economics_of_money_banking__financial_markets

Factors Affecting

the Prices of

Option Premiums

Similar reasoning indicates that the bank manager might prefer to use options to conduct the macro hedge to immunize the entire bank portfolio from interest-rate risk. Again, the strategy of using options rather than futures has the disadvantage that the First National Bank has to pay the premiums on these contracts up front. By contrast, using options allows the bank to keep the gains from a decline in interest rates (which will raise the value of the bankÕs assets relative to its liabilities), because these gains will not be offset by large losses on the option contracts.

In the case of a macro hedge, there is another reason why the bank might prefer option contracts to futures contracts. Profits and losses on futures contracts can cause accounting problems for banks because such profits and losses are not allowed to be offset by unrealized changes in the value of the rest of the bankÕs portfolio. Consider what happens when interest rates fall. If First National sells futures contracts to conduct the macro hedge, then when interest rates fall and the prices of the Treasury bond futures contracts rise, it will have large losses on these contracts. Of course, these losses are offset by unrealized profits in the rest of the bankÕs portfolio, but the bank is not allowed to offset these losses in its accounting statements. So even though the macro hedge is serving its intended purpose of immunizing the bankÕs portfolio from interest-rate risk, the bank would experience large accounting losses when interest rates fall. Indeed, bank managers have lost their jobs when perfectly sound hedges with interest-rate futures have led to large accounting losses. Not surprisingly, bank managers might shrink from using financial futures to conduct macro hedges for this reason.

Futures options, however, can come to the rescue of the managers of banks and other financial institutions. Suppose that First National conducted the macro hedge by buying put options instead of selling Treasury bond futures. Now if interest rates fall and bond prices rise well above the exercise price, the bank will not have large losses on the option contracts, because it will just decide not to exercise its options. The bank will not suffer the accounting problems produced by hedging with financial futures. Because of the accounting advantages of using futures options to conduct macro hedges, option contracts have become important to financial institution managers as tools for hedging interest-rate risk.

If we again look closely at the Wall Street Journal entry for Treasury bond futures options in the ÒFollowing the Financial NewsÓ box on page 321, we learn several interesting facts about how the premiums on option contracts are priced. The first thing you may have noticed is that when the strike (exercise) price for a contract is set at a higher level, the premium for the call option is lower and the premium for the put option is higher. For example, in going from a contract with a strike price of 112 to one with 115, the premium for the March call option falls from 1 45/64 to 16/64, and the premium for the March put option rises from 19/64 to 1 54/64.

Our understanding of the profit function for option contracts illustrated in Figure 1 helps explain this fact. As we saw in panel (a), a higher price for the underlying financial instrument (in this case a Treasury bond futures contract) relative to the optionÕs exercise price results in higher profits on the call (buy) option. Thus the lower the strike price, the higher the profits on the call option contract and the greater the

Summary

C H A P T E R 1 3 Financial Derivatives 327

premium that investors like Irving are willing to pay. Similarly, we saw in panel (b) that a higher price for the underlying financial instrument relative to the exercise price lowers profits on the put (sell) option, so that a higher strike price increases profits and thus causes the premium to increase.

The second thing you may have noticed in the Wall Street Journal entry is that as the period of time over which the option can be exercised (the term to expiration) gets longer, the premiums for both call and put options rise. For example, at a strike price of 112, the premium on the call option increases from 1 45/64 in March to 1 50/64 in April and to 2 28/64 in May. Similarly, the premium on the put option increases from 19/64 in March to 1 43/64 in April and to 2 22/64 in May. The fact that premiums increase with the term to expiration is also explained by the nonlinear profit function for option contracts. As the term to expiration lengthens, there is a greater chance that the price of the underlying financial instrument will be very high or very low by the expiration date. If the price becomes very high and goes well above the exercise price, the call (buy) option will yield a high profit, but if the price becomes very low and goes well below the exercise price, the losses will be small because the owner of the call option will simply decide not to exercise the option. The possibility of greater variability of the underlying financial instrument as the term to expiration lengthens raises profits on average for the call option.

Similar reasoning tells us that the put (sell) option will become more valuable as the term to expiration increases, because the possibility of greater price variability of the underlying financial instrument increases as the term to expiration increases. The greater chance of a low price increases the chance that profits on the put option will be very high. But the greater chance of a high price does not produce substantial losses for the put option, because the owner will again just decide not to exercise the option.

Another way of thinking about this reasoning is to recognize that option contracts have an element of Òheads, I win; tails, I donÕt lose too badly.Ó The greater variability of where the prices might be by the expiration date increases the value of both kinds of options. Since a longer term to the expiration date leads to greater variability of where the prices might be by the expiration date, a longer term to expiration raises the value of the option contract.

