source of materials or a single outlet for its products.

Most of the time we take risk as God-given. A company’s cash flow is exposed to changes in demand, raw material costs, technology, and a seemingly endless list of other uncertainties. There’s nothing the manager can do about it other than to ensure that the business is not overwhelmed.

That’s not wholly true. The manager can avoid some risks. We have already come across one way to do so: Firms can use real options to provide flexibility. For example, a petrochemical plant that is designed to use either oil or natural gas as a feedstock reduces the risk of an unfavorable shift in the price of raw materials. As another example, think of a company that employs standard machine tools rather than custom machinery and thereby lowers the cost of bailing out if its products do not sell. In other words, the standard machinery provides the firm with a valuable abandonment option.

We covered real options in Chapter 22. This chapter explains how companies also use financial contracts to protect against various hazards. We discuss the pros and cons of corporate insurance policies that protect against specific risks, such as fire, floods, or environmental damage. We then describe forward and futures contracts, which can be used to lock in the future price of commodities such as oil, copper, or soybeans. Financial forward and futures contracts allow the firm to lock in the prices of financial assets such as interest rates or foreign exchange rates. We also describe swaps, which are packages of forward contracts.

Most of this chapter describes how financial contracts may be used to reduce business risks. But why bother? Why should shareholders care whether the company’s future profits are linked to future changes in interest rates, exchange rates, or commodity prices? We start the chapter with that question.

Country	Event	Trough Year	Decline in Real GDP per Head (%)
Argentina	Currency crisis	2002	–22
Chile	Pinochet revolution	1975	–24
Germany	Aftermath of WWII	1946	–74
Greece	WWII	1942	–66
Indonesia	Asian currency crisis	1999	–16
Japan	WWII	1944	–50
Russia	Revolution	1921	–62
Spain	Civil war	1938	–31
United States	Great depression	1933	–29
Venezuela	Maduro government	2018	–62Est

TABLE 26.1 Major economic disasters

26-1Why Manage Risk?

Financial transactions undertaken solely to reduce risk do not add value in perfect and efficient markets. Why not? There are two basic reasons.

· Reason 1: Hedging is a zero-sum game. A corporation that insures or hedges a risk does not eliminate it. It simply passes the risk to someone else. For example, suppose that a heating-oil distributor contracts with a refiner to buy all of next winter’s heating-oil deliveries at a fixed price. This contract is a zero-sum game because the refiner loses what the distributor gains, and vice versa.² If next winter’s price of heating oil turns out to be unusually high, the distributor wins from having locked in a below-market price, but the refiner is forced to sell below the market. Conversely, if the price of heating oil is unusually low, the refiner wins because the distributor is forced to buy at the high fixed price. Of course, neither party knows next winter’s price at the time that the deal is struck, but they consider the range of possible prices, and in an efficient market they negotiate terms that are fair (zero-NPV) on both sides of the bargain.

· Reason 2: Investors’ do-it-yourself alternative. Corporations cannot increase the value of their shares by undertaking transactions that investors can easily do on their own. When the shareholders in the heating-oil distributor made their investment, they were presumably aware of the risks of the business. If they did not want to be exposed to the ups and downs of energy prices, they could have protected themselves in several ways. Perhaps they bought shares in both the distributor and refiner, and do not care whether one wins next winter at the other’s expense.

Of course, shareholders can adjust their exposure only when companies keep investors fully informed of the transactions that they have made. For example, when a group of European central banks announced in 1999 that they would limit their sales of gold, the gold price immediately shot up. Investors in gold-mining shares rubbed their hands at the prospect of rising profits. But when they discovered that some mining companies had protected themselves against price fluctuations and would not benefit from the price rise, the hand-rubbing by investors turned to hand-wringing.³

Some stockholders of these gold-mining companies wanted to make a bet on rising gold prices; others didn’t. But all of them gave the same message to management. The first group said, “Don’t hedge! I’m happy to bear the risk of fluctuating gold prices, because I think gold prices will increase.” The second group said, “Don’t hedge! I’d rather do it myself.” We have seen this do-it-yourself principle before. Think of other ways that the firm could reduce risk. It could do so by diversifying, for example, by acquiring another firm in an unrelated industry. But we know that investors can diversify on their own, and so diversification by corporations is redundant.⁴

Corporations can also lessen risk by borrowing less. But we showed in Chapter 17 that just reducing financial leverage does not make shareholders any better or worse off, because they can instead reduce financial risk by borrowing less (or lending more) in their personal accounts. Modigliani and Miller (MM) proved that a corporation’s debt policy is irrelevant in perfect financial markets. We could extend their proof to say that risk management is also irrelevant in perfect financial markets.

Of course, in Chapter 18, we decided that debt policy is relevant, not because MM were wrong, but because of other things, such as taxes, agency problems, and costs of financial distress. The same line of argument applies here. If risk management affects the value of the firm, it must be because of “other things,” not because risk shifting is inherently valuable.

Let’s review the reasons that risk-reducing transactions can make sense in practice.⁵

Reducing the Risk of Cash Shortfalls or Financial Distress

Transactions that reduce risk make financial planning simpler and reduce the odds of an embarrassing cash shortfall. This shortfall might mean only an unexpected trip to the bank, but a financial manager’s worst nightmare is landing in a financial pickle and having to pass up a valuable investment opportunity for lack of funds. In extreme cases an unhedged setback could trigger financial distress or even bankruptcy.

Banks and bondholders recognize these dangers. They try to keep track of the firm’s risks, and before lending, they may require the firm to carry insurance or to implement hedging programs. Risk management and conservative financing are therefore substitutes, not complements. Thus, a firm might hedge part of its risk in order to operate safely at a higher debt ratio.

Smart financial managers make sure that cash (or ready financing) will be available if investment opportunities expand. That happy match of cash and investment opportunities does not necessarily require hedging, however. Let’s contrast two examples.

Cirrus Oil produces from several oil fields and also invests to find and develop new fields. Should it lock in future revenues from its existing fields by hedging oil prices? Probably not, because its investment opportunities expand when oil prices rise and contract when they fall. Locking in oil prices could leave it with too much cash when oil prices fall and too little, relative to its investment opportunities, when prices rise.

Cumulus Pharmaceuticals sells worldwide and half of its revenues are received in foreign currencies. Most of its R&D is done in the United States. Should it hedge at least some of its foreign exchange exposure? Probably yes, because pharmaceutical R&D programs are very expensive, long-term investments. Cumulus can’t turn its R&D program on or off depending on a particular year’s earnings, so it may wish to stabilize cash flows by hedging against fluctuations in exchange rates.

Agency Costs May Be Mitigated by Risk Management

In some cases, hedging can make it easier to monitor and motivate managers. Suppose your confectionery division delivers a 60% profit increase in a year when cocoa prices fall by 12%. Does the division manager deserve a stern lecture or a pat on the back? How much of the profit increase is due to good management and how much to lower cocoa prices? If the cocoa prices were hedged, it’s probably good management. If they were not hedged, you will have to sort things out with hindsight, probably by asking, “What would profits have been if cocoa prices had been hedged?”

The fluctuations in cocoa prices are outside the manager’s control. But she will surely worry about cocoa prices if her bottom line and bonus depend on them. Hedging prices ties her bonus more closely to risks that she can control and allows her to spend worrying time on these risks.

Hedging external risks that would affect individual managers does not necessarily mean that the firm ends up hedging. Some large firms allow their operating divisions to hedge away risks in an internal “market.” The internal market operates with real (external) market prices, transferring risks from the division to the central treasurer’s office. The treasurer then decides whether to hedge the firm’s aggregate exposure.

This sort of internal market makes sense for two reasons. First, divisional risks may cancel out. For example, your refining division may benefit from an increase in heating-oil prices at the same time that your distribution division suffers. Second, because operating managers do not trade actual financial contracts, there is no danger that the managers will cause the firm to take speculative positions. For example, suppose that profits are down late in the year, and hope for end-year bonuses is fading. Could you be tempted to make up the shortfall with a quick score in the cocoa futures market? Well . . . not you, of course, but you can probably think of some acquaintances who would try just one speculative fling.

The dangers of permitting operating managers to make real speculative trades should be obvious. The manager of your confectionery division is an amateur in the cocoa futures market. If she were a skilled professional trader, she would probably not be running chocolate factories.⁶

Risk management requires some degree of centralization. These days many companies appoint a chief risk officer to develop a risk strategy for the company as a whole. The risk manager needs to come up with answers to the following questions:

1. What are the major risks that the company is facing and what are the possible consequences? Some risks are scarcely worth a thought, but there are others that might cause a serious setback or even bankrupt the company.

2. Is the company being paid for taking these risks? Managers are not paid to avoid all risks, but if they can reduce their exposure to risks for which there are no corresponding rewards, they can afford to place larger bets when the odds are stacked in their favor.

3. How should risks be controlled? Should the company reduce risk by building extra flexibility into its operations? Should it change its operating or financial leverage? Or should it insure or hedge against particular hazards?

The Evidence on Risk Management

Which firms use financial contracts to manage risk? Almost all do to some extent. For example, they may have contracts that fix prices of raw materials or output, at least for the near future. Most take out insurance policies against fire, accidents, and theft. In addition, as we shall see, managers employ a variety of specialized tools for hedging risk. These are known collectively as derivatives. A survey of the world’s 500 largest companies found that most of them use derivatives to manage their risk.⁷ Eighty-three percent of the companies employ derivatives to control interest rate risk. Eighty-eight percent use them to manage currency risk, and 49% to manage commodity price risk.

Risk policies differ. For example, some natural resource companies work hard to hedge their exposure to price fluctuations; others shrug their shoulders and let prices wander as they may. Explaining why some hedge and others don’t is not easy. Peter Tufano’s study of the gold-mining industry suggests that managers’ personal risk aversion may have something to do with it. Hedging of gold prices appears to be more common when top management has large personal shareholdings in the company. It is less common when top management holds lots of stock options. (Remember that the value of an option falls when the risk of the underlying security is reduced.) David Haushalter’s study of oil and gas producers found the firms that hedged the most had high debt ratios, no debt ratings, and low dividend payouts. It seems that for these firms hedging programs were designed to improve the firms’ access to debt finance and to reduce the likelihood of financial distress.⁸

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Derivatives usage

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26-2Insurance

Most businesses buy insurance against a variety of hazards—the risk that their plants will be damaged by fire; that their ships, planes, or vehicles will be involved in accidents; that the firm will be held liable for environmental damage; and so on.

