bkmsol_ch23

# Stock portfolio may not closely track index

• Notes
• 11

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• 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

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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, annualized using simple interest. Therefore, to express rates on a per quarter basis, we divide these rates by 4: Japanese government Swiss government Convert \$1 million to local currency \$1,000,000 × 133.05 = ¥133,050,000 \$1,000,000 × 1.5260 = SF1,526,000 Invest in local currency for 90 days ¥133,050,000 × [1 + (0.076/4)] = ¥135,577,950 SF1,526,000 × [1 + (0.086/4)] = SF1,558,809 Convert to \$ at 90-day forward rate 135,577,950/133.47 = \$1,015,793 1,558,809/1.5348 = \$1,015,643 b. The results in the two currencies are nearly identical. This near-equality reflects the interest rate parity theorem. This theory asserts that the pricing relationships between interest rates and spot and forward exchange rates must make covered (that is, fully hedged and riskless) investments in any currency equally attractive. c. The 90-day return in Japan is 1.5793%, which represents a bond-equivalent yield of 1.5793% × 365/90 = 6.405%. The 90-day return in Switzerland is 1.5643%, which represents a bond-equivalent yield of 1.5643% × 365/90 = 6.344%. The estimate for the 90-day risk-free U.S. government money market yield is in this range.
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