438 Planning and Forecasting A Foreign Currency Hedge Suppose an American electronics manufacturer has just delivered a large ship- ment of finished products to a customer in France. The French buyer has agreed to pay 1 million French francs in exactly 30 days. The manufacturer is worried that the French franc may be devalued relative to the American dollar during that interval. If the franc is devalued, the dollar value of the promised payment will fall and the American manufacturer will suffer losses. The Amer- ican manufacturer can shed this foreign currency exposure by going short in a franc forward contract or a franc future. The contract will specify a quantity of francs to be exchanged for dollars, at a fixed exchange rate, 30 days in the future. The contract locks in the terms at which the deferred franc revenue can be converted to dollars. No matter what happens to the franc-dollar ex- change rate, the American manufacturer now knows exactly how many dollars he will receive. A Short-Term Interest Rate Hedge Suppose a manufacturer of automotive parts has just delivered a shipment of finished products to a client. Business has been growing, and the company has approved plans to expand capacity next year. The manufacturer expects to receive payment from the customer in 60 days, but will need to use those funds for the planned capital expenditure 90 days after that. The plan is to invest the revenue in three-month Treasury bills as soon as the revenue is re- ceived. Interest rates are currently high. Managers worry that by the time the receivables are collected from the customer, however, interest rates will fall, resulting in less interest earned on the invested funds. The company can hedge against this risk by buying a Treasury bill futures contract, which es- sentially locks in the price and yield of Treasury bills to be purchased 60 days hence. Longer-Term Interest Rate Hedge A manufacturer of speed boats notices that when interest rates rise, sales fall, and the value of the firm’s stock gets battered. The correlation is easy to un- derstand. Customers buy boats on credit, and so when rates rise, the boats ef- fectively become more expensive to buy. In order to insulate the company’s fortunes from the vicissitudes of interest rates, the company could enter a con- tract that pays money when rates rise. A short position in a Treasury bond futures contract would pay off when rates rise and could thus be a desirable hedge. Each time the futures contract expires, the company can roll over into a new contract. The size of the position in the futures should be geared to the fluctuation in sales resulting from changes in interest rates. The Treasury bond hedge can reduce the volatility in the firm’s net income, and the volatility of the firm’s equity value. Financial Management of Risks 439 Synthetic Cash A company’s pension fund is invested primarily in the stocks of the Standard & Poor’s 500. The pension fund manager worries that there may be a downturn in the stock market sometime over the next six months. She considers selling all of the stock and investing the funds in Treasury bills. An alternate hedge strategy that will save considerable transaction costs would be to short S&P 500 futures contracts. By establishing a short futures position, she locks in the price at which the stocks will be sold six months hence. The fund is now insu- lated from any fluctuations in stock prices. Since the fund is now essentially risk free, it will earn the risk-free interest rate. Selling futures while holding the underlying spot instrument is a strategy known as “synthetic cash.” The strategy essentially turns stock into cash. The fund performs as if it were in- vested in Treasury bills. Synthetic Stock A company’s pension fund is invested primarily in Treasury bills. The stock market has been rising rapidly in recent weeks, and the pension fund manager wishes to participate in the boom. One strategy would be to sell the T-bills and invest the proceeds in equities. A more economical strategy would be to leave the value parked in T-bills, and gain exposure to the stock market by going long in stock futures. When the market rises, the futures will pay off. Should the market fall, the fund will suffer losses. The fund will thus behave as if it were invested in stocks. Ergo the name, “synthetic stock.” Market Timing A manager wishes to be exposed to the stock market when he anticipates a market rise, and be out of stocks and into T-bills when he anticipates a drop. Buying and selling stocks to achieve this purpose is very expensive in terms of commissions. But entering and exiting the market via futures is very cheap. The manager should keep all his funds invested in T-bills. When he feels the market will rise, he should go long in stock index futures, such as S&P 500 fu- tures. When he feels the market will drop, he should sell those futures, un- winding the position. If alternatively he wished to assemble a diversified portfolio such as the S&P 500 the old fashion way—a portfolio consisting of actual stocks and no derivatives—he would have to buy each of the 500 stock issues while selling his Treasury bills. This positioning would involve 501 sepa- rate transactions. Turning the actual stock portfolio back into T-bills would similarly require 501 transactions. Turning T-bills effectively into stocks via long futures contracts, on the other hand, involves just one futures trade. Un- winding the futures position would also be just one single trade. Market timing is much more economically executed with futures contracts than with actual equity trades. 