When a firm takes out insurance, it is simply transferring the risk to the insurance 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 policies. 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 market or macroeconomic risks; firms generally use insurance policies to reduce their diversifiable 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 in a storm. Thus, the expected loss from storm damage is $1 billion/10,000 = $100,000.

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.⁹ Such a premium would make insurance a zero-NPV deal for your company. Unfortunately, no insurance company 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 exam 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 or require the owners to share any losses.

· 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.

The extreme forms of adverse selection and moral hazard (like the fire in the farmer’s barn) are rarely encountered in professional corporate finance. But these problems arise in more subtle ways. That oil platform may not be a “bad risk,” but the oil company knows more about the platform’s weaknesses than the insurance company does. The oil company will not purposely scuttle the platform, but once insured it could be tempted to save on maintenance or structural reinforcements. Thus, the insurance company may end up paying for engineering studies or for a program to monitor maintenance. All these costs are rolled into the insurance premium.

When the costs of administration, adverse selection, and moral hazard are small, insurance may be close to a zero-NPV transaction. When they are large, insurance is a costly way to protect against risk.

Many insurance risks are jump risks; one day there is not a cloud on the horizon and the next day the hurricane hits. The risks can also be huge. For example, the attack on the World Trade Center on September 11, 2001, cost insurance companies about $36 billion; the Japanese tsunami involved payments of $35–$40 billion; Hurricanes Katrina, Harvey, and Irma are each estimated to cost companies in excess of $40 billion.

If the losses from such disasters can be spread more widely, the cost of insuring them should decline. Therefore, insurance companies have been looking for ways to share catastrophic risks with investors. One solution is for the companies to issue catastrophe bonds (or Cat bonds). If a catastrophe occurs, the payment on a Cat bond is reduced or eliminated.¹⁰ For example, in 2017, the insurance company, Swiss Re, issued $925 million worth of Cat bonds. The bonds cover the company for three years against any losses from earthquakes in California.

26-3Reducing Risk with Options

Managers regularly buy options on currencies, interest rates, and commodities to limit downside risk. Consider, for example, the problem faced by the Mexican government. A hefty portion of its revenue comes from Pemex, the state-owned oil company. So, when oil prices fall, the government may be compelled to reduce its planned spending.

The government’s solution has been to arrange an annual hedge against a possible fall in the oil price. Although the details of its hedging program are a closely guarded secret, it is reported that in 2017 the Mexican government bought put options that gave it the right to sell about 250 million barrels of oil over the coming year at an exercise price of $46 per barrel. If oil prices rose above this figure, Mexico would reap the benefit. But if oil prices fell below $46, the payoff to the put options would exactly offset the revenue shortfall. In effect, the options put a floor of $46 a barrel on the value of its oil. Of course, the hedge did not come free. The Mexican government was said to have spent $1.25 billion to buy the contracts from a group of international banks.

Figure 26.1 illustrates the nature of Mexico’s insurance strategy. Panel a shows the revenue derived from selling 250 million barrels of oil. As the price of oil rises or falls, so do the government’s revenues. Panel b shows the payoffs to the government’s options to sell 250 million barrels at $46 a barrel. The payoff on these options rises as oil prices fall below $46 a barrel. This payoff exactly offsets any decline in oil revenues. Panel c shows the government’s total revenues after buying the put options. For prices below $46 per barrel, revenues are fixed at 250 × $46 = $11,500 million. But for every dollar that oil prices rise above $46, revenues increase by $250 million. The profile in panel c should be familiar to you. It represents the payoffs to the protective put strategy that we first encountered in Section 20-2.¹¹

FIGURE 26.1 How put options protected Mexico against a fall in oil prices

26-4Forward and Futures Contracts

Hedging involves taking on one risk to offset another. It potentially removes all uncertainty, eliminating the chance of both happy and unhappy surprises. We explain shortly how to set up a hedge, but first we give some examples and describe some tools that are specially designed for hedging. These are forwards, futures, and swaps. Together with options, they are known as derivative instruments or derivatives because their value depends on the value of another asset.

A Simple Forward Contract

We start with an example of a simple forward contract. Arctic Fuels, the heating-oil distributor, plans to deliver one million gallons of heating oil to its retail customers next January. Arctic worries about high heating-oil prices next winter and wants to lock in the cost of buying its supply. Northern Refineries is in the opposite position. It will produce heating oil next winter, but doesn’t know what the oil can be sold for. So the two firms strike a deal: Arctic Fuels agrees in September to buy one million gallons from Northern Refineries at $2.40 per gallon, to be paid on delivery in January. Northern agrees to sell and deliver one million gallons to Arctic in January at $2.40 per gallon.

Arctic and Northern are now the two counterparties in a forward contract. The forward price is $2.40 per gallon. This price is fixed today, in September in our example, but payment and delivery occur later. (The price for immediate delivery is called the spot price.) Arctic, which has agreed to buy in January, has the long position in the contract. Northern Refineries, which has agreed to sell in January, has the short position.

We can think of each counterparty’s long and short positions in balance-sheet format, with long positions on the left (asset) side and short positions on the right (liability) side.

Northern Refineries starts with a long position because it will produce heating oil. Arctic Fuels starts with a short position, because it will have to buy to supply its customers. The forward contract creates an offsetting short position for Northern Refineries and an offsetting long position for Arctic Fuels. The offsets mean that each counterparty ends up locking in a price of $2.40, regardless of what happens to future spot prices.

Do not confuse this forward contract with an option. Arctic does not have the option to buy. It has committed to buy at $2.40 per gallon, even if spot prices in January turn out much lower than this. Northern does not have the option to sell. It cannot back away from the deal, even if spot prices for delivery in January turn out much higher than $2.40 per gallon. Note, however, that both the distributor and refiner have to worry about counterparty risk, that is, the risk that the other party will not perform as promised.

We confess that our heating oil example glossed over several complications. For example, we assumed that the risk of both companies is reduced by locking in the price of heating oil. But suppose that the retail price of heating oil moves up and down with the wholesale price. In that case the heating-oil distributor is naturally hedged because costs and revenues move together. Locking in costs with a futures contract could actually make the distributor’s profits more volatile.

BEYOND THE PAGE

The pros and cons of hedging airline fuel costs

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Futures Exchanges

Our heating-oil distributor and refiner do not have to negotiate a one-off, bilateral contract. Each can go to an exchange where standardized forward contracts on heating oil are traded. The distributor would buy contracts and the refiner would sell.

Here we encounter some tricky vocabulary. When a standardized forward contract is traded on an exchange, it is called a futures contract—same contract, but a different label. The exchange is called a futures exchange. The distinction between “futures” and “forward” does not apply to the contract, but to how the contract is traded. We describe futures trading in a moment.

Table 26.2 lists a few of the most important commodity futures contracts and the exchanges on which they are traded.¹² Our refiner and distributor can trade heating-oil futures on the New York Mercantile Exchange (NYMEX). A forest products company and a home-builder can trade lumber futures on the Chicago Mercantile Exchange (CME). A wheat farmer and a miller can trade wheat futures on the Chicago Board of Trade (CBOT) or on a smaller regional exchange.

Future	Exchange	Future	Exchange
Corn	CBOT, DCE	Aluminum	LME, SHFE
Wheat	CBOT	Copper	COMEX, LME, MCX, SHFE
		Gold	COMEX, MCX
Palm oil	CME, DCE	Lead	LME, MCX
Soybeans	CBOT, TGE	Nickel	LME, MCX
Soybean meal	CBOT, DCE	Silver	COMEX, MCX, TOCOM
Soybean oil	CBOT, DCE	Tin	LME
		Zinc	LME, MCX, SHFE
Live cattle	CME
Lean hogs	CME	Crude oil	ICE, MCX, NYMEX, TOCOM
		Gas oil	ICE, NFX
Cocoa	ICE, NYMEX	Heating oil	ICE, NYMEX
Coffee	ICE	Natural gas	ICE, NYMEX
Cotton	ICE	Unleaded gasoline	ICE, NYMEX, TOCOM
Lumber	CME
Orange juice	ICE	Electricity	NYMEX
Rubber	SHFE, TOCOM
Sugar	ICE, NYMEX, Z

TABLE 26.2 Some important commodity futures and some of the exchanges on which they are traded

Key to abbreviations:

CBOT	Chicago Board of Trade (part of CME Group)
CME	Chicago Mercantile Exchange
COMEX	Commodity Exchange Division (part of CME Group)
DCE	Dalian Commodity Exchange (China)
ICE	Intercontinental Exchange
LME	London Metal ExchangeTGE
NFX	Nasdaq FuturesTOCOM
MCX	Multi Commodity Exchange (India)
NYMEX	New York Mercantile Exchange (part of CME Group)
SHFE	Shanghai Futures Exchange
TGE	Tokyo Grain Exchange
TOCOM	Tokyo Commodity Exchange
ZCE	Zhengzhou Commodity Exchange (China)

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 placing 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 26.3 lists some important financial futures. Like Table 26.2 it is far from complete. For example, you can also trade futures on the Thai stock market index, the Chilean peso, Spanish government bonds, and many other financial assets.

Future	Exchange	Future	Exchange
U.S. Treasury bonds	CBOT	U.S. house prices	CME
U.S. Treasury notes	CBOT
German government bonds (bunds)	Eurex, ICE	S&P 500 Index	CME
Japanese government bonds (JGBs)	CME, JPX, SGX	French equity index (CAC)	Euronext
British government bonds (gilts)	ICE	German equity index (DAX)	Eurex
U.S. Treasury bills	CME	Japanese equity index (Nikkei)	CME, JPX, SGX
		U.K. equity index (FTSE)	ICE
LIBOR	CME	Euro	CME, Eurex
Euribor	CME, ICE	Japanese yen	CME
Eurodollar deposits	CME, ICE
Euroyen deposits	CME, SGX, TFX	Bitcoins	CBOE, CME

TABLE 26.3 Some important financial futures and some of the exchanges on which they are traded

Key to abbreviations:

CBOE	CBOE Global Markets
CBOT	Chicago Board of Trade (part of CME Group)
CME	Chicago Mercantile Exchange
Eurex	Eurex Exchange
ICE	Intercontinental Exchange
JPX	Japan Exchange Group
SGX	Singapore Exchange
TFX	Tokyo Financial Futures Exchange

Almost every day, some new futures contract seems to be invented. At first, there may be just a few private deals between a bank and its customers, but if the idea proves popular, one of the futures exchanges will try to muscle in on the business. For example, in 2017 the Chicago Mercantile Exchange and the CBOE Futures Exchange began to offer futures contracts on the bitcoin.

