economics_of_money_banking__financial_markets
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316 P A R T I I I Financial Institutions
Table 1 Widely Traded Financial Futures Contracts
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Open Interest |
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January 30, 2003 |
Type of Contract |
Contract Size |
Exchange* |
Reflects March 2003 Futures |
Treasury Rate Contracts |
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Treasury bonds |
$100,000 |
CBT |
393,546 |
Treasury notes |
$100,000 |
CBT |
746,015 |
Five-year Treasury notes |
$100,000 |
CBT |
683,499 |
Two-year Treasury notes |
$200,000 |
CBT |
106,184 |
Thirty-day Fed levels |
$5 million |
CBT |
49,069 |
Treasury bills |
$1 million |
CME |
292 |
One-month LIBOR |
$3 million |
CME |
6,389 |
Municipal Bond Index |
$1,000 |
CBT |
2,683 |
Eurodollar |
$4 million |
CME |
747,691 |
Euroyen |
$100 million |
CME |
10,765 |
Sterling |
£500,000 |
LIFFE |
159,800 |
Long Gilt |
£100,000 |
LIFFE |
90,093 |
Three-month Euribor |
€€1 million |
LIFFE |
497,688 |
Euroswiss franc |
SF 1 million |
LIFFE |
85,366 |
Ten-year Euronational bonds |
€€100,000 |
EUREX |
812,029 |
Canadian bankerÕs acceptance |
C$1 million |
ME |
64,333 |
Stock Index Contracts |
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Standard & PoorÕs 500 Index |
$250 index |
CME |
577,661 |
Standard & PoorÕs MIDCAP 400 |
$500 index |
CME |
13,652 |
NASDAQ 100 |
$100 index |
CME |
71,233 |
Nikkei 225 Stock Average |
$5 index |
CME |
16,193 |
Financial TimesÐStock Exchange |
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100-Share Index |
£10 per index point |
LIFFE |
460,997 |
Currency Contracts |
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Yen |
12,500,000 yen |
CME |
90,508 |
Euro |
125,000 euros |
CME |
102,536 |
Canadian dollar |
100,000 Canadian $ |
CME |
89,651 |
British pound |
100,000 pounds |
CME |
102,536 |
Swiss franc |
125,000 francs |
CME |
55,402 |
Mexican peso |
500,000 new pesos |
CME |
29,774 |
*Exchange abbreviations: CBT, Chicago Board of Trade; CME, Chicago Mercantile Exchange; LIFFE, London International Financial Futures Exchange; EUREX, European Exchange; ME, Montreal Exchange.
Source: Wall Street Journal, January 31, 2003, p. C21.
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Financial Institutions |
a result, the person who has cornered the market can set exorbitant prices for the securities that investors with a short position must buy to fulfill their obligations under the futures contract. The person who has cornered the market makes a fortune, but investors with a short position take a terrific loss. Clearly, the possibility that corners might occur in the market will discourage people from taking a short position and might therefore decrease the size of the market. By allowing many different securities to be delivered, the futures contract makes it harder for anyone to corner the market, because a much larger amount of securities would have to be purchased to establish the corner. Corners are a concern to both regulators and the organized exchanges that design futures contracts.
Trading in the futures market has been organized differently from trading in forward markets to overcome the default risk problems arising in forward contracts. In both types, for every contract, there must be a buyer who is taking a long position and a seller who is taking a short position. However, the buyer and seller of a futures contract make their contract not with each other but with the clearinghouse associated with the futures exchange. This setup means that the buyer of the futures contract does not need to worry about the financial health or trustworthiness of the seller, or vice versa, as in the forward market. As long as the clearinghouse is financially solid, buyers and sellers of futures contracts do not have to worry about default risk.