440 Planning and Forecasting A Cross-Hedge A manufacturer of plastic water pistols wishes to hedge against increases in raw plastic pellet prices. Unfortunately, there are no futures contracts covering plastic prices. There is, however, a contract on oil prices, and the price of plas- tic is highly correlated with the price of oil. By going long in an oil contract, the manufacturer will be paid money when oil prices rise, which will likely be also when plastic prices rise. Hedging an exposure with a contract tied to a correlated underlying instrument is called a cross-hedge. A Common Pitfall The ease with which futures facilitate hedging sometimes coaxes managers to occasionally take speculative positions. A photographic film manufacturer, for example, might become experienced and comfortable hedging silver prices by going long in silver futures. Managers at the firm might come to believe that no one is better able to forecast silver prices than they are. A time may come when they wholeheartedly believe that silver prices will fall. Not only might they choose not to enter a long silver future hedge at this time, but they may choose to go short in silver futures so as to capitalize on the falling price. If silver prices fall they will not only benefit from a cheaper raw input, but the short sil- ver futures will pay off as well. The danger here is that the manufacturer has lost sight of the fact that it is in the film manufacturing business, and not the business of speculating on commodity prices. Although silver prices might be expected to fall, there is always the possibility that they will rise instead. The probability of a rise might be small, but the consequences would be cata- strophic. Not only will the firm’s raw material price rise, but the firm will suf- fer additionally as it loses on the futures contract. The lesson here is that firms should stay clearly focused on what their business line is, and what role the use of futures plays in their business. Futures use should generally be authorized only for hedging and not for speculation. Auditing systems should be in place to oversee that futures are used appropriately. Futures and Forwards Summary As the above examples illustrate, futures and forwards are useful tools for hedging a wide variety of business and financial risks. Futures and forward contracts essentially commit the two parties to a deferred transaction. No money changes hands initially. As prices subsequently change, however, one party wins at the other’s expense. Futures and forwards thus enable businesses to shed or take on exposure to changing prices. When used to offset an expo- sure the firm faces naturally, futures and forwards reduce risk. Options Options are another breed of derivatives. They share some similarities with futures and forwards, but they also differ in many important respects. Like Financial Management of Risks 441 fu tures and forwards, option prices are a function of the value of an underlying asset, thus they satisfy the definition of derivative. Unlike futures and for- wards, however, options are assets that must be paid for initially. Recall that no money changes hands initially as parties enter into forwards and futures. Op- tions, though, are an asset that has to be bought for a price at the outset. There are two kinds of options, call and puts. A call option is an asset that gives the owner the right but not the obligation to buy some other underlying asset, for a set price, on or up to a set date. For example, consider a call option on Disney stock, that gives the owner the right to purchase one share of Dis- ney stock for $70 per share, on or up to next June 15. (Actually, options are usu- ally sold in blocks covering 100 shares. For expository purposes, however, we will describe an option on only one single share.) The underlying asset would be one share of Disney stock. The prespecified price, known as the “strike price,” would be $70 per share. The expiration date would be June 15. The Dis- ney option might cost $3 initially. If on the expiration date, June 15, the market price of Disney stock stood at $75, the call option owner would exercise the option, allowing him to buy a share of Disney stock for $70. He could then turn around and sell the share for $75 in the marketplace, realizing a terminal payoff from the option of $5. The terminal payoff is $5, so the profit net of the $3 initial option price is $2. Suppose, alternatively, that the market price of Disney stock on June 15 were $69. It would not be profitable to exercise the call option and thereby purchase for $70 what is elsewhere available for $69. In such a case, the op- tion owner would choose not to exercise, and the call would expire worthless. It is the right not to execute the transaction that is the major difference be- tween options and forwards. The long party in a forward contract must buy the goods upon expiration whether it is advantageous to do so or not. By con- trast, a call option owner does not have to buy the underlying asset if he chooses not to. At expiration, a call option should be exercised if and only if the market price exceeds the strike price. When the market price is above the strike price, the call option is said to be “in the money.” When