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 in September Arctic Fuels buys 1 million gallons of January heating-oil futures contracts at a futures price of $2.40 per gallon. The next day the price of the January contract increases to $2.44 per gallon. Arctic now has a profit of $.04 × 1,000,000 = $40,000. The exchange’s clearinghouse therefore pays $40,000 into Arctic’s margin account. If the price then drops back to $2.42, Arctic’s margin account pays $20,000 back to the clearing house.

Of course, Northern Refineries is in the opposite position. Suppose it sells 1 million gallons of January heating-oil futures contracts at a futures price of $2.40 per gallon. If the price increases to $2.44 cents per gallon, it loses $.04 × 1,000,000 = $40,000 and must pay this amount into the clearinghouse. Notice that neither the distributor nor the refiner has to worry about whether the other party will honor the other side of the bargain. The futures exchange guarantees the contracts and protects itself by settling up profits or losses each day. Futures trading eliminates counterparty risk.

Now consider what happens over the life of the futures contract. We’re assuming that Arctic and Northern take offsetting long and short positions in the January contract (not directly with each other, but with the exchange). Suppose that a severe cold snap pushes the spot price of heating oil in January up to $2.60 per gallon. Then the futures price at the end of the contract will also be $2.60 per gallon.¹³ So Arctic gets a cumulative profit of (2.60 − 2.40) × 1,000,000 = $200,000. It can take delivery of 1 million gallons, paying $2.60 per gallon, or $2,600,000. Its net cost, counting the profits on the futures contract, is $2,600,000 − 200,000 = $2,400,000, or $2.40 per gallon. Thus it has locked in the $2.40 per gallon price quoted in September when it first bought the futures contract. You can easily check that Arctic’s net cost always ends up at $2.40 per gallon, regardless of the spot price and ending futures price in January.

Northern Refineries suffers a cumulative loss on the futures contract of $200,000 if the January price is $2.60. That’s the bad news; the good news is that it can sell and deliver heating oil for $2.60 per gallon. Its net revenues are $2,600,000 − 200,000 = $2,400,000, or $2.40 per gallon, the futures price in September. Again, you can easily check that Northern’s net selling price always ends up at $2.40 per gallon.

Taking delivery directly from an exchange can be costly and inconvenient. For example, the NYMEX heating-oil contract calls for delivery in New York Harbor. Arctic Fuels will be better off taking delivery from a local source such as Northern Refineries. Northern Refineries will likewise be better off delivering heating oil locally than shipping it to New York. Therefore, both parties will probably close out their futures positions just before the end of the contract, and take their profits or losses.¹⁴ Nevertheless the NYMEX futures contract has allowed them to hedge their risks.

The effectiveness of this hedge depends on the correlation between changes in heating-oil prices locally and in New York Harbor. Prices in both locations will be positively correlated because of a common dependence on world energy prices. But the correlation is not perfect. What if a local cold snap hits Arctic Fuels’s customers but not New York? A long position in NYMEX futures won’t hedge Arctic Fuels against the resulting increase in the local spot price. This is an example of basis risk. We return to the problems created by basis risk later in this chapter.

Trading and Pricing Financial Futures Contracts

Financial futures trade in the same way as commodity futures. Suppose your firm’s pension fund manager thinks that the French stock market will outperform other European markets over the next six months. She forecasts a 10% six-month return. How can she place a bet? She can buy French stocks, of course. But she could also buy futures contracts on the CAC index of French stocks, which are traded on the Euronext exchange. Suppose she buys 15 six-month futures contracts at 5,000. Each contract pays off 10 times the level of the index, so she has a long position of 15 × 10 × 5,000 = €750,000. This position is marked to market daily. If the CAC goes up, the exchange puts the profits into your fund’s margin account; if the CAC falls, the margin account falls too. If your pension manager is right about the French market, and the CAC ends up at 5,500 after six months, then your fund’s cumulative profit on the futures position is 15 × (5,500 − 5,000) × 10 = €75,000.

If you want to buy a security, you have a choice. You can buy for immediate delivery at the spot price, or you can “buy forward” by placing an order for future delivery at the futures price. You end up with the same security either way, but there are two differences. First, if you buy forward, you don’t pay up front, and so you can earn interest on the purchase price.¹⁵ Second, you miss out on any interest or dividend that is paid in the meantime. This tells us the relationship between spot and futures prices:

F_t = S₀ (1 + r_f − y₎ ^t

where F_t is the futures price for a contract lasting t periods, S₀ is today’s spot price, r_f is the risk-free interest rate, and y is the dividend yield or interest rate.¹⁶ The following example shows how and why this formula works.

EXAMPLE 26.1 Valuing Index Futures

Suppose that the six-month CAC futures contract trades at 5,000 when the current (spot) CAC index is 5,045.41. The interest rate is 1% per year (about .5% over six months) and the dividend yield on the index is 2.8 (about 1.4% over six months). These numbers fit the formula perfectly because

F_t = 5,045.41 × (1 + .005 − .014) = 5,000

But why are the numbers consistent?

Suppose you just buy the CAC index for 5,045.41 today. Then in six months, you will own the index and also have dividends of .014 × 5,045.41 = 70.64. But you decide to buy a futures contract for 5,000 instead, and you put €5,045.41 in the bank. After six months, the bank account has earned interest at .5%, so you have 5,045.41 × 1.005 = 5,070.64, enough to buy the index for 5,000 with €70.64 left over—just enough to cover the dividend you missed by buying futures rather than spot. You get what you pay for.¹⁷

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.

Let’s express storage costs and convenience yield as fractions of the spot price. For commodities, the futures price for t periods ahead is¹⁸

F_t = S₀ (1 × r_f + storage costs − convenience yield₎ ^t

It’s interesting to compare this formula with the formula for a financial future. Convenience yield plays the same role as dividends or interest foregone (y) on securities. But financial assets cost nothing to store, and storage costs do not appear in the formula for financial futures.

Usually, you can’t observe storage cost or convenience yield, but you can infer the difference between them by comparing spot and futures prices. This difference—that is, convenience yield less storage cost—is called net convenience yield (net convenience yield = convenience yield − storage costs).

EXAMPLE 26.2 Calculating Net Convenience Yield

In December 2017, the spot price of crude oil was $57.57 a barrel and the six-month futures price was $56.91 per barrel. The interest rate was about 1.2% for six months. Thus

So net convenience yield was positive, that is, net convenience yield = convenience yield − storage costs = .0235 or 2.35% over six months, equivalent to an annual net convenience yield of 4.8%. Evidently the convenience yield from having crude oil in the storage tanks was slightly greater than the storage cost of those inventories.

Figure 26.2 plots the annualized net convenience yield for crude oil since 1983. Notice how much the spread between the spot and futures price can bounce around. When there are shortages or fears of an interruption of supply, traders may be prepared to pay a hefty premium for the convenience of having inventories of crude oil rather than the promise of future delivery. The reverse is true when storage tanks are full to the brim as in 2016.

FIGURE 26.2 Annualized percentage net convenience yield (convenience yield less storage costs) for crude oil

Source: www.quandl.com.

There is one further complication that we should note. There are some commodities that cannot be stored at all. You cannot easily store electricity, for example. As a result, electricity supplied in, say, six-months’ time is a different commodity 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, generators and electricity users will have their own views of what the spot price is likely to be, and the futures price will reveal these views to some extent.¹⁹

More about Forward Contracts

Each day, billions of dollars of futures contracts are bought and sold. This liquidity is possible only because futures contracts are standardized and mature on a limited number of dates each year.

Fortunately, there is usually more than one way to skin a financial cat. If the terms of futures contracts do not suit your particular needs, you may be able to buy or sell a tailor-made forward contract. The main forward market is in foreign currency. We discuss this market in Chapter 27.

It is also possible to enter into a forward interest rate contract. For example, suppose you know that at the end of three months you are going to need a six-month loan. If you are worried that interest rates will rise over the three-month period, you can lock in the interest rate on the loan by buying a forward rate agreement (FRA) from a bank.²⁰ For example, the bank might sell you a 3-against-9 month (or 3 × 9) FRA at 7%. If, at the end of three months, the six-month interest rate is higher than 7%, then the bank will make up the difference;²¹ if it is lower, then you must pay the bank the difference.²²

Homemade Forward Rate Contracts

Suppose that you borrow $90.91 for one year at 10% and lend $90.91 for two years at 12%. These interest rates are for loans made today; therefore, they are spot interest rates.

The cash flows on your transactions are as follows:

	Year 0	Year 1	Year 2
Borrow for 1 year at 10%	+90.91	−100
Lend for 2 years at 12%	−90.91		+114.04
Net cash flow	0	−100	+114.04

Notice that you do not have any net cash outflow today but you have contracted to pay out money in year 1. The interest rate on this forward commitment is 14.04%. To calculate this forward interest rate, we simply worked out the extra return for lending for two years rather than one:

In our example, you manufactured a forward loan by borrowing short term and lending long. But you can also run the process in reverse. If you wish to fix today the rate at which you borrow next year, you borrow long and lend the money until you need it next year.

26-5Swaps

Some company cash flows are fixed. Others vary with the level of interest rates, rates of exchange, prices of commodities, and so on. These characteristics may not always result in the desired risk profile. For example, a company that pays a fixed rate of interest on its debt might prefer to pay a floating rate, while another company that receives cash flows in euros might prefer to receive them in yen. Swaps allow them to change their risk in these ways.

The market for swaps is huge. In 2017, the total notional amount of interest rate and currency swaps outstanding was more than $300 trillion. By far, the major part of this figure consisted of interest rate swaps.²³ We therefore show first how interest rate swaps work and then describe a currency swap. We conclude with a brief look at some other types of swap.

Interest Rate Swaps

Friendly Bancorp has made a five-year, $50 million loan to fund part of the construction cost of a large cogeneration project. The loan carries a fixed interest rate of 8%. Annual interest payments are therefore $4 million. Interest payments are made annually, and all the principal will be repaid at year 5.

Suppose that instead of receiving fixed interest payments of $4 million a year, the bank would prefer to receive floating-rate payments. It can do so by swapping the $4 million, five-year annuity (the fixed interest payments) into a five-year floating-rate annuity. We show first how Friendly Bancorp can make its own homemade swap. Then we describe a simpler procedure.

