CHAPTER 21

PROBLEM 3: JUNE KLEIN, CFA, MANGES A $ 100 MILLION (MARKET VALUE) U.S. GOVERNMENT BOND PORTFOLIO FOR AND INSTITUTION. She anticipates a small parallel shift in the yield curve and wants to fully hedge the portfolio against any such change.

PORTFOLIO AND TREASURY BOND FUTURES CONTRACT CHARACTERISTICS

CONVERSION

FACTOR FOR PORTFOLIO VALUE/

MODIFIED BASIC POINT CHEAPEST TO FUTURE CONTRACT

SECURITY DURATION VALUE DELIVER BOND PRICE

PORTFOLIO 10 YEARS $ 100,000.00 NOT APPLICABLE $ 1000,000.00

U.S. TREA BOND 8 YEARS $ 75.32 1 94-05

(a) DISCUSS THE TWO REASONS FOR USING FUTURES RATHER THAN SELLING BONDS TO HEDGE A BOND PORTFOLIO. NO CALCULATIONS REQURED.

(e) Described a zero-duration hedging strategy using only the government bond portfolio and options on U.S. Treasury bond futures contracts. No calculations required.

PROBLEM 4: A BOND SPECULATOR CURRENTLY HAS POSITIONS IN TWO SEPARATE CORPORATE BOND PORTFOLIOS: A LONG HOLDING NIN PORTFOLIO 1 AND A SHOR HOLDING IN PORTFOLIO 2. ALL THE BONDS HAVE THE SAME CREDT QUALITY. OTHER RELEVANT INFORMATION ON THESE POSITIONS INCLUDES.

MARKET COUPON COMPOUNDING YIELD TO

PORTFOLIO BOND VALUE (MIL) RATE FREQUENCY MATURITY MATUR

1 A $ 6.0 0.0% Annual 3yrs 7.31%

B 4-0 0-0 Annual 14yrs 7-31

2 C 11.5 4.6 Annual 9yrs 7.31

Treasury bond futures (based on $ 100,000 face value of 20-year T-bonds having an 8 percent semi-annual coupon) with a maturity exactly six months from now are currently priced at 109-24 with a corresponding yield to maturity of 7.082 percent. The “yield betas” between the future contract and Bond A, B, and C are 1.13, 1.03, and 1.01, respectively. Finally the modified duration for the T-bond underlying the future contract is 10.355 years.

(a) Calculate the modified duration (expressed in years) for each of the two bond portfolios. What will be the approximate percentage change in the value of each f all yields increase by 60 basis points on an annual basis.

(b) Assuming the bond speculator wants to hedge her net bond position, what is the optimal number of futures contracts that must be bought or sold? Start by calculating the optimal hedge ratio between the futures contract and the two bond portfolios separately and then combine them.

PROBLEM 6: As a relationship officer for a money-center commercial bank, one of your corporate accounts has just approached you about a one-year loan for $ 1,000,000. The customer would pay a quarterly interest expense based on the prevailing level of LIBOR at the beginning of each three-month period. As is the bank’s convention on all such loans, the amount of the interest payment would then be paid at the end of the quarterly cycle when the new rate for the next cycle is determined. You observe the following LIBOR yield curve in the cash market.

90-days LIBOR 4.60%

180-day LIBOR 4.75

270-day LIBOR 5.00

360-day LIBOR 5.30

(a) If 90-day LIBOR rises to the levels “predicted” by the implied forward rates, what will the dollar level of the bank’s interest receipt be at the end of each quarter during the one-year loan period.

(b) Assuming the yield interred from the Eurodollar futures contract prices for the next three settlement periods are equal to the implied forward rates, calculate the annuity value that would leave the bank indifferent between making the floating-rate loan and hedging it in the futures market and making a one-year fixed-rate loan. Express this annuity value in both dollar and annual (360-day) percentage terms.

PROBLEM 9: Alex Andrew, who manages a $ 95 million large-capitalization U.S. equity portfolio, currently forecasts that equity market will decline soon. Andrew prefers to avoid the transaction coast of making sales but wants to hedge $ 15 million of the portfolio’s current value using S&P 500 futures.

Because Andrew realizes that his portfolio will not track the S&P 500 Index exactly, he performs a regression analysis on his actual portfolio returns versus the S&P futures return over the past year. The regression analysis indicates a risk-minimizing beta of 0.88 with an R2 of 0.92

FUTURES CONTRACT DATA

S&P 500 futures price 1,000

S&P 500 index 999

S&P 500 index multiplier 250

(a) Calculate the number of futures contracts required to hedge $ 15 million of Andrew’s portfolio, using the date shown. State whether the hedge is long or short. Show all calculations.

(b) Identify two alternative methods (other than selling securities from the portfolio or using futures) that replicate the strategy in part a. Contract each of these methods with the futures strategy.

PROBLEM 10: The treasurer of a middle market, import-export company has approached you for advice on how to best invest some of the firm’s short-term cash balances. The company, which had been a client of the bank that employs you for a few years, has $ 250,000 that it is able to commit for a one-year holding period. The treasurer is currently considering two alternatives: (1) invest all the funds in a one-year U.S. Treasury bill offering a bond equivalent yield of 4.25 percent, and (2) invest all the funds in a Swiss government security over the same horizon, locking in the spot and forward currency exchanges in the FX market. A quick call to the bank’s FX desk gives you the following two-way currency exchange quotes.

SWISS FRANCS PER U.S. DOLLARS PER

U.S. DOLLAR SWISS FRANC (CHF)

Spot 1.5035 0.6651

1-year CHF futures ------ 0.6586

(a) Calculate the one-year bond equivalent yield for the Swiss government security that would support the interest rate parity condition.

(b) Describe the transactions that arbitrageur could use to take advantage of this apparent mispricing, and calculate what the profit would be for a $ 250,000 transaction.

PROBLEM 11: Bonita Singer is a hedge fund manager specializing in futures arbitrage involving stock index contracts. She is investigating potential trading opportunities in the S&P 500 stock index futures to see if there are any inefficiencies that she can exploit. She knows that the S&P 500 stock index is currently trading at 1.100.

(a) Assume that the Treasury yield curve is flat at 3.2 percent and annualized dividend yield on the S&P index is 1.8 percent. Using the cost of carry model, demonstrate what the theoretical contract price should be for a futures position expiring six months from now.

(b) Assuming that total round-trip arbitrage transaction costs are #20 for the set trades described in part B, calculate the upper and lower bounds for the theoretical contract price such that arbitrage trading would not be profitable.

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