The reasoning that we have just developed also explains another important fact about option premiums. When the volatility of the price of the underlying instrument is great, the premiums for both call and put options will be higher. Higher volatility of prices means that for a given expiration date, there will again be greater variability of where the prices might be by the expiration date. The Òheads, I win; tails, I donÕt lose too badlyÓ property of options then means that the greater variability of possible prices by the expiration date increases average profits for the option and thus increases the premium that investors are willing to pay.

Our analysis of how profits on options are affected by price movements for the underlying financial instrument leads to the following conclusions about the factors that determine the premium on an option contract:

1.The higher the strike price, everything else being equal, the lower the premium on call (buy) options and the higher the premium on put (sell) options.

2.The greater the term to expiration, everything else being equal, the higher the premiums for both call and put options.

3.The greater the volatility of prices of the underlying financial instrument, everything else being equal, the higher the premiums for both call and put options.

Interest-Rate

Swap Contracts

In addition to forwards, futures, and options, financial institutions use one other important financial derivative to manage risk. Swaps are financial contracts that obligate each party to the contract to exchange (swap) a set of payments (not assets) it owns for another set of payments owned by another party. There are two basic kinds of swaps: Currency swaps involve the exchange of a set of payments in one currency for a set of payments in another currency. Interest-rate swaps involve the exchange of one set of interest payments for another set of interest payments, all denominated in the same currency.

Interest-rate swaps are an important tool for managing interest-rate risk, and they first appeared in the United States in 1982, when, as we have seen, there was an increase in the demand for financial instruments that could be used to reduce interest-rate risk. The most common type of interest-rate swap (called the plain vanilla swap) specifies

(1) the interest rate on the payments that are being exchanged; (2) the type of interest payments (variable or fixed-rate); (3) the amount of notional principal, which is the amount on which the interest is being paid; and (4) the time period over which the exchanges continue to be made. There are many other more complicated versions of swaps, including forward swaps and swap options (called swaptions), but here we will look only at the plain vanilla swap. Figure 2 illustrates an interest-rate swap between the Midwest Savings Bank and the Friendly Finance Company. Midwest Savings agrees to pay Friendly Finance a fixed rate of 7% on $1 million of notional principal for the next ten years, and Friendly Finance agrees to pay Midwest Savings the one-year Treasury bill rate plus 1% on $1 million of notional principal for the same period. Thus, as shown in Figure 2, every year the Midwest Savings Bank would be paying the Friendly Finance Company 7% on $1 million, while Friendly Finance would be paying Midwest Savings the one-year T-bill rate plus 1% on $1 million.

F I G U R E 2 Interest-Rate Swap

Payments

In this swap arrangement with a notional principal of $1 million and a term of ten years, the Midwest Savings Bank pays a fixed rate of 7% $1 million to the Friendly Finance Company, which in turn agrees to pay the one-year Treasury bill rate plus 1% $1 million to the Midwest Savings Bank.

Application

Advantages of

Interest-Rate

Swaps

Hedging with Interest-Rate Swaps

You might wonder why these two parties find it advantageous to enter into this swap agreement. The answer is that it may help both of them hedge interest-rate risk.

Suppose that the Midwest Savings Bank, which tends to borrow shortterm and then lend long-term in the mortgage market, has $1 million less of rate-sensitive assets than it has of rate-sensitive liabilities. As we learned in Chapter 9, this situation means that as interest rates rise, the rise in the cost of funds (liabilities) is greater than the rise in interest payments it receives on its assets, many of which are fixed-rate. The result of rising interest rates is thus a shrinking of Midwest SavingsÕ net interest margin and a decline in its profitability. As we saw in Chapter 9, to avoid this interest-rate risk, Midwest Savings would like to convert $1 million of its fixed-rate assets into $1 million of rate-sensitive assets, in effect making rate-sensitive assets equal ratesensitive liabilities, thereby eliminating the gap. This is exactly what happens when it engages in the interest-rate swap. By taking $1 million of its fixedrate income and exchanging it for $1 million of rate-sensitive Treasury bill income, it has converted income on $1 million of fixed-rate assets into income on $1 million of rate-sensitive assets. Now when interest rates increase, the rise in rate-sensitive income on its assets exactly matches the rise in the rate-sensitive cost of funds on its liabilities, leaving the net interest margin and bank profitability unchanged.