The bank (we assume) can borrow at a 6% fixed rate for five years.²⁴ Therefore, the $4 million interest it receives can support a fixed-rate loan of 4/.06 = $66.67 million. The bank can now construct the homemade swap as follows: It borrows $66.67 million at a fixed interest rate of 6% for five years and simultaneously lends the same amount at LIBOR. We assume that LIBOR is initially 5%.²⁵ LIBOR is a short-term interest rate, so future interest receipts will fluctuate as the bank’s investment is rolled over.

The net cash flows to this strategy are shown in the top portion of Table 26.4. Notice that there is no net cash flow in year 0 and that in year 5 the principal amount of the short-term investment is used to pay off the $66.67 million loan. What’s left? A cash flow equal to the difference between the interest earned (LIBOR × 66.67) and the $4 million outlay on the fixed loan. The bank also has $4 million per year coming in from the project financing, so it has transformed that fixed payment into a floating payment keyed to LIBOR.

TABLE 26.4 The top panel shows the cash flows in millions of dollars to a homemade fixed-to-floating interest rate swap. The bottom panel shows the cash flows to a standard swap transaction.

Of course, there’s an easier way to do this, shown in the bottom portion of Table 26.3. The bank can just enter into a five-year swap.²⁶ Naturally, Friendly Bancorp takes this easier route. Let’s see what happens.

Friendly Bancorp calls a swap dealer, which is typically a large commercial or investment bank, and agrees to swap the payments on a $66.67 million fixed-rate loan for the payments on an equivalent floating-rate loan. The swap is known as a fixed-to-floating interest rate swap and the $66.67 million is termed the notional principal amount of the swap. Friendly Bancorp and the dealer are the counterparties to the swap.

The dealer is quoting a rate for five-year swaps of 6% against LIBOR.²⁷ This figure is sometimes quoted as a spread over the yield on U.S. Treasuries. For example, if the yield on five-year Treasury notes is 5.25%, the swap spread is .75%.

The first payment on the swap occurs at the end of year 1 and is based on the starting LIBOR rate of 5%.²⁸ The dealer (who pays floating) owes the bank 5% of $66.67 million, while the bank (which pays fixed) owes the dealer $4 million (6% of $66.67 million). The bank, therefore, makes a net payment to the dealer of 4 − (.05 × 66.67) = $.67 million:

Bank		0.05 × $66.67 = $3.33		Counterparty
Bank		$4		Counterparty
Bank		Net = $0.67		Counterparty

The second payment is based on LIBOR at year 1. Suppose it increases to 6%. Then the net payment is zero:

Bank		0.06 × $66.67 = $4		Counterparty
Bank		$4		Counterparty
Bank		Net = 0		Counterparty

The third payment depends on LIBOR at year 2, and so on.

The notional value of this swap is $66.67 million. The fixed and floating interest rates are multiplied by the notional amount to calculate dollar amounts of fixed and floating interest. But the notional value vastly overstates the economic value of the swap. At creation, the economic value of the swap is zero because the NPV of the cash flows to each counterparty is zero. The NPV drifts away from zero as time passes and interest rates change. But the economic value will always be far less than notional value. Careless references to notional values give the impression that swap markets are impossibly gigantic; in fact, they are merely very large.

The economic value of a swap depends on the path of long-term interest rates. For example, suppose that after two years, interest rates are unchanged, so a 6% note issued by the bank would continue to trade at its face value. In this case, the swap still has zero value. (You can confirm this by checking that the NPV of a new three-year homemade swap is zero.) But if long rates increase over the two years to 7% (say), the value of a three-year note falls to

Now the fixed payments that the bank has agreed to make are less valuable and the swap is worth 66.67 − 64.92 = $1.75 million.

How do we know the swap is worth $1.75 million? Consider the following strategy:

1. The bank can enter a new three-year swap deal in which it agrees to pay LIBOR on the same notional principal of $66.67 million.

2. In return it receives fixed payments at the new 7% interest rate, that is, .07 × 66.67 = $4.67 per year.

The new swap cancels the cash flows of the old one, but it generates an extra $.67 million for three years. This extra cash flow is worth

Remember, ordinary interest rate swaps have no initial cost or value (NPV = 0), but their value drifts away from zero as time passes and long-term interest rates change. One counter-party wins as the other loses.

In our example, the swap dealer loses from the rise in interest rates. Dealers will try to hedge the risk of interest rate movements by engaging in a series of futures or forward contracts or by entering into an offsetting swap with a third party. As long as Friendly Bancorp and the other counterparty honor their promises, the dealer is fully protected against risk. The recurring nightmare for swap managers is that one party will default, leaving the dealer with a large unmatched position. This is another example of counterparty risk.

The market for interest rate swaps is large and liquid. Consequently, financial analysts often look at swap rates when they want to know how interest rates vary with maturity. For example, Figure 26.3 shows swap rates in December 2017 for the U.S. dollar, the euro, and the British pound. You can see that in each country, long-term interest rates are much higher than short-term rates, though the level of swap rates varies from one country to another.

FIGURE 26.3 Swap curves for three currencies, December 2017

Currency Swaps

We now look briefly at an example of a currency swap.

Suppose that the Possum Company needs 11 million euros to help finance its European operations. We assume that the euro interest rate is about 5%, whereas the dollar rate is about 6%. Since Possum is better known in the United States, the financial manager decides not to borrow euros directly. Instead, the company issues $10 million of five-year 6% notes in the United States. Then it arranges with a counterparty to swap this dollar loan into euros. Under this arrangement the counterparty agrees to pay Possum sufficient dollars to service its dollar loan, and in exchange Possum agrees to make a series of annual payments in euros to the counterparty.

Here are Possum’s cash flows (in millions):

Look first at the cash flows in year 0. Possum receives $10 million from its issue of dollar notes, which it then pays over to the swap counterparty. In return the counterparty sends Possum a check for €8 million. (We assume that at current rates of exchange $10 million is worth €8 million.)

Now move to years 1 through 4. Possum needs to pay interest of 6% on its debt issue, which works out at .06 × 10 = $.6 million. The swap counterparty agrees to provide Possum each year with sufficient cash to pay this interest and in return Possum makes an annual payment to the counterparty of 5% of €8 million, or €.4 million. Finally, in year 5 the swap counterparty pays Possum enough to make the final payment of interest and principal on its dollar notes ($10.6 million), while Possum pays the counterparty €8.4 million.

The combined effect of Possum’s two steps (line 3) is to convert a 6% dollar loan into a 5% euro loan. You can think of the cash flows for the swap (line 2) as a series of contracts to buy euros in years 1 through 5. In each of years 1 through 4 Possum agrees to purchase $.6 million at a cost of .4 million euros; in year 5 it agrees to buy $10.6 million at a cost of 8.4 million euros.²⁹

Some Other Swaps

While interest rate and currency swaps are the most popular type of contract, there is a wide variety of other possible swaps or related contracts. For example, in Chapter 23 we encountered credit default swaps that allow investors to insure themselves against the default on a corporate bond.

Inflation swaps allow a company to protect against inflation risk. One party in the swap receives a fixed payment while the other receives a payment that is linked to the rate of inflation. In effect, the swap creates a made-to-measure inflation-linked bond, which can be of any maturity.³⁰

You can also enter into a total return swap where one party (party A) makes a series of agreed payments and the other (party B) pays the total return on a particular asset. This asset might be a common stock, a loan, a commodity, or a market index. For example, suppose that B owns $10 million of IBM stock. It now enters into a two-year swap agreement to pay A each quarter the total return on this stock. In exchange A agrees to pay B interest of LIBOR + 1%. B is known as the total return payer and A is the total return receiver. Suppose LIBOR is 5%. Then A owes B 6% of $10 million, or about 1.5% a quarter. If IBM stock returns more than this, there will be a net payment from B to A; if the return is less than 1.5%, A must make a net payment to B. Although ownership of the IBM stock does not change hands, the effect of this total return swap is the same as if B had sold the asset to A and bought it back at an agreed future date.

26-6How to Set Up a Hedge

There can be many ways to hedge a risk exposure. Some hedges are zero maintenance: Once established, the financial manager can walk away and worry about other matters. Other hedges are dynamic: They work only if adjusted at frequent intervals.

The forward contract between Northern Refineries and Arctic Fuels, which we described in Section 26-4, was zero maintenance because each counterparty locked in the price of heating oil at $2.40 per gallon, regardless of the future path of heating-oil prices. Now we look at an example where the financial manager will probably implement a dynamic hedge.

Hedging Interest Rate Risk

Potterton Leasing has acquired a warehouse and leased it to a manufacturer for fixed payments of $2 million per year for 20 years. The lease cannot be canceled by the manufacturer, so Potterton has a safe, debt-equivalent asset. The interest rate is 10%, and we ignore taxes for simplicity. The PV of Potterton’s rental income is $17 million:

The lease exposes Potterton to interest rate risk. If interest rates increase, the PV of the lease payments falls. If interest rates decrease, the PV rises. Potterton’s CFO therefore decides to issue an offsetting debt liability:

PV (lease)			PV (debt)
= $17 million			= $17 million

Thus, Potterton is long $17 million and also short $17 million. But it may not be hedged. Simply borrowing $17 million at some arbitrary maturity does not eliminate interest rate risk. Suppose the CFO took out a one-year, $17 million bank loan, with a plan to refinance the loan annually. Then she would be borrowing short and lending long (via the 20-year lease), which amounts to a $17 million bet that interest rates will fall. If instead they rise, her company will end up paying more interest in years 2 to 20, with no compensating increase in the lease cash flows.

To hedge interest rate risk, the CFO needs to design the debt issue so that any change in interest rates has the same (and thus offsetting) impact on both the PV of the lease payments and the PV of the debt. There are two ways to accomplish this:

1. Zero-maintenance hedge. Issue debt requiring interest and principal payments of exactly $2 million per year for 20 years. This debt would be similar to a real estate mortgage with level payments. In this case, lease payments would exactly cover debt service in each year. The PVs of the lease payments and the offsetting debt would always be identical, regardless of the level of future interest rates.

2. Duration hedge. Issue debt with the same duration as the lease payments. Here, debt service does not have to match the lease payments in each (or any) year. If durations are matched, then small changes in interest rates—say, from 10% down to 9.5% or up to 10.5%—will have the same impact on the PVs of the lease payments and the debt.