the market price is less than the strike price, the call is “out of the money.” When the market price equals the strike price, the option is “at the money.” An option that is out of the money, or even at the money, at expiration, will expire unex- ercised and worthless. An option’s payoff is defined as the maximum amount of money the op- tion owner would receive at expiration, if she totally liquidated her position. If the option expires out of the money, the payoff is zero. If the option expires in the money, the payoff is the amount of money received from exercising the call option, and then selling the stock in the open market. For example, if the strike price is $70 and the terminal stock price is $60, the payoff would be zero, since the option would be out of the money and should not be exercised. If the ter- minal stock price were $80, the payoff would be $10, since the option should be exercised, allowing the owner to buy the stock for $70, and then sell that stock for $80 in the open market. Mathematically, the payoff is the maximum of zero or the stock price minus the strike price. 442 Planning and Forecasting The payoff ignores the initial price that was paid for the option. Payoff treats the initial price as a sunk cost, and measures only what the option owner might subsequently receive. The payoff minus the initial price is known as the option profit. The option payoff is the same for all owners of the option, re- gardless of what they each initially paid for it. Profit, however, depends on what was initially paid and therefore differs from one investor to another. A payoff diagram is a valuable analytical device for understanding op- tions. A payoff diagram graphs the payoff of an option as a function of the underlying asset’s spot price at expiration. Exhibit 13.1 depicts the payoff dia- gram for the Disney call option with a strike price of $70. The payoff diagram is a picture of the option. It tells you when you will receive money and when you will not. It helps to visualize how the contract will perform, and whether or not the option is appropriate for any particular application. The payoff diagram is flat and equal to zero in the entire range where the option is out of the money—that is, where the stock price is less than the strike price. This means that someone who buys an option might lose his entire in- vestment in that option. You may pay $3 for the option, and lose 100% of that $3 by the expiration date. On the brighter side, the payoff diagram confirms that the most you can lose in an option is the initial premium, the $3 you paid for it. Unlike, futures or forwards, you will never be called on to make addi- tional payments at a later date. Initially, you pay for the option, perhaps $3. From then on you can only receive cash inflows. Note that the payoff diagram begins to rise at the point where the stock price equals the strike price. The payoff is dollar for dollar greater than zero for every dollar that the stock price exceeds the strike price. Thus we see that a call option rises in value as the underlying asset rises in price. For this reason, some people refer to call options as “bullish” instruments. EXHIBIT 13.1 Call option payoff diagram. 0 10 5 15 20 25 30 0 102030405060708090100 Payoff (dollars) Terminal stock price (Strike price = $70) Financial Management of Risks 443 Hedging with a Call Option Consider the trucking company whose rates are regulated yet costs fluctuate with market prices. The chief raw material purchased by the company is diesel fuel. If fuel prices rise, the trucking company will suffer losses, and may in fact be put out of business. As we saw above, the company can guarantee a fixed price for fuel by going long in a future or forward. Another strategy would be to buy a diesel fuel call option contract. The strike price of the call option would lock in the highest price that the company will have to pay for fuel. If fuel prices should drop below the strike price, the company would be under no obligation to exercise the option. It would simply buy fuel at the low market price. If, however, fuel prices rise above the strike price, the company would exercise the option and buy fuel at the relatively low strike price. The added flexibility of the option over the futures strategy comes at a cost. When the company buys the call option it must pay a price or “premium.” The call option is essentially an oil price insurance contract for the firm, insur- ing that fuel prices will not exceed the strike price. If fuel prices remain low, below the strike price, the company will not collect on this insurance policy, and the initial premiums will be lost. Pricing Options At this point the reader may wonder how the initial price of an option is deter- mined. Option pricing is no trivial exercise, and a thorough treatment of option pricing is beyond the scope of this chapter. Some basic principles, however, can be explained here. First, an option’s “intrinsic value” prior to expiration is equal to its payoff. That is, if an option is out of the money, its intrinsic value is zero. If a call option is in the money, for example, if the strike price is $70 and the current stock price is $80, then the intrinsic value equals the stock price minus the strike price, $10. The value of an option, however, exceeds its intrinsic value. An out-of- the-money option is worth more than zero, and the in-the-money option de- scribed above is