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F the portfolio plus futures position cost 12 million

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f. The portfolio-plus-futures position cost \$12 million to establish. The expected end-of-period value is \$12,360,000. The rate of return is therefore 3%. 23-4

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g. The beta of the hedged position is 0. The fair return should be r f = 1%. Therefore, the alpha of the position is (3% – 1%) = 2%, the same as the alpha of the portfolio. Now, however, one can take a position on the alpha without incurring systematic risk. 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. a. The strategy would be to sell Japanese stock index futures to hedge the market risk of Japanese stocks, and to sell yen futures to hedge the currency exposure. b. Some possible practical difficulties with this strategy include: • Contract size on futures may not match size of portfolio. • Stock portfolio may not closely track index portfolios on which futures trade. • Cash flow management issues from marking to market. • Potential mispricing of futures contracts (violations of parity). 11. 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. 12. a. From parity: 541 . 1 08 . 1 04 . 1 60 . 1 r 1 r 1 E F UK US 0 0 = × = + + × = b. Suppose that F 0 = \$1.58/£. 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 \$1.58 0 Collect \$1.58, deliver £1 \$1.58 – \$E 1 Buy £1/1.08 in spot market; invest at the British risk-free rate –1.60/1.08 = –\$1.481 Exchange £1 for \$E 1 \$E 1 Borrow \$1.481 \$1.481 Repay loan; U.S. interest rate = 4% –\$1.540 Total 0 Total \$0.04 23-5
13. 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: % 66 . 5 0566 . 0 1 60 . 1 58 . 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 with the covering of interest rate risk: Action Now CF in \$ Action at period-end CF in \$ Borrow \$1.60 in U.S. \$1.60 Repay loan –\$1.60 × 1.04 Convert borrowed dollars to pounds; lend £1 pound in U.K. –\$1.60 Collect repayment; exchange proceeds for dollars 1.07 × E 1 Sell forward £1.07 at F 0 = \$1.58 0 Unwind forward 1.07 × (\$1.58 – E 1 ) Total 0 Total \$0.0266 14. a. The hedged investment involves converting the \$1 million to foreign currency, investing in that country, and selling forward the foreign currency in order to lock in the dollar value of the investment. Because the interest rates are for 90-day periods, we assume they are quoted as bond equivalent yields,

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f The portfolio plus futures position cost 12 million to...

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