# 23 2 chapter 23 futures swaps and risk management 4

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Chapter 23 - Futures, Swaps, and Risk Management 4. Municipal bond yields, which are below T-bond yields because of their tax-exempt status, are expected to close in on Treasury yields. Because yields and prices are inversely related, this means that municipal bond prices will perform poorly compared to Treasuries. Therefore you should establish a spread position, buying Treasury-bond futures and selling municipal bond futures. The net bet on the general level of interest rates is approximately zero. You have simply made a bet on relative performances in the two sectors. 5. a.S 0 × (1 + r M ) - D = (1,425 × 1.06) – 15 = 1,495.50 b. S 0 × (1 + r f ) - D = (1,425 × 1.03) – 15 = 1,452.75 c. The futures price is too low. Buy futures, short the index, and invest the proceeds of the short sale in T-bills: CF Now CF in 6 months Buy futures 0 S T - 1,422 Short index 1,425 - S T - 15 Buy T-bills - 1,425 1,467.75 Total 0 30.75 6. a.The value of the underlying stock is: \$250 × 1,350 = \$337,500 \$25/\$337,500 = 0.000074 = 0.0074% of the value of the stock b. \$40 × 0.000074 = \$0.0030 (less than half of one cent) c.\$0.15/\$0.0030 = 50 The transaction cost in the stock market is 50 times the transaction cost in the futures market. 23-3
Chapter 23 - Futures, Swaps, and Risk Management 7. a.You should be short the index futures contracts. If the stock value falls, you need futures profits to offset the loss. b. Each contract is for \$250 times the index, currently valued at 1,350. Therefore, each contract controls stock worth: \$250 × 1,350 = \$337,500 In order to hedge a \$13.5 million portfolio, you need: 40 500 , 337 \$ 000 , 500 , 13 \$ = contracts c.Now, your stock swings only 0.6 as much as the market index. Hence, you need 0.6 as many contracts as in (b): 0.6 × 40 = 24 contracts 8. If the beta of the portfolio were 1.0, she would sell \$1 million of the index. Because beta is 1.25, she should sell \$1.25 million of the index. 9. You would short \$0.50 of the market index contract and \$0.75 of the computer industry stock for each dollar held in IBM. 10. The dollar is depreciating relative to the euro. To induce investors to invest in the U.S., the U.S. interest rate must be higher. 11. a.From parity: 962 . 1 06 . 1 04 . 1 00 . 2 r 1 r 1 E F UK US 0 0 = × = + + × = b. Suppose that F 0 = \$2.03/£. Then dollars are relatively too cheap in the forward market, or equivalently, pounds are too expensive. Therefore, you should borrow the present value of £1, use the proceeds to buy pound-denominated bills in the spot market, and sell £1 forward: Action Now CF in \$ Action at period-end CF in \$ Sell £1 forward for \$2.03 0 Collect \$2.03, deliver £1 \$2.03 – \$E 1 Buy £1/1.06 in spot market; invest at the British risk-free rate –2.00/1.06 = –\$1.887 Exchange £1 for \$E 1 \$E 1 Borrow \$1.887 \$1.887 Repay loan; U.S. interest rate = 4% –\$1.962 Total 0 Total \$0.068 23-4

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Chapter 23 - Futures, Swaps, and Risk Management 12. a.Lend in the U.K. b. Borrow in the U.S. c.Borrowing in the U.S. offers a 4% rate of return. Borrowing in the U.K. and covering interest rate risk with futures or forwards offers a rate of return of: % 93 . 5 0593 . 0 1 00 . 2 98 . 1 07 . 1 1 E F ) r (1 r 0 0 UK US = = - × = - × + = It appears advantageous to borrow in the U.S., where rates are lower, and to lend in the U.K. An arbitrage strategy involves simultaneous lending and borrowing
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