worth more than $10. This extra value is due to the fact that the downside losses are capped off, but the upside potential is unlimited. As long as there is still time remaining in the option’s life, it is possible that an out- of-the-money option can go in-the-money. An in-the-money option can go fur- ther in the money, and has more upside potential than downside. A call option’s value is a function of the underlying stock price, the strike price, the amount of time remaining to expiration, the interest rate, the stock’s dividend rate, and the volatility of the underlying asset price. As the underly- ing stock price rises, so will the call option’s value. Holding the other variables constant, a call option’s value will be greater when there is a higher stock price, lower strike price, longer time to expiration, higher interest rate, lower divi- dend rate, and more volatility in the underlying asset. Researchers have suc- ceeded in formalizing an equation that prices options as a function of these 444 Planning and Forecasting input variables. The formula is known as the Black-Scholes option pricing for- mula. It is widely available on programmed computer software and in many option theory textbooks. A Written Call Option In the case of life insurance or automobile insurance, when the insured party collects another party must pay. It is a zero sum game. So it is with options. The party that sells the option is liable for the future payoff. “Writing” an option, and “shorting” an option are synonymous with selling an option. The payoff di- agram for a written call option position is the mirror image of the long or bought call option position. As shown in Exhibit 13.2, the x-axis is the reflect- ing surface. Note that once the call option writer has received the initial premium, all subsequent cash flows will be outflows. The best the writer can hope for is that the call will expire out of the money. Note that the potential liability of the written option position is unlimited. Notice as well, that the amount of money the buyer of the option might receive at expiration is the exact amount that writer will have to pay. Thus, when the media report that a particular company has lost millions of dollars in options, the reader should realize that this means some other party has made millions. The newspapers tend to focus on the losers. Strategies Using Written Call Options Why would anybody wish to sell a call option if doing so subjects them to the possibility of unlimited future liabilities? One answer is that speculators some- times deem the risks worthwhile in light of the expected reward. They may be confident that the underlying asset price will not rise and the option will ex- pire worthless. EXHIBIT 13.2 Payoff diagram for a written call option position. –30 –10 –20 0 10 20 30 0 10203040506070 9080 100 Payoff (dollars) Terminal stock price (Strike price = $70) Financial Management of Risks 445 Written call options can also be used to hedge in certain circumstances. Consider oil exporting nations such as Mexico and Venezuela. When oil prices are low they are hungry for funds, funds that are much needed for national development projects. When oil prices are high, they have plenty of excess revenue. A reasonable strategy would be to sell high strike price oil call op- tions when oil prices are low. The country thus receives premiums when funds are most needed, and incurs a liability that only needs to be paid when funds are most plentiful. The oil call options help to smooth the flow of funds into the country. Abken and Feinstein (1994) elaborate on the use of written call options in such a setting. Warrants Warrants are call options that are sold by the company whose stock is the under- lying asset. If Microsoft pays its executive with Microsoft call options, those op- tions will be called warrants. When the warrants are exercised, the total outstanding supply of Microsoft stock will rise. Warrants are valuable, even if they are not yet in the money. Clearly they must be worth something, otherwise executives would not want them and would give them away! Offering warrants as compensation to executives is not free for the firm’s shareholders. Stories abound nowadays of young Internet executives who became fabulously wealthy when they exercised warrants paid to them as part of their employment compensation. Put Options The second type of option is a put. A put option is a contract that gives the owner the right but not the obligation to sell some underlying asset for a pre- specified price, on or up to a given date. Consider a put option on Microsoft stock. Suppose the strike price is $100 and the expiration date is December 15th. The put option owner has the right, but not the obligation to sell a share of Microsoft stock for $100, on or up to December 15. If the market price of Microsoft is above $100, for example $120, the put option owner would not ex- ercise. Why should he force someone to pay $100 for the stock? He can make more money by selling the stock in the open market. Thus, a put option is out of the money if the stock price is above the strike price. If the stock price is below the strike price, however, then the put option is in the money. If the market price of Microsoft is $80 on December 15, the owner of the put can reap a $20 payoff. To realize this payoff, he would buy the Microsoft stock in the marketplace for $80, and then turn around and sell it