The duration-matching strategy is usually more convenient, but it is not zero maintenance because durations will drift out of line as interest rates change and time passes. Thus, the CFO will have to revisit and reset the hedge. She will have to execute a dynamic strategy to make duration matching work.

Potterton’s CFO first calculates the duration of the lease payments:³¹

Therefore, to hedge its interest rate risk, Potterton needs to issue a package of bonds with a duration of 7.5 years. The simplest solution is to issue a 12-year bond with a 10% coupon, which has a 7.5-year duration. But this is not the only possible strategy. For example, the company could issue $7.9 million of 10% 20-year bonds and $9.1 million of 10% 8-year bonds. The duration of this package would also be 7.5 years.³²

Figure 26.4 plots the PVs of the lease payments and the 12-year bond as a function of the interest rate. Both the PV curves are downward-sloping but convex; note how each curve comes down steeply at low interest rates but flattens out at higher interest rates.

FIGURE 26.4 Hedging Potterton’s interest rate risk by matching duration. The PV of the lease cash inflows is shown by the blue curve; the PV of a 10% 12-year bond is shown by the red curve. Both have a duration of 7.5 years, so the slopes of the PV curves are identical at the current 10% interest rate. Therefore, Potterton’s net exposure to small changes in interest rates is zero.

Now compare the slope of the PV curve for the lease payments with the slope of the 12-year bond. The slopes are identical at the current 10% interest rate because the duration is identical at this rate. Therefore, so long as the interest rate does not stray too far from the current level of 10%, the PV of the lease cash flows change by almost the same amount as the PV of the bond. In this case, Potterton is hedged. But you can see from Figure 26.4 that if interest rates change by, say, 5%, the value of the lease payments changes by a little bit more than the value of the bond. In this case, Potterton’s CFO will have to reset the hedge.

She will also need to reset the hedge at some point even if interest rates do not change because the duration of the 12-year bond will decrease faster than that of the 20-year lease. For example, think forward 12 years: The bond will mature, while the lease will still have 8 years to run.

Duration is not a complete measure of interest rate risk. It measures only exposure to the level of interest rates, not to changes in the shape of the term structure. Duration in effect assumes that the term structure is “flat.” It is widely used, however, because it is a good first approximation to interest rate risk exposure. The mini-case at the end of this chapter offers another opportunity to use this concept.

Hedge Ratios and Basis Risk

In our example of Potterton Leasing, the CFO matched lease cash flows worth $17 million against debt worth $17 million. In other words, the hedge ratio for Potterton was exactly 1.

Hedge ratios can be much higher or lower than 1. For example, suppose a farmer owns 100,000 bushels of wheat and wishes to hedge by selling wheat futures. In practice, the wheat that the farmer owns and the wheat that he sells in the futures markets are unlikely to be identical. If he sells wheat futures on the Kansas City exchange, he agrees to deliver hard, red winter wheat in Kansas City in September. But perhaps he is growing northern spring wheat many miles from Kansas City; in this case, the prices of the two wheats will not move exactly together.

Figure 26.5 shows how changes in the prices of the two types of wheat may have been related in the past. The slope of the fitted line shows that a 1% change in the price of Kansas wheat was, on average, associated with an .8% change in the price of the farmer’s wheat. Because the price of the farmer’s wheat is relatively insensitive to changes in Kansas prices, he needs to sell .8 × 100,000 bushels of wheat futures to minimize risk.

FIGURE 26.5 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% change in the futures price implies, on average, a .8% change in the price of the farmer’s wheat.

Let us generalize. Suppose that you already own an asset, A (e.g., wheat), and you wish to hedge against changes in the value of A by making an offsetting sale of another asset, B (e.g., wheat futures). Suppose also that percentage changes in the value of A are related in the following way to percentage changes in the value of B:

Expected change in value of A = α + δ (change in value of B)

Delta (δ) measures the sensitivity of A to changes in the value of B. It is also equal to the hedge ratio—that is, the number of units of B that should be sold to hedge the purchase of A. You minimize risk if you offset your position in A by the sale of delta units of B.

The trick in setting up a hedge is to estimate the delta or hedge ratio. Our farmer could use past experience to do so, but often a strong dose of judgment is called for. For example, suppose that Antarctic Air would like to protect itself against a hike in oil prices. As the financial manager, you need to decide how much a rise in oil price would affect firm value.

Suppose the company spent $200 million on fuel last year. Other things equal, a 10% increase in the price of oil will cost the company an extra .1 × 200 = $20 million. But perhaps you can partially offset the higher costs by charging higher ticket prices, in which case earnings will fall by less than $20 million. Or perhaps an oil price rise will lead to a slowdown in business activity and therefore lower passenger numbers. In that case earnings will decline by more than $20 million. Working out the likely effect on firm value is even trickier because it depends on whether the rise is likely to be permanent. Perhaps the price rise will induce an increase in production or encourage consumers to economize on energy usage.

Whenever the two sides of the hedge do not move exactly together, there will be some basis risk. That is not a problem for the CFO of Potterton. As long as interest rates do not change sharply, any changes in the value of Potterton’s lease should be almost exactly offset by changes in the value of the debt. In this case there is no basis risk, and Potterton is perfectly hedged.

BEYOND THE PAGE

WTI and Brent oil futures

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Our wheat farmer is less fortunate. The scatter of points in Figure 26.5 shows that it is not possible for the farmer to construct a perfect hedge using wheat futures. Since the underlying commodity (the farmer’s wheat) and the hedging instrument (Kansas City wheat futures) are imperfectly correlated, some basis risk remains.

26-7Is “Derivative” a Four-Letter Word?

Our wheat farmer sold wheat futures to reduce business risk. But if you were to copy the farmer and sell futures without an offsetting holding of wheat, you would increase risk, not reduce it. You would be speculating.

BEYOND THE PAGE

Major derivatives losses

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Speculators in search of large profits (and prepared to tolerate large losses) are attracted by the leverage that derivatives provide. By this we mean that it is not necessary to lay out much money up front and the profits or losses may be many times the initial outlay. “Speculation” has an ugly ring, but a successful derivatives market needs speculators who are prepared to take on risk and provide more cautious people such as farmers or millers with the protection they need. For example, if there is an excess of farmers wishing to sell wheat futures, the price of futures will be forced down until enough speculators are tempted to buy in the hope of a profit. If there is a surplus of millers wishing to buy wheat futures, the reverse will happen. The price of wheat futures will be forced up until speculators are drawn in to sell.

BEYOND THE PAGE

LTCM

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Speculation may be necessary to a thriving derivatives market, but it can get companies into serious trouble. The nearby Beyond the Page feature describes how the French bank Société Générale took a €4.9 billion bath from unauthorized trading by one of its staff. The bank has plenty of company. In 2011, Swiss bank UBS reported that a rogue trader had notched up losses of $2.3 billion. And in 1995, Baring Brothers, a blue-chip British merchant bank with a 200-year history, became insolvent. The reason: Nick Leeson, a trader in Baring’s Singapore office, had placed very large bets on the Japanese stock market index that resulted in losses of $1.4 billion.

BEYOND THE PAGE

Metallgesellschaft

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BEYOND THE PAGE

The World’s Poorest Man

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These tales of woe have some cautionary messages for all corporations. During the 1970s and 1980s, many firms turned their treasury operations into profit centers and proudly announced their profits from trading in financial instruments. But it is not possible to make large profits in financial markets without also taking large risks, so these profits should have served as a warning rather than a matter for congratulation.

An Airbus 380 weighs 400 tons, flies at nearly 600 miles per hour, and is inherently very dangerous. But we don’t ground A380s; we just take precautions to ensure that they are flown with care. Similarly, it is foolish to suggest that firms should ban the use of derivatives, but it makes obvious sense to take precautions against their misuse. Here are two bits of horse sense:

· Precaution 1: Don’t be taken by surprise. By this we mean that senior management needs to monitor regularly the value of the firm’s derivatives positions and to know what bets the firm has placed. At its simplest, this might involve asking what would happen if interest rates or exchange rates were to change by 1%. But large banks and consultants have also developed sophisticated models for measuring the risk of derivatives positions.

· Precaution 2: Place bets only when you have some comparative advantage that ensures the odds are in your favor. If a bank were to announce that it was drilling for oil or launching a new soap powder, you would rightly be suspicious about whether it had what it takes to succeed. You should be equally suspicious if an oil producer or consumer products company announced that it was placing a bet on interest rates or currencies.

Imprudent speculation in derivatives is undoubtedly an issue of concern for the company’s shareholders, but is it a matter for more general concern? Some people believe, like Warren Buffett, that derivatives are “financial weapons of mass destruction.” They point to the huge volume of trading in derivatives and argue that speculative losses could lead to major defaults that might threaten the whole financial system. These worries have led to increased regulation of derivatives markets.

Now, this is not the place for a discussion of regulation, but we should warn you about careless measures of the size of the derivatives markets and the possible losses. In June 2017, the notional value of outstanding derivative contracts was $628 trillion.³³ This is a very large sum, but it tells you nothing about the money that was being put at risk. For example, suppose that a bank enters into a $10 million interest rate swap and the other party goes bankrupt the next day. How much has the bank lost? Nothing. It hasn’t paid anything up front; the two parties simply promised to pay sums to each other in the future. Now the deal is off.

Suppose that the other party does not go bankrupt until a year after the bank entered into the swap. In the meantime interest rates have moved in the bank’s favor, so it should be receiving more money from the swap than it is paying out. When the other side defaults on the deal, the bank loses the difference between the interest that it is due to receive and the interest that it should pay. But it doesn’t lose $10 million.³⁴

The only meaningful measure of the potential loss from default is the amount that it would cost firms showing a profit to replace their positions.

SUMMARY

As a manager, you are paid to take risks, but you are not paid to take just any risks. Some risks are simply bad bets, and others could jeopardize the value of the firm. Hedging risks, when it is practical to do so, can make sense if it reduces the chance of cash shortfalls or financial distress. In some cases, hedging can also make it easier to monitor and motivate operating managers. Relieving managers of risk outside their control helps them concentrate on what can be controlled.

Most businesses insure against possible losses. Insurance companies specialize in assessing risks and can pool risks by holding a diversified portfolio of policies. Insurance works less well when policies are taken up by companies that are most at risk (adverse selection) or when the insured company is tempted to skip on maintenance or safety procedures (moral hazard).