To make sure that the clearinghouse is financially sound and does not run into financial difficulties that might jeopardize its contracts, buyers or sellers of futures contracts must put an initial deposit, called a margin requirement, of perhaps $2,000 per Treasury bond contract into a margin account kept at their brokerage firm. Futures contracts are then marked to market every day. What this means is that at the end of every trading day, the change in the value of the futures contract is added to or subtracted from the margin account. Suppose that after you buy the Treasury bond contract at a price of 115 on Wednesday morning, its closing price at the end of the day, the settlement price, falls to 114. You now have a loss of 1 point, or $1,000, on the contract, and the seller who sold you the contract has a gain of 1 point, or $1,000. The $1,000 gain is added to the sellerÕs margin account, making a total of $3,000 in that account, and the $1,000 loss is subtracted from your account, so you now only have $1,000 in your account. If the amount in this margin account falls below the maintenance margin requirement (which can be the same as the initial requirement but is usually a little less), the trader is required to add money to the account. For example, if the maintenance margin requirement is also $2,000, you would have to add $1,000 to your account to bring it up to $2,000. Margin requirements and marking to market make it far less likely that a trader will default on a contract, thus protecting the futures exchange from losses.
A final advantage that futures markets have over forward markets is that most futures contracts do not result in delivery of the underlying asset on the expiration date, whereas forward contracts do. A trader who sold a futures contract is allowed to avoid delivery on the expiration date by making an offsetting purchase of a futures contract. Because the simultaneous holding of the long and short positions means that the trader would in effect be delivering the bonds to itself, under the exchange rules the trader is allowed to cancel both contracts. Allowing traders to cancel their contracts in this way lowers the cost of conducting trades in the futures market relative to the forward market in that a futures trader can avoid the costs of physical delivery, which is not so easy with forward contracts.
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$3,000 ($5,000 $2,000). The $3,000 profit at a price of 120 is plotted as point C. Similarly, if the price of the futures contract rose to 125, the option contract would yield a net profit of $8,000 ($10,000 from exercising the option minus the $2,000 premium), plotted as point D. Plotting these points, we get the kinked profit curve for the call option that we see in panel (a).
Suppose that instead of purchasing the futures option contract in February, Irving decides instead to buy the $100,000 June Treasury bond futures contract at the price of 115. If the price of the bond on the expiration day at the end of June declines to 110, meaning that the price of the futures contract also falls to 110, Irving suffers a loss of 5 points, or $5,000. The loss of $5,000 on the futures contract at a price of 110 is plotted as point A in panel (a). At a price of 115 on the expiration date, Irving would have a zero profit on the futures contract, plotted as point B . At a price of 120, Irving would have a profit on the contract of 5 points, or $5,000 (point C ), and at a price of 125, the profit would be 10 percentage points, or $10,000 (point D ). Plotting these points, we get the linear (straight-line) profit curve for the futures contract that appears in panel (a).
Now we can see the major difference between a futures contract and an option contract. As the profit curve for the futures contract in panel (a) indicates, the futures contract has a linear profit function: Profits grow by an equal dollar amount for every point increase in the price of the underlying financial instrument. By contrast, the kinked profit curve for the option contract is nonlinear, meaning that profits do not always grow by the same amount for a given change in the price of the underlying financial instrument. The reason for this nonlinearity is that the call option protects Irving from having losses that are greater than the amount of the $2,000 premium. In contrast, IrvingÕs loss on the futures contract is $5,000 if the price on the expiration day falls to 110, and if the price falls even further, IrvingÕs loss will be even greater. This insurance-like feature of option contracts explains why their purchase price is referred to as a premium. Once the underlying financial instrumentÕs price rises above the exercise price, however, IrvingÕs profits grow linearly. Irving has given up something by buying an option rather than a futures contract. As we see in panel (a), when the price of the underlying financial instrument rises above the exercise price, IrvingÕs profits are always less than that on the futures contract by exactly the $2,000 premium he paid.