for $100 by exercis- ing his put option. Thus, a put option is in the money when the stock price is below the strike price. A put option’s payoff at expiration, and its intrinsic value prior to expiration, is the strike price minus the stock price, or zero, whichever is greater. Exhibit 13.3 presents the payoff diagram for a put option. Should the stock price fall to zero, the put option’s payoff would be equal to the strike 446 Planning and Forecasting price. At that point the put option owner would have the right to sell a worth- less stock for $100. From that point, the put option payoff falls one dollar for each dollar that the stock price rises. The payoff reaches zero when the stock price equals the strike price, and then remains at zero no matter how much higher the stock price goes. As is the case with call options, the put option can- not fall in value below zero. Once the put option premium is paid, the owner is never called upon to make another payment. Any subsequent cash flow is posi- tive. It is altogether possible, however, for the buyer of the put option to lose the entire premium, so one should not think that buying a put option is a safe investment. Notice that the put option payoff rises as the stock price falls. For this reason, puts are thought of as “bearish” instruments—instruments that are more profitable the more the underlying asset falls in value. Because of this negative relationship with the underlying asset, puts can be good hedging in- struments for someone who owns the underlying asset. Like the call option’s payoff diagram, the put’s payoff diagram is kinked—that is, there is an elbow at the strike price. A kinked payoff diagram is the hallmark of an option. If a payoff diagram has no kink, then the instru- ment depicted is not an option. The payoff diagram for a written put option position is the mirror image of the put’s payoff diagram. Such a payoff diagram is shown in Exhibit 13.4. The possible payoff reaped by the buyer of the put option is exactly equal to the possible outflow paid by the writer. Put options too are a zero-sum game. Notice that whereas the writer of a call option has unlimited potential liability, the writer of a put option has a potential liability limited to the strike price. Furthermore, notice that a long put option payoff looks nothing like a short call option. Similarly, notice that a long call option payoff is not the same as a short put. Both long puts and short calls are bearish positions, just as both short puts and long calls are bullish positions, but each of these four positions is unique in the direction, size, and timing of cash flows. Long calls and long puts EXHIBIT 13.3 Put option payoff diagram. 0 40 20 60 80 100 120 0 10203040506070 9080 110100 130120 Payoff (dollars) Terminal stock price (Strike price = $100) Financial Management of Risks 447 have to be paid for up front, and then receive a subsequent positive payoff de- pending on what happens to the underlying stock. Short calls and short puts re- ceive all of their cash inflows up front and then become potential liabilities. A Protective Put Strategy A put option can be thought of as price insurance for someone who owns the underlying asset. For example, suppose you are a pension fund manager, and you hold hundreds of shares of Microsoft stock. You hold the stock because you believe the stock will rise in value. You worry, however, that the stock price can fall, and losses will be so great that the fund will be unable to meet the needs of the retirees. An effective hedging strategy would be to buy Microsoft put options. You would choose the strike price to be at a level that would guar- antee the solvency of the fund. If Microsoft stock falls below the strike price of the put options, the put options will pay off the difference between the new lower market price and the strike price. If Microsoft stock rises, the put op- tions would expire out of the money. The insurance would not pay off, but you would reap the high return of the rising stock. This strategy is known as buy- ing a protective put. It is essentially portfolio insurance. The strategy allows for the upside appreciation of the portfolio, yet sets a floor below which the value of the portfolio cannot fall. A protective put strategy can also be implemented by a producer who faces the risk of his product’s price falling. For example, a cattle rancher can buy put options on cattle, thereby fixing the lowest price at which he will be able to sell his herd. Swaps The third category of derivative we will examine is swaps. A swap is an agree- ment between two parties to exchange cash flows over a period of time. The EXHIBIT 13.4 Payoff diagram for a written put option position. –110 –70 –90 –50 –30 –10 10 30 0 10203040506070 9080 110100 130120 Payoff (dollars) Terminal stock price (Strike price = $100) . business line is, and what role the use of futures plays in their business. Futures use should generally be authorized only for hedging and not for speculation. Auditing systems should be in. to participate in the boom. One strategy would be to sell the T-bills and invest the proceeds in equities. A more economical strategy would be to leave the value parked in T-bills, and gain exposure. position in the futures should be geared to the fluctuation in sales resulting from changes in interest rates. The Treasury bond hedge can reduce the volatility in the firm’s net income, and the