Firms can also hedge with options and with forward and futures contracts. A forward contract is an advance order to buy or sell an asset. The forward price is fixed today, but payment is not made until the delivery date at the end of the contract. Forward contracts that are traded on organized futures exchanges are called futures contracts. Futures contracts are standardized and traded in huge volumes. The futures markets allow firms to lock in future prices for dozens of different commodities, securities, and currencies.

Instead of buying or selling a standardized futures contract, you may be able to arrange a tailor-made forward contract with a bank. Firms can protect against changes in foreign exchange rates by buying or selling forward currency contracts. Forward rate agreements (FRAs) provide protection against changes in interest rates. You can construct homemade forward contracts. For example, if you borrow for two years and at the same time lend for one year, you have effectively taken out a forward loan.

Firms also hedge with swap contracts. For example, a firm can make a deal to pay interest to a bank at a fixed long-term rate and receive interest from the bank at a floating short-term rate. The firm swaps a fixed for a floating rate. Such a swap could make sense if the firm has relatively easy access to short-term borrowing but dislikes the exposure to fluctuating short-term interest rates.

The theory of hedging is straightforward. You find two closely related assets. You then buy one and sell the other in proportions that minimize the risk of your net position. If the assets are perfectly correlated, you can make the net position risk-free. If they are less than perfectly correlated, you will have to absorb some basis risk.

The trick is to find the hedge ratio or delta—that is, the number of units of one asset that is needed to offset changes in the value of the other asset. Sometimes the best solution is to look at how the prices of the two assets have moved together in the past. For example, suppose you observe that a 1% change in the value of B has been accompanied on average by a 2% change in the value of A. Then delta equals 2.0; to hedge each dollar invested in A, you need to sell two dollars of B.

On other occasions theory can help to set up the hedge. For example, the effect of a change in interest rates on an asset’s value depends on the asset’s duration. If two assets have the same duration, they will be equally affected by fluctuations in interest rates.

Many of the hedges described in this chapter are static. Once you have set up the hedge, you can take a long vacation, confident that the firm is well protected. However, some hedges, such as those that match durations, are dynamic. As time passes and prices change, you need to rebalance your position to maintain the hedge.

Hedging and risk reduction sound as wholesome as mom’s apple pie. But remember that hedging solely to reduce risk cannot add value. It is a zero-sum game: Risks aren’t eliminated, just shifted to some counterparty. And remember that your shareholders can also hedge by adjusting the composition of their portfolios or by trading in futures or other derivatives. Investors won’t reward the firm for doing something that they can do perfectly well for themselves.

Some companies have decided that speculation is much more fun than hedging. This view can lead to serious trouble. We do not believe that speculation makes sense for an industrial company, but we caution against assuming that derivatives are a threat to the financial system.

FURTHER READING

Three general articles on corporate risk management are:

K. A. Froot, D. S. Scharfstein, and J. C. Stein, “A Framework for Risk Management,” Harvard Business Review 72 (November–December 1994), pp. 59–71.

B. W. Nocco and R. M. Stulz, “Enterprise Risk Management: Theory and Practice,” Journal of Applied Corporate Finance 18 (Fall 2006), pp. 8–20.

C. H. Smithson and B. Simkins, “Does Risk Management Add Value? A Survey of the Evidence,” Journal of Applied Corporate Finance 17 (Summer 2005), pp. 8–17.

The Summer 2005 and Fall 2006 issues of the Journal of Applied Corporate Finance are devoted to risk management, and current news and developments are discussed in Risk magazine. You may also wish to refer to the following texts:

J. C. Hull, Options, Futures, and Other Derivatives, 10th ed. (Cambridge, England: Pearson, 2017).

C. H. Smithson, Managing Financial Risk, 3rd ed. (New York: McGraw-Hill, 1998).

R. M. Stulz, Risk Management and Derivatives (Cincinnati, OH: Thomson-Southwestern Publishing, 2003).

Schaefer’s paper is a useful review of how duration measures are used to immunize fixed liabilities:

S. M. Schaefer, “Immunisation and Duration: A Review of Theory, Performance and Applications,” Midland Corporate Finance Journal 2 (Autumn 1984), pp. 41–59.

PROBLEM SETS

 Select problems are available in McGraw-Hill’s Connect. Please see the preface for more information.

1. Vocabulary check* Define the following terms:

a. Spot price

b. Forward vs. futures contract

c. Long vs. short position

d. Basis risk

e. Mark to market

f. Net convenience yield

2. Insurance Large businesses spend millions of dollars annually on insurance. Why? Should they insure against all risks or does insurance make more sense for some risks than others?

3. Catastrophe bonds On some catastrophe bonds, payments are reduced if the claims against the issuer exceed a specified sum. In other cases, payments are reduced only if claims against the entire industry exceed some sum. What are the advantages and disadvantages of the two structures? Which involves more basis risk? Which may create a problem of moral hazard?

4. Futures and options A gold-mining firm is concerned about short-term volatility in its revenues. Gold currently sells for $1,300 an ounce, but the price is extremely volatile and could fall as low as $1,220 or rise as high as $1,380 in the next month. The company will bring 1,000 ounces to the market next month.

a. What will be total revenues if the firm remains unhedged for gold prices of $1,220, $1,300, and $1,380 an ounce?

b. The futures price of gold for delivery one month ahead is $1,310. What will be the firm’s total revenues at each gold price if the firm enters into a one-month futures contract to deliver 1,000 ounces of gold?

c. What will total revenues be if the firm buys a one-month put option to sell gold for $1,300 an ounce? The put option costs $110 per ounce.

5. Futures and options Petrochemical Parfum (PP) is concerned about a possible increase in the price of heavy fuel oil, which is one of its major inputs. Show how PP can use either options or futures contracts to protect itself against a rise in the price of crude oil. Show how the payoffs in each case would vary if the oil price were $70, $80, or $90 a barrel. What are the advantages and disadvantages for PP of using futures rather than options to reduce risk? Assume the current price of oil is $70 per barrel, the futures price is $80, and the option exercise price is $80.

6. Futures contracts* True or false?

a. Hedging transactions in an active futures market have zero or slightly negative NPVs.

b. When you buy a futures contract, you pay now for delivery at a future date.

c. The holder of a financial futures contract misses out on any dividend or interest payments made on the underlying security.

d. The holder of a commodities futures contract does not have to pay for storage costs, but foregoes convenience yield.

7. Futures contracts List some of the commodity futures contracts that are traded on exchanges. Who do you think could usefully reduce risk by buying each of these contracts? Who do you think might wish to sell each contract?

8. Marking to market* Yesterday, you sold six-month futures on the German DAX stock market index at a price of 13,200. Today, the DAX closed at 13,150 and DAX futures closed at 13,250. You get a call from your broker, who reminds you that your futures position is marked to market each day. Is she asking you to pay money, or is she about to offer to pay you?

9. Futures prices Calculate the value of a six-month futures contract on a Treasury bond. You have the following information:

· Six-month interest rate: 10% per year, or 4.9% for six months.

· Spot price of bond: 95.

· The bond pays an 8% coupon, 4% every six months.

10. Futures prices* In December 2017, six-month futures on the Australian S&P/ASX 200 Index traded at 5,947. Spot was 6,001. The interest rate was 1.8% a year, and the dividend yield was about 4.4% a year. Were the futures fairly priced?

11. Futures prices If you buy a nine-month T-bill future, you undertake to buy a $1 million three-month bill in nine months’ time. Suppose that Treasury bills and notes currently offer the following yields

Months to Maturity	Annual Yield
3	6%
6	6.5
9	7
12	8

12. What is the dollar value of a nine-month bill future?

Commodity	Spot Price	Futures Price	Comments
Magnoosium	$2,550 per ton	$2,728.50 per ton	Monthly storage cost = monthly convenience yield.
Frozen quiche	$0.50 per pound	$0.514 per pound	Six months’ storage costs = $.10 per pound; six months’ convenience yield = $.05 per pound.
Nevada Hydro 8s of 2002	77	78.39	4% semiannual coupon payment is due just before futures contract expires.
Costaguanan pulgas (currency)	9,300 pulgas = $1	6,900 pulgas = $1	Costaguanan interest rate is 95% per year.
Establishment Industries common stock	$95	$97.54	Establishment pays dividends of $2 per quarter. Next dividend is paid two months from now.
Cheap white wine	$12,500 per 10,000-gal tank	$14,200 per 10,000-gal tank	Six months’ convenience yield = $250 per tank. Your company has surplus storage and can store 50,000 gallons at no cost.

TABLE 26.5 Spot and six-month futures prices for selected commodities and securities. See Problem 12.

12. Futures prices Table 26.5 contains spot and six-month futures prices for several commodities and financial instruments. There may be some money-making opportunities. See if you can find them, and explain how you would trade to take advantage of them. The interest rate is 14.5%, or 7% over the six-month life of the contracts.

13. Futures prices The following table shows 2014 gold futures prices for varying contract lengths. Gold is predominantly an investment good, not an industrial commodity. Investors hold gold because it diversifies their portfolios and because they hope its price will rise. They do not hold it for its convenience yield.

	Contract Length (months)
	3	6	9
Futures price	$1,188.5	$1,189.5	$1,190.0

14. Calculate the interest rate faced by traders in gold futures, assuming a zero net convenience yield, for each of the contract lengths shown above. The spot price is $1,188.2 per ounce.

15. Futures prices Consider the commodities and financial assets listed in Table 26.6. The risk-free interest rate is 6% a year, and the term structure is flat.

a. Calculate the six-month futures price for each case.

b. Explain how a magnoosium producer would use a futures market to lock in the selling price of a planned shipment of 1,000 tons of magnoosium six months from now.

c. Suppose the producer takes the actions recommended in your answer to part (b), but after one month magnoosium prices have fallen to $2,200. What happens? Will the producer have to undertake additional futures market trades to restore its hedged position?

d. Does the biotech index futures price provide useful information about the expected future performance of biotech stocks?

e. Suppose Allen Wrench stock falls suddenly by $10 per share. Investors are confident that the cash dividend will not be reduced. What happens to the futures price?

Asset	Spot Price	Comments
Magnoosium	$2,800 per ton	Net convenience yield = 4% per year
Oat bran	$0.44 per bushel	Net convenience yield = 0.5% per month
Biotech stock index	$140.2	Dividend = 0
Allen Wrench Co. common stock	$58.00	Cash dividend = $2.40 per year
5-year Treasury note	$108.93	8% coupon
Westonian ruple	3.1 ruples = $1	12% interest rate in ruples

f. TABLE 26.6 Spot prices for selected commodities and financial assets. See Problem 14.

g. Suppose interest rates suddenly fall to 4%. The term structure remains flat. What happens to the six-month futures price on the five-year Treasury note? What happens to a trader who shorted 100 notes at the futures price calculated in part (a)?

h. An importer must make a payment of one million ruples three months from now. Explain two strategies the importer could use to hedge against unfavorable shifts in the ruple– dollar exchange rate.