Panel (b) plots the results of the same profit calculations if Irving buys not a call but a put option (an option to sell) with an exercise price of 115 for a premium of $2,000 and if he sells the futures contract rather than buying one. In this case, if on the expiration date the Treasury bond futures have a price above the 115 exercise price, the put option is Òout of the money.Ó Irving would not want to exercise the put option and then have to sell the futures contract he owns as a result at a price below the market price and lose money. He would not exercise his option, and he would be out only the $2,000 premium he paid. Once the price of the futures contract falls below the 115 exercise price, Irving benefits from exercising the put option because he can sell the futures contract at a price of 115 but can buy it at a price below this. In such a situation, in which the price of the underlying instrument is below the exercise price, the put option is Òin the money,Ó and profits rise linearly as the price of the futures contract falls. The profit function for the put option illustrated in panel (b) of Figure 1 is kinked, indicating that Irving is protected from losses greater than the amount of the premium he paid. The profit curve for the sale of the futures contract is just the negative of the profit for the futures contract in panel (a) and is therefore linear.
Panel (b) of Figure 1 confirms the conclusion from panel (a) that profits on option contracts are nonlinear but profits on futures contracts are linear.
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C H A P T E R 1 3 Financial Derivatives 325 |
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Study Guide |
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To make sure you understand how profits and losses on option and futures contracts |
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are generated, calculate the net profits on the put option and the short position in the |
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futures contract at prices on the expiration day of 110, 115, 120, and 125. Then ver- |
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ify that your calculations correspond to the points plotted in panel (b) of Figure 1. |
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Two other differences between futures and option contracts must be mentioned. |
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The first is that the initial investment on the contracts differs. As we saw earlier in the |
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chapter, when a futures contract is purchased, the investor must put up a fixed |
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amount, the margin requirement, in a margin account. But when an option contract is |
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purchased, the initial investment is the premium that must be paid for the contract. |
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The second important difference between the contracts is that the futures contract |
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requires money to change hands daily when the contract is marked to market, whereas |
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the option contract requires money to change hands only when it is exercised. |
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Application |
Hedging with Futures Options |
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Earlier in the chapter, we saw how the First National Bank could hedge the |
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interest-rate risk on its $5 million holdings of 8s of 2023 by selling $5 mil- |
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lion of T-bond futures. A rise in interest rates and the resulting fall in bond |
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prices and bond futures contracts would lead to profits on the bankÕs sale of |
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the futures contracts that would exactly offset the losses on the 8s of 2023 |
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the bank is holding. |
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As panel (b) of Figure 1 suggests, an alternative way for the manager to |
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protect against a rise in interest rates and hence a decline in bond prices is to |
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buy $5 million of put options written on the same Treasury bond futures. As |
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long as the exercise price is not too far from the current price as in panel (b), |
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the rise in interest rates and decline in bond prices will lead to profits on the |
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futures and the futures put options, profits that will offset any losses on the |
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$5 million of Treasury bonds. |
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The one problem with using options rather than futures is that the First |
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National Bank will have to pay premiums on the options contracts, thereby |
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lowering the bankÕs profits in order to hedge the interest-rate risk. Why might |
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the bank manager be willing to use options rather than futures to conduct the |
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hedge? The answer is that the option contract, unlike the futures contract, |
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allows the First National Bank to gain if interest rates decline and bond prices |
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rise. With the hedge using futures contracts, the First National Bank does not |
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gain from increases in bond prices because the profits on the bonds it is hold- |
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ing are offset by the losses from the futures contracts it has sold. However, as |
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panel (b) of Figure 1 indicates, the situation when the hedge is conducted |
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with put options is quite different: Once bond prices rise above the exercise |
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price, the bank does not suffer additional losses on the option contracts. At |
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the same time, the value of the Treasury bonds the bank is holding will |
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increase, thereby leading to a profit for the bank. Thus using options rather |
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than futures to conduct the micro hedge allows the bank to protect itself from |
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rises in interest rates but still allows the bank to benefit from interest-rate |
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declines (although the profit is reduced by the amount of the premium). |
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