The Friendly Finance Company, which issues long-term bonds to raise funds and uses them to make short-term loans, finds that it is in exactly the opposite situation to Midwest Savings: It has $1 million more of rate-sensitive assets than of rate-sensitive liabilities. It is therefore concerned that a fall in interest rates, which will result in a larger drop in income from its assets than the decline in the cost of funds on its liabilities, will cause a decline in profits. By doing the interest-rate swap, it eliminates this interest-rate risk because it has converted $1 million of rate-sensitive income into $1 million of fixed-rate income. Now the Friendly Finance Company finds that when interest rates fall, the decline in rate-sensitive income is smaller and so is matched by the decline in the rate-sensitive cost of funds on its liabilities, leaving its profitability unchanged.

To eliminate interest-rate risk, both the Midwest Savings Bank and the Friendly Finance Company could have rearranged their balance sheets by converting fixed-rate assets into rate-sensitive assets, and vice versa, instead of engaging in an interest-rate swap. However, this strategy would have been costly for both financial institutions for several reasons. The first is that financial institutions incur substantial transaction costs when they rearrange their balance sheets. Second, different financial institutions have informational advantages in making loans to certain customers who may prefer certain maturities. Thus, adjusting the balance sheet to eliminate interest-rate risk might result in a loss of these informational advantages, which the financial institution is unwilling to give up. Interest-rate swaps solve these problems for financial institutions, because in effect, they allow the institutions to convert fixed-rate assets

Disadvantages of

Interest-Rate

Swaps

Financial

Intermediaries in

Interest-Rate

Swaps

into rate-sensitive assets without affecting the balance sheet. Large transaction costs are avoided, and the financial institutions can continue to make loans where they have an informational advantage.

We have seen that financial institutions can also hedge interest-rate risk with other financial derivatives such as futures contracts and futures options. Interest-rate swaps have one big advantage over hedging with these other derivatives: They can be written for very long horizons, sometimes as long as 20 years, whereas financial futures and futures options typically have much shorter horizons, not much more than a year. If a financial institution needs to hedge interest-rate risk for a long horizon, financial futures and option markets may not do it much good. Instead it can turn to the swap market.

Although interest-rate swaps have important advantages that make them very popular with financial institutions, they also have disadvantages that limit their usefulness. Swap markets, like forward markets, can suffer from a lack of liquidity. LetÕs return to looking at the swap between the Midwest Savings Bank and the Friendly Finance Company. As with a forward contract, it might be difficult for the Midwest Savings Bank to link up with the Friendly Finance Company to arrange the swap. In addition, even if the Midwest Savings Bank could find a counterparty like the Friendly Finance Company, it might not be able to negotiate a good deal because it couldnÕt find any other institution with which to negotiate.

Swap contracts also are subject to the same default risk that we encountered for forward contracts. If interest rates rise, the Friendly Finance Company would love to get out of the swap contract, because the fixed-rate interest payments it receives are less than it could get in the open market. It might then default on the contract, exposing Midwest Savings to a loss. Alternatively, the Friendly Finance Company could go bust, meaning that the terms of the swap contract would not be fulfilled.

As we have just seen, financial institutions do have to be aware of the possibility of losses from a default on swaps. As with a forward contract, each party to a swap must have a lot of information about the other party to make sure that the contract is likely to be fulfilled. The need for information about counterparties and the liquidity problems in swap markets could limit the usefulness of these markets. However, as we saw in Chapter 8, when informational and liquidity problems crop up in a market, financial intermediaries come to the rescue. That is exactly what happens in swap markets. Intermediaries such as investment banks and especially large commercial banks have the ability to acquire information cheaply about the creditworthiness and reliability of parties to swap contracts and are also able to match up parties to a swap. Hence large commercial banks and investment banks have set up swap markets in which they act as intermediaries.

Summary

1.Interest-rate forward contracts, which are agreements to sell a debt instrument at a future (forward) point in time, can be used to hedge interest-rate risk. The advantage of forward contracts is that they are flexible, but the disadvantages are that they are subject to default risk and their market is illiquid.

2.A financial futures contract is similar to an interest-rate forward contract, in that it specifies that a debt instrument must be delivered by one party to another on a stated future date. However, it has advantages over a forward contract in that it is not subject to default risk and is more liquid. Forward and futures contracts can

be used by financial institutions to hedge (protect) against interest-rate risk.

3.An option contract gives the purchaser the right to buy (call option) or sell (put option) a security at the exercise (strike) price within a specific period of time. The profit function for options is nonlinearÑprofits do not always grow by the same amount for a given change in the price of the underlying financial instrument. The nonlinear profit function for options explains why their value (as reflected by the premium paid for them) is negatively related to the exercise price for call options, positively related to the exercise price for put options, positively related to the term to expiration for both call and put options, and positively related to the volatility of the prices of the underlying financial instrument for both call and put options. Financial institutions use

C H A P T E R 1 3 Financial Derivatives 331

futures options to hedge interest-rate risk in a similar fashion to the way they use financial futures and forward contracts. Futures options may be preferred for macro hedges because they suffer from fewer accounting problems than financial futures.