16. Convenience yield Calculate convenience yield for magnoosium scrap from the following information:

· Spot price: $2,550 per ton.

· Futures price: $2,408 for a one-year contract.

· Interest rate: 12%.

· Storage costs: $100 per year.

17. Convenience yield Residents of the northeastern United States suffered record-setting low temperatures throughout November and December 2024. Spot prices of heating oil rose 25%, to over $7 a gallon.

a. What effect did this have on the net convenience yield and on the relationship between futures and spot prices?

b. In late 2025 refiners and distributors were surprised by record-setting high temperatures. What was the effect on net convenience yield and spot and futures prices for heating oil?

18. Convenience yield After a record harvest, grain silos are full to the brim. Are storage costs likely to be high or low? What does this imply for the net convenience yield?

19. Convenience yield In March 2018, six-month bitcoin futures were priced at $7,925. The spot price was $7,946. The six-month interest rate was 1.92%.

a. What was the convenience yield?

b. Is your answer to part (a) consistent with what you would expect? Explain.

20. Interest rate swaps A year ago, a bank entered into a $50 million five-year interest rate swap. It agreed to pay company A each year a fixed rate of 6% and to receive in return LIBOR. When the bank entered into this swap, LIBOR was 5%, but now interest rates have risen, so on a four-year interest rate swap the bank could expect to pay 6.5% and receive LIBOR.

a. Is the swap showing a profit or loss to the bank?

b. Suppose that at this point company A approaches the bank and asks to terminate the swap. If there are four annual payments still remaining, how much should the bank charge A to terminate?

21. Interest rate swaps In September 2020, swap dealers were quoting a rate for five-year euro interest-rate swaps of 4.5% against Euribor (the short-term interest rate for euro loans). Euribor at the time was 4.1%. Suppose that A arranges with a dealer to swap a €10 million five-year fixed-rate loan for an equivalent floating-rate loan in euros.

a. Assume the swap is fairly priced. What is the value of this swap at the time that it is entered into?

b. Suppose that immediately after A has entered into the swap, the long-term interest rate rises by 1%. Who gains and who loses?

c. What is now the value of the swap for each €1,000 of notional value?

22. Total return swaps Is a total return swap on a bond the same as a credit default swap (see Section 23-1)? Why or why not?

23. Hedging “Speculators want futures contracts to be incorrectly priced; hedgers want them to be correctly priced.” Why?

24. Hedging “Northern Refineries does not avoid risk by selling oil futures. If prices stay above $2.40 a gallon, then it will actually have lost by selling oil futures at that price.” Is this a fair comment?

25. Hedging What is meant by “delta” (δ) in the context of hedging? Give examples of how delta can be estimated or calculated.

26. Hedging* You own a $1 million portfolio of aerospace stocks with a beta of 1.2. You are very enthusiastic about aerospace but uncertain about the prospects for the overall stock market. Explain how you could hedge out your market exposure by selling the market short. How much would you sell? How in practice would you go about “selling the market”?

27. Hedging

a. Marshall Arts has just invested $1 million in long-term Treasury bonds. Marshall is concerned about increasing volatility in interest rates. He decides to hedge using bond futures contracts. Should he buy or sell such contracts?

b. The treasurer of Zeta Corporation plans to issue bonds in three months. She is also concerned about interest rate volatility and wants to lock in the price at which her company could sell 5% coupon bonds. How would she use bond futures contracts to hedge?

28. Hedging Phoenix Motors wants to lock in the cost of 10,000 ounces of platinum to be used in next quarter’s production of catalytic converters. It buys three-month futures contracts for 10,000 ounces at a price of $1,300 per ounce.

a. Suppose the spot price of platinum falls to $1,200 in three months’ time. Does Phoenix have a profit or loss on the futures contract? Has it locked in the cost of purchasing the platinum it needs?

b. How do your answers change if the spot price of platinum increases to $1,400 after three months?

29. Hedging Legs Diamond owns shares in a Vanguard Index 500 mutual fund worth $1 million on July 15. (This is an index fund that tracks the Standard and Poor’s 500 Index.) He wants to cash in now, but his accountant advises him to wait six months so as to defer a large capital gains tax. Explain to Legs how he can use stock index futures to hedge out his exposure to market movements over the next six months. Could Legs “cash in” without actually selling his shares?

30. Hedging Price changes of two gold-mining stocks have shown strong positive correlation. Their historical relationship is

Average percentage change in A = .001 + .75 (percentage change in B)

Changes in B explain 60% of the variation of the changes in A (R² = .6).

a. Suppose you own $100,000 of A. How much of B should you sell to minimize the risk of your net position?

b. What is the hedge ratio?

c. Here is the historical relationship between stock A and gold prices:

Average percentage change in A = −.002 + 1.2 (percentage change in gold price)

If R² = .5, can you lower the risk of your net position by hedging with gold (or gold futures) rather than with stock B? Explain.

31. Hedging Your investment bank has an investment of $100 million in the stock of the Swiss Roll Corporation and a short position in the stock of the Frankfurter Sausage Company. Here is the recent price history of the two stocks:

	Percentage Price Change
Month	Frankfurter Sausage	Swiss Roll
January	−10	−10
February	−10	−5
March	−10	0
April	+10	0
May	+10	+5
June	+10	+10

32. On the evidence of these six months, how large would your short position in Frankfurter Sausage need to be to hedge as far as possible against movements in the price of Swiss Roll?

33. Duration hedging* Securities A, B, and C have the following cash flows:

	Year 1	Year 2	Year 3
A	$ 40	$40	$ 40
B	120	—	—
C	10	10	110

a. Calculate their durations if the interest rate is 8%.

b. Suppose that you have an investment of $10 million in A. What combination of B and C would hedge this investment against interest rate changes?

c. Now suppose that you have a $10 million investment in B. How would you hedge?

34. Basis risk* What is basis risk? In which of the following cases would you expect basis risk to be serious?

a. A broker owning a large block of Disney common stock hedges by selling index futures.

b. An lowa corn farmer hedges the selling price of her crop by selling Chicago corn futures.

c. An importer must pay 900 million euros in six months. He hedges by buying euros forward.

CHALLENGE

33. Interest rate swaps Phillip’s Screwdriver Company has borrowed $20 million from a bank at a floating interest rate of 2 percentage points above three-month Treasury bills, which now yield 5%. Assume that interest payments are made quarterly and that the entire principal of the loan is repaid after five years.

Phillip’s wants to convert the bank loan to fixed-rate debt. It could have issued a fixed-rate five-year note at a yield to maturity of 9%. Such a note would now trade at par. The five-year Treasury note’s yield to maturity is 7%.

a. Is Phillip’s stupid to want long-term debt at an interest rate of 9%? It is borrowing from the bank at 7%.

b. Explain how the conversion could be carried out by an interest rate swap. What will be the initial terms of the swap? (Ignore transaction costs and the swap dealer’s profit.)

One year from now short and medium-term Treasury yields decrease to 6%, so the term structure then is flat. (The changes actually occur in month 5.) Phillip’s credit standing is unchanged; it can still borrow at 2 percentage points over Treasury rates.

c. What net swap payment will Phillip’s make or receive?

d. Suppose that Phillip’s now wants to cancel the swap. How much would it need to pay the swap dealer? Or would the dealer pay Phillip’s? Explain.

FINANCE ON THE WEB

1. The websites of the major commodities exchanges provide futures prices. Calculate the annualized net convenience yield for a commodity of your choice. (Note: You may need to use the futures price of a contract that is about to mature as your estimate of the current spot price.)

2. You can find swap rates for the U.S. dollar and the euro on www.ft.com. Plot the current swap curves as in Figure 26.3.

3. You can find spot and futures prices for a variety of equity indexes on www.wsj.com. Pick one and check whether it is fairly priced. You will need to do some detective work to find the dividend yield on the index and the interest rate.

MINI-CASE

Rensselaer Advisers

You are a vice president of Rensselaer Advisers (RA), which manages portfolios for institutional investors (primarily corporate pension plans) and wealthy individuals. In mid-2018, RA had about $1.1 billion under management, invested in a wide range of common-stock and fixed-income portfolios. Its management fees average 55 basis points (.55%), so RA’s total revenue for 2018 is about .0055 × $1.1 billion = $6.05 million.

You are attempting to land a new client, Madison Mills, a conservative, long-established manufacturer of papermaking felt. Madison has established a defined-benefit pension plan for its employees. RA would manage the pension assets that Madison has set aside to cover defined-benefit obligations for retired employees.

Defined benefit means that an employer is committed to pay retirement income according to a formula. For example, annual retirement income could equal 40% of the employee’s average salary in the five years prior to retirement. In a defined-benefit plan, retirement income does not depend on the performance of the pension assets. If the assets in the fund are not sufficient to cover pension benefits, the company is required to contribute enough additional cash to cover the shortfall. Thus, the PV of promised retirement benefits is a debt-equivalent obligation of the company.³⁵

Table 26.7 shows Madison’s obligations to its already retired employees from 2019 to 2040. Each of these employees receives a fixed dollar amount each month. Total dollar payments decline as the employees die off. The PV of the obligations in Table 26.7 is about $89 million at the current (2018) 5% long-term interest rate. Table 26.7 also calculates the duration of the obligations at 7.87 years.

Madison has set aside $90 million in pension assets to cover the obligations in Table 26.7, so this part of its pension plan is fully funded.³⁶ The pension assets are now invested in a diversified portfolio of common stocks, corporate bonds, and notes.

TABLE 26.7 Madison Mills Pension Fund, projected benefits for retired employees

After reviewing Madison’s existing portfolio, you schedule a meeting with Hendrik van Wie, Madison’s CFO. Mr. van Wie stresses Madison’s conservative management philosophy and warns against “speculation.” He complains about the performance of the previous manager of the pension assets. He suggests that you propose a plan of investing in safe assets in a way that minimizes exposure to equity markets and changing interest rates. You promise to prepare an illustration of how this goal could be achieved.

