# ch05.doc

Chapter 5: Interest Yields, Interest Rate Risk, and Derivative Securities I. Chapter Overview Chapter 5 begins with a presentation of the concept of discounted present value and how it relates the market price of a bond to its yield. This discussion is followed by an explanation of how term to maturity affects interest-rate risk. The next section introduces the term structure of interest rates and the representation of the yield curve. This section proceeds with a discussion of various theories of the term structure and with an evaluation of the extent to which they are able to explain regular features of the yield curve, such as its upward slope. The theories discussed are (1) the segmented markets theory, (2) the expectations theory and (3) the preferred habitat theory. Finally, the section ends with an elaboration of the various sources of interest rate risk, and other reasons for interest rate differentials between instruments with similar maturities. These include (1) differences in the degree of default risk, (2) differences in the degree of liquidity and (3) differences in tax obligations. The following section examines how excess returns arising from failure of uncovered interest parity contribute to differences among national interest rates. It explains the concept of excess returns, discusses recent evidence concerning excess returns for various nations, and evaluates how varying sizes of excess returns can help explain international interest rate differentials. The next section defines real interest rates. It explains how combining the purchasing power parity and uncovered interest parity conditions leads to a real interest parity condition, which in principle can be used to provide a measure of international market arbitrage. The chapter then turns to a discussion of ways in which investors can hedge against interest rate risk using derivatives. The section points out that forward exchange contracts are simply one example of a derivative security. Just as investors use forward exchange rate markets to hedge against exchange risk, investors can use derivative securities that are based on forward interest rates to hedge against interest rate risk. The chapter then describes some of the most common forms of available derivatives, such as interest rate futures, stock index futures, and currency futures. The uses of currency futures, options and swaps are also discussed. The chapter ends with a brief discussion of the types of risks associated with derivatives. II. Chapter Outline A. Interest Rates 1. Instrument Yields and Financial Instrument Prices a. Interest Rates and Discounted Present Value b. Discounted Present Value and the Market Price of Bonds c. Perpetuities and the Relationship between Interest Yields and Bond Prices 2. Term to Maturity and Interest-Rate Risk 3. Term Structure of Interest Rates a. Yield Curves b. Segmented Markets Theory c. The Expectations Theory d. The Preferred Habitat Theory 4. Risk Structure of Interest Rates a. Default Risk b. Liquidity c. Tax Differences B. Interest Rate Differentials—Excess Returns and Failure of Uncovered Interest Parity 1. Breakdowns of Uncovered Interest Parity and Excess Returns a. Excess Returns b. Evidence on Excess Returns 2. Accounting for Differences in Excess Returns to Help Explain Interest Rate Differences C. Real Interest Rates and Real Interest Parity 1. Real Interest Rates: The Fisher Equation 2 . Real Interest Parity a. Combining Relative Interest Parity and Uncovered Interest Parity b. Deviations from Real Interest Parity as a Measure of International Market Arbitrage D. Hedging, Speculation, and Derivative Securities 1. Possible Responses to Interest Rate Risk a. Some Strategies for Limiting Interest Rate Risk b. Hedging 2. Derivative Securities a. Hedging with Forward Contracts b. Speculation with Derivatives c. Speculative Gains and Losses E. Common Derivative Securities and Their Risks 1. Forward Contracts 2. Futures a. Interest-Rate Futures b. Stock-Index Futures c. Currency Futures 1) Hedging with Currency Futures 2) Daily Futures Settlement 3. Options a. Stock Options and Futures Options b. Currency Options 1) Limited Losses and Potential Profits from Using Currency Call Options 2) Limited Losses and Potential Profits from Using Currency Put Options 3) Netting 4. Swaps a. Currency Swaps b. Types of Swaps 5. Derivatives Risks and Regulation a. Measuring Derivatives Risks b. Types of Derivatives Risks F. Chapter Summary III. Fundamental Issues 1. How are interest yields, financial instrument prices, and interest-rate risk interrelated? 2. Why do market interest yields vary with differences in financial instruments terms to maturity and risks? 