4.Interest-rate swaps involve the exchange of one set of interest payments for another set of interest payments and have default risk and liquidity problems similar to those of forward contracts. As a result, interest-rate swaps often involve intermediaries such as large commercial banks and investment banks that make a market in swaps. Financial institutions find that interest-rate swaps are useful ways to hedge interestrate risk. Interest-rate swaps have one big advantage over financial futures and options: They can be written for very long horizons.

Questions marked with an asterisk are answered at the end of the book in an appendix, ÒAnswers to Selected Questions and Problems.Ó

1.If the pension fund you manage expects to have an inflow of $120 million six months from now, what forward contract would you seek to enter into to lock in current interest rates?

*2. If the portfolio you manage is holding $25 million of 8s of 2023 Treasury bonds with a price of 110, what forward contract would you enter into to hedge the interest-rate risk on these bonds over the coming year?

3.If at the expiration date, the deliverable Treasury bond is selling for 101 but the Treasury bond futures contract is selling for 102, what will happen to the futures price? Explain your answer.

*4. If you buy a $100,000 June Treasury bond contract for 108 and the price of the deliverable Treasury bond at the expiration date is 102, what is your profit or loss on the contract?

5.Suppose that the pension you are managing is expecting an inflow of funds of $100 million next year and you want to make sure that you will earn the current

interest rate of 8% when you invest the incoming funds in long-term bonds. How would you use the futures market to do this?

*6. How would you use the options market to accomplish the same thing as in Problem 5? What are the advantages and disadvantages of using an options contract rather than a futures contract?

7.If you buy a put option on a $100,000 Treasury bond futures contract with an exercise price of 95 and the price of the Treasury bond is 120 at expiration, is the contract in the money, out of the money, or at the money? What is your profit or loss on the contract if the premium was $4,000?

*8. Suppose that you buy a call option on a $100,000 Treasury bond futures contract with an exercise price of 110 for a premium of $1,500. If on expiration the futures contract has a price of 111, what is your profit or loss on the contract?

9.Explain why greater volatility or a longer term to maturity leads to a higher premium on both call and put options.

*10. Why does a lower strike price imply that a call option will have a higher premium and a put option a lower premium?

11.If the finance company you manage has a gap of $5 million (rate-sensitive assets greater than rate-sensitive liabilities by $5 million), describe an interest-rate swap that would eliminate the companyÕs income gap.

*12. If the savings and loan you manage has a gap of $42 million, describe an interest-rate swap that would eliminate the S&LÕs income risk from changes in interest rates.

13.If your company has a payment of 200 million euros due one year from now, how would you hedge the foreign exchange risk in this payment with 125,000 euro futures contracts?

*14. If your company has to make a 10 million euro payment to a German company in June, three months from now, how would you hedge the foreign exchange risk in this payment with a 125,000 euro futures contract?

15.Suppose that your company will be receiving 30 million euros six months from now and the euro is currently selling for 1 euro per dollar. If you want to hedge the foreign exchange risk in this payment, what kind of forward contract would you want to enter into?

Web Exercises

1.We have discussed the various stock markets in detail throughout this text. Another market that is less well known is the New York Mercantile Exchange. Here contracts on a wide variety of commodities are traded on a daily basis. Go to www.nymex.com/welcome /info_01.htm and read the discussion explaining the origin and purpose of the mercantile exchange. Write a one-page summary discussing this material.

2.The following site can be used to demonstrate how the features of an option affect the optionÕs prices. Go to www.intrepid.com/~robertl/option-pricer4.html. What happens to the price of an option under each of the following situations?

a.The strike price increases

b.Interest rates increase

c.Volatility increases

d.The time until the option matures increases

PREVIEW

Among the most important players in financial markets throughout the world are central banks, the government authorities in charge of monetary policy. Central banksÕ actions affect interest rates, the amount of credit, and the money supply, all of which have direct impacts not only on financial markets, but also on aggregate output and inflation. To understand the role that central banks play in financial markets and the overall economy, we need to understand how these organizations work. Who controls central banks and determines their actions? What motivates their behavior? Who holds the reins of power?

In this chapter, we look at the institutional structure of major central banks, and focus particularly on the Federal Reserve System, the most important central bank in the world. We start by focusing on the formal institutional structure of the Fed and then examine the more relevant informal structure that determines where the true power within the Federal Reserve System lies. By understanding who makes the decisions, we will have a better idea of how they are made. We then look at several other major central banks and see how they are organized. With this information, we will be more able to comprehend the actual conduct of monetary policy described in the following chapters.