Later, you discover that RA has competition for Madison’s investment management business. SPX Associates is proposing a strategy of investing 70% of the portfolio ($63 million) in index funds tracking the U.S. stock market and 30% of the portfolio ($27 million) in U.S. Treasury securities. SPX argues that their strategy is “safe in the long run” because the U.S. stock market has delivered an average risk premium of about 7% per year. In addition, SPX argues that the growth in its stock market portfolio will far outstrip Madison’s pension obligations. SPX also claims that the $27 million invested in Treasuries will provide ample protection against short-term stock market volatility. Finally, SPX proposes to charge an investment management fee of only 20 basis points (.20%). RA had planned to charge 30 basis points (.30%).

QUESTIONS

1. Prepare a memo for Mr. van Wie explaining how RA would invest to minimize both risk and exposure to changing interest rates. Give an example of a portfolio that would accomplish this objective. Explain how the portfolio would be managed as time passes and interest rates change. Also explain why SPX’s proposal is not advisable for a conservative company like Madison.

RA manages several fixed-income portfolios. For simplicity, you decide to propose a mix of the following three portfolios:

· A portfolio of long-term Treasury bonds with an average duration of 14 years.

· A portfolio of Treasury notes with an average duration of 7 years.

· A portfolio of short-term Treasury bills and notes with an average duration of 1 year.

The term structure is flat, and the yield on all three portfolios is 5%.

2. Sorry, you lost. SPX won and implemented its proposed strategy. Now the recession of 2019 has knocked down U.S. stock prices by 20%. The value of the Madison portfolio, after paying benefits for 2019, has fallen from $90 million to $78 million. At the same time interest rates have dropped from 5% to 4% as the Federal Reserve relaxes monetary policy to combat the recession.

Mr. van Wie calls again, chastened by the SPX experience, and he invites a new proposal to invest the pension assets in a way that minimizes exposure to the stock market and changing interest rates. Update your memo with a new example of how to accomplish Mr. van Wie’s objectives. You can use the same portfolios and portfolio durations as in Question 1. You will have to recalculate the PV and duration of the pension benefits from 2019 onward. Assume a flat term structure with all interest rates at 4%. (Hint: Madison’s pension obligations are now underfunded. Nevertheless, you can hedge interest rate risk if you increase the duration of the pension assets.)

¹R. Barro and J. F. Ursua, “Rare Macroeconomic Disasters,” Annual Review of Economics 4 (2012), pp. 83–109.

²In game theory, “zero-sum” means that the payoffs to all players add up to zero, so that one player can win only at the others’ expense.

³The news was worst for the shareholders of Ashanti Goldfields, the huge Ghanaian mining company. Ashanti had gone to the opposite extreme and placed a bet that gold prices would fall. The 1999 price rise nearly drove Ashanti into bankruptcy.

⁴See Section 7-5 and also our discussion of diversifying mergers in Chapter 31. Note that diversification reduces overall risk, but not market risk.

⁵There may be other, special reasons not covered here. For example, governments are quick to tax profits but may be slow to rebate taxes when there are losses. In the United States, losses cannot be set against earlier tax payments but can only be carried forward and used to shield future profits. Thus a firm with volatile income and more frequent losses has a higher effective tax rate. A firm can reduce the fluctuations in its income by hedging. For most firms, this motive for risk reduction is not a big deal. See J. R. Graham and C. W. Smith, Jr., “Tax Incentives to Hedge,” Journal of Finance 54 (December 1999), pp. 2241–2262.

⁶Amateur speculation is doubly dangerous when the manager’s initial trades are losers. At that point, the manager is already in deep trouble and has nothing more to lose by going for broke. “Going for broke” is often called “gambling for redemption.”

⁷International Swap Dealers Association (ISDA), “2009 Derivatives Usage Survey,” www.isda.org.

⁸See P. Tufano, “The Determinants of Stock Price Exposure: Financial Engineering and the Gold Mining Industry,” Journal of Finance 53 (June 1998), pp. 1015–1052; and G. D. Haushalter, “Financing Policy, Basis Risk and Corporate Hedging : Evidence from Oil and Gas Producers,” Journal of Finance 55 (February 2000), pp. 107–152.

⁹If 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/(1 + r).

¹⁰For a discussion of Cat bonds and other techniques to spread insurance risk, see N. A. Doherty, “Financial Innovation in the Management of Catastrophe Risk,” Journal of Applied Corporate Finance 10 (April 2005), pp. 84–95; K. Froot, “The Market for Catastrophe Risk: A Clinical Examination,” Journal of Financial Economics 60 (2001), pp. 529–571; and J. D. Cummins, “CAT Bonds and Other Risk-Linked Securities: State of the Market and Recent Developments,” Risk Management and Insurance Review 11 (Spring 2008), pp. 23–47.

¹¹The Mexican government option position was slightly more complicated than our description. On some of the production, it agreed to take a hit if prices fell below some minimum price.

¹²By the time you read this, the list of futures contracts will almost certainly be out of date because thinly traded contracts are terminated and new contracts are introduced. The list of futures exchanges may also be out of date. There have been plenty of mergers in recent years. In July 2007, the CME and CBOT merged to form the CME Group, and the following year, the group acquired NYMEX Holdings, which operated the NYMEX and COMEX exchanges. Also in 2007, the Intercontinental Exchange (ICE) acquired the New York Board of Trade and NYSE merged with Euronext, which owned the futures exchange, LIFFE. Six years later, NYSE Euronext was itself acquired by the ICE, which kept Euronext’s futures business but split off its stock exchange operation.

¹³Recall that the spot price is the price for immediate delivery. The futures contract also calls for immediate delivery when the contract ends in January. Therefore, the ending price of a futures or forward contract must converge to the spot price at the end of the contract.

¹⁴Some financial futures contracts prohibit delivery. All positions are closed out at the spot price at contract maturity.

¹⁵In the Appendix to Chapter 19, we pointed out that companies effectively earn the after-tax interest rate when they lend and they pay the after-tax interest rate when they borrow. Therefore, when we value the leverage provided by a forward contract, we should also use the after-tax rather than the pretax rate. You will generally see the formula for the value of a forward contract written without a tax term. For convenience we have followed that convention here, but when valuing a forward contract, remember to use the after-tax rate. See S. C. Myers and J. A. Read, Jr., “Real Options, Taxes and Leverage,” Critical Finance Review, forthcoming.

¹⁶This formula is strictly true only for forward contracts that are not marked to market. Otherwise, the value of the future depends on the path of interest rates over the life of the contract. In practice, this qualification is usually not important, and the formula works for futures as well as forward contracts.

¹⁷We can derive our formula as follows. Let S₆ be the value of the index after six months. Today S₆ is unknown. You can invest S₀ in the index today and get S₆ + yS₀ after six months. You can also buy the futures contract, put S₀ in the bank, and use your bank balance to pay the futures price F₆ in six months. In the latter strategy you get S₆ − F₆ + S₀ (1 + r_f) after six months. Since the investment is the same, and you get S₆ with either strategy, the payoffs must be the same:

Here we assume that r_f and y are six-month rates. If they are monthly rates, the general formula is F_t = S₀ (1 + r_f – y) ^t, where t is the number of months. If they are annual rates, the formula is F_t = S₀ (1 + r_f − y)^t/12.

¹⁸This formula could overstate the futures price if no one is willing to hold the commodity, that is, if inventories fall to zero or some absolute minimum.

¹⁹Critics and proponents of futures markets sometimes argue about whether the markets provide “price discovery.” That is, they argue about whether futures prices reveal traders’ forecasts of spot prices when the futures contract matures. If one of these fractious personalities comes your way, we suggest that you respond with a different question: Do futures prices reveal information about spot prices that is not already in today’s spot price? Our formulas reveal the answer to this question. There is useful information in futures prices, but it is information about convenience yields and storage costs, or about dividend or interest payments in the case of financial futures. Futures prices reveal information about spot prices only when a commodity is not stored or cannot be stored. Then the link between spot and futures prices is broken, and futures prices can assist with price discovery.

²⁰Note that the party that profits from a rise in rates is described as the “buyer.” In our example, you would be said to “buy three against nine months” money, meaning that the forward rate agreement is for a six-month loan in three months’ time.

²¹The interest rate is usually measured by LIBOR. LIBOR (London interbank offered rate) is the interest rate at which major international banks in London borrow dollars (or euros, yen, etc.) from each other.

²²These payments would be made when the loan matures nine months from now.

²³Data on swaps are provided by the International Swaps and Derivatives Association (www.isda.org) and the Bank for International Settlements (www.bis.org).

²⁴ The spread between the bank’s 6% borrowing rate and the 8% lending rate is the bank’s profit on the project financing.

²⁵Maybe the short-term interest rate is below the five-year interest rate because investors expect interest rates to rise.

²⁶Both strategies are equivalent to a series of forward contracts on LIBOR. The forward prices are $4 million each for LIBOR₁ × $66.67, LIBOR₂ × $66.67, and so on. Separately negotiated forward prices would not be $4 million for any one year, but the PVs of the “annuities” of forward prices would be identical.

²⁷Notice that the swap rate always refers 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 short-term debt.

²⁸More commonly, interest rate swaps are based on three-month LIBOR and involve quarterly cash payments.

²⁹Usually in a currency swap the two parties make an initial payment to each other (i.e., Possum pays the bank $10 million and receives €8 million). However, this is not necessary, and Possum might prefer to buy the €8 million from another bank.

³⁰If the inflation swap involves only a single payment, it is known as a zero-coupon swap. If it provides a sequence of payments, each linked to the rate of inflation, it is called a year-on-year swap.

³¹Look back at Section 3-2 if you need a revision session on calculating duration.

³²The duration of the 20-year bonds is 9.37 years and that of the 8-year bonds is 5.87 years. The duration of the package is (7.9 × 9.37 + 9.1 × 5.87)/17 = 7.5 years.

³³Bank for International Settlements, Derivatives Statistics (www.bis.org/statistics/derstats.htm).

³⁴This does not mean that firms don’t worry about the possibility of default, and there are a variety of ways that they try to protect themselves. In the case of swaps, firms are reluctant to deal with banks that do not have the highest credit rating.

³⁵In defined contribution plans, the corporation contributes to the pension fund on behalf of its employees. Each employee has a claim on part of the fund, just as if the employee held shares in a mutual fund. Employees’ retirement benefits depend on their balances in the fund at retirement. If the benefits fall short of an employee’s plans or expectations, he or she has no recourse to the company.

³⁶Madison must also set pension assets aside for current employees. For this mini-case, we concentrate only on retired employees’ benefits.