3. What factors explain why international interest rate differentials are often inconsistent with the uncovered interest parity condition? 4. What are real interest rates, and how can real interest rate differentials serve as indicators of the extent to which international markets are open to arbitrage? 5. What are derivative securities? 6. What are the most commonly traded derivative securities? IV. Chapter Features 1. Management Notebook: “Why Uncovered Interest Parity May Hold, But Not for Very Long“ This management notebook considers one theory for why uncovered interest parity rarely appears to hold, which is that the time immediately before interest returns are about to be received by holders of financial instruments is when the greatest arbitrage opportunity exists. It discusses recent research by two Federal Reserve economists indicating that the uncovered interest parity condition indeed appears more likely to be satisfied during the last few minutes before instruments mature. For Critical Analysis: The interest rate on this financial instrument and the interest rate on a similar foreign instrument cannot change during this time just before transmission of interest payments to the holders of these instruments. Exchange rates can still adjust in foreign exchange markets, however. 2. Management Notebook: “Bad Days for the Badla“ The subject of this management notebook is a traditional method used in Indian financial markets to carry forward trades of commodities, stocks, or currencies without engaging in final settlement. It discusses the fact that recently introduced Western-style futures contracts appear to be gradually replacing this informal type of futures mechanism. For Critical Analysis: Traders tend to prefer lower prices (and hence higher returns) but also are averse to risk. If Western-style futures contracts are sufficiently less risky, this can help explain why they have tended to crowd out badla even when the latter instruments trade at lower prices. 3. Management Notebook: “Following the Money in Derivatives Markets“ This management notebook provides comparative data on derivatives traded in organized exchanges and in over-the-counter (OTC) markets. It provides information about which types of derivatives are most commonly used. For Critical Analysis: The three key factors are likely to be the price of the derivative security, the risks associated with its use, and the transactions costs entailed in purchasing the derivative and managing the instrument over the life of the contract. V. Answers to End of Chapter Questions 1. Given that: PB = C/(1+R) + C/(1+R)2 + C/(1+R)3 + C/(1+R)4 + .; multiply each side by (1+R): PB (1+R) = C + C/(1+R) + C/(1+R)2 +.; and subtract PB from each side: PB (1+R) - PB = [C + C/(1+R) + C/(1+R)2 +.] - [C/(1+R) + C/(1+R)2 +.]; Simplifying: PB * R = C. Therefore, PB = C/R. 2. In this situation, annual yields decline as the term to maturity increases, which means that the yield curve slopes downward. According to the expectations theory of the term structure of interest rates, this situation arises because bond-market traders anticipates that short-term interest rates will fall sharply. Thus, an average of current and future short-term rates, which, when added to any term premium applicable to a longer maturity, is lower than the current short-term rate. 3. Yes, the excess return on the German government bond equals 3.5 percent – (5 percent – 3 percent) = 1.5 percent. 4. Parity Conditions: a. Using uncovered interest parity, R - R* = (S+1e - S) / S. Because the left-hand-side is negative, we would expect the right-hand side to be negative, indicating a domestic currency appreciation. b. Using relative PPP, B-B* = %)S. Because the left -hand-side is negative, we would expect the right-hand side to be negative, indicating a domestic currency appreciation. 5. The domestic real interest rate is 5 percent less 2 percent, or 3 percent. The foreign real interest rate is 6 percent less 4 percent, or 2 percent. Real interest rates are not equal, so the real interest parity condition does not hold. We would expect funds to flow into the domestic country and out of the foreign country, which would drive the domestic real interest rate down and the foreign real interest rate up. 6. In contrast to forward currency contracts, currency futures require delivery of standard quantities of currencies. In addition, holders of currency futures experience profits of losses on the contracts during the entire period before the contracts expire, whereas profits or losses occur only at the expiration date of a forward currency contract. 7. A currency future already is a derivative, because its value varies with the exchange rate. The value of a currency futures option, in turn, depends on the underlying value of a currency futures contract, so its value is derived from the futures derivative. In this way, a currency futures option is a “derivative of a derivative.“ 8. a. The company owes 500,000 Sfr and is concerned about the future spot exchange value of the U.S. dollar-Swiss franc. It can therefore purchase future contracts to set a limit to its potential exchange rate losses. b. The Sfr is purchased in 125,000 franc increments. Therefore, the firm would want to purchase 500,000/125,000 = 4 futures contracts. Given the initial margin on a franc contract, the total initial margin the firm establishes is: 4($1,688) = $6,752. The daily margin changes are as follows: First: (0.6252 - 0.6251)(125,000)(4) = +$50. Therefore its margin equals $6,802. Second: (0.6127 - 0.6252)(125,000)(4) = -$6250. Therefore the margin would fall to $552. However, the maintenance margin is equal to $1,250. Thus, the margin will equal $1,250. Third: (0.6115 - 0.6127)(125,000)(4) = -$600. Again, the margin must remain at $1,250. Fourth: (0.6806 - 0.6115)(125,000)(4) = -$1450. Again, this daily change would fall beneath the maintenance margin. Thus, it remains at $1,250. c. As the dollar continues to appreciate relative to the Swiss franc, the value of the futures contract falls. However, the cost of 500,000 franc payment is becoming cheaper on terms of the U.S. dollar. 9. a. The call option is currently out of the money. b. (0.0188)(62,500) = $1,175 ($1,175)(8 contracts) = $9,400 Net Profit Break Even 0.960 0.980 1.02 0.9988 In the money At the money Out of the money 0 Net Loss 9,400 10,600 c. At S = $0.96/ € the option is not exercised and the firm is out $9,400 At S = $1.02/ € the option is exercised. The firm earns $10,600 At S = $0.9657/€, the firm does not exercise the option and is out $9,400 d. Break even: $0.9988/€ e. See Diagram given in part (b). 10. The pros and cons of forward contracts and swaps lie within how each works. A forward contract can be arranged between a purchaser and a seller, and is dependent upon each participant s beliefs of what will happen in the future. Sometimes it can be difficult to match counterparties to such contracts. Swaps, on the other hand, directly match traders who require flows of currencies held by one another. Swaps may also allow borrowers to receive better loan rates by issuing debt in their home currency rather than in a foreign currency; thereby potentially avoiding a risk premium. Considerations of the reason for the long position on a currency and which currency is at issue will influence the decision of which derivative to use. VI. Multiple Choice Questions 1. The amount of credit extended via the purchase of a financial instrument is the A. principal. B. front load. C. sum of the coupons. D. present discounted value. Answer: A 2. To calculate the price of a financial instrument, one must find the A. present discounted value of the stream of coupon payments and principal. B. principal plus the present discounted value of the coupons. C. sum of the coupons divided by the principal. D. sum of the coupons plus the principal. Answer: A 3. A bond with no fixed maturity date is called a A. discount bond. B. callable bond. C. treasury bill. D. perpetuity. Answer: D 4. A bond with an infinite payment life will have a price A. equal to the present discounted value of its principal. B. equal to the coupon amount divided by the interest rate. C. equal to the coupon amount divided by one plus the interest rate. D. that is arbitrarily high, as it will produce coupon payments forever. Answer: B 5. Suppose the price of a perpetuity is $1,000 and that the perpetuity pays a coupon of $60 per year. The interest rate on this bond is A. 0.06 percent. B. 0.60 percent. C. 6 percent. D. 60 percent. Answer: C 6. Suppose the interest rate on a perpetuity is 5 percent, and its price is $1,500. The annual coupon must therefore equal A. $75. B. $300. C. $750. D. $30,000. Answer: A 7. Suppose a perpetuity pays $100 per year and its interest rate is 8%. Its price is equal to A. $80. B. $125. C. $800. D. $1,250. Answer: D 8. Zero coupon bonds have the distinguishing feature that they A. have an indefinite life. B. pay a lump sum at maturity. C. are issued only by the Treasury. D. pay only coupons that carry an interest rate equal to the real interest rate. Answer: B 9. Interest-rate risk arises because A. shorter terms to maturity expose bonds to greater risk of capital loss when interest rates rise. B. shorter terms to maturity expose bonds to greater risk of capital loss when interest rates fall. C. longer terms to maturity expose bonds to greater risk of capital loss when interest rates rise. D. longer terms to maturity expose bonds to greater risk of capital loss whe