ProblemSet2_solution - International Financial Management...

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International Financial Management Prof Choi Problem Set 2 Spring 2008 This problem set is due Wednesday, March 5. Remember to show any calculations. 1.Suppose that the treasurer of IBM has an extra cash reserve of $100,000,000 to invest for six months. The six-month interest rate is 8 percent per annum in the United States and 6 percent per annum in Germany. Currently, the spot exchange rate is €1.01 per dollar and the six-month forward exchange rate is €0.99 per dollar. The treasurer of IBM does not wish to bear any exchange risk. Where should he/she invest to maximize the return? ( the question is identical to asking “does the covered interest parity hold”?) The market conditions are summarized as follows: I $ = 4.0%; i = 3.0 %; S = €1.01/$; F = €0.99/$. If $100,000,000 is invested in the U.S., the maturity value in six months will be $104, 00,000 = $100,000,000 (1 + .040). Alternatively, $100,000,000 can be converted into euros and invested at the German interest rate, with the euro maturity value sold forward. In this case the dollar maturity value will be $105,080,000 = ($100,000,000 x 1.01)(1 + .030)(1/0.99) Clearly, it is better to invest $100,000,000 in Germany with exchange risk hedging. 2. Currently, the spot exchange rate is $1.50/£ and the three-month forward exchange rate is $1.52/£. The three-month interest rate is 8.0% per annum in the U.S. and 5.8% per annum in the U.K. Assume that you can borrow as much as $1,500,000 or £1,000,000. a. Determine whether the interest rate parity is currently holding. b. If the IRP is not holding, how would you carry out covered interest arbitrage? Show all the steps and determine the arbitrage profit. c. Explain how the IRP will be restored as a result of covered arbitrage activities. Solution: Let’s summarize the given data first: S = $1.5/£; F = $1.52/£; I $ = 2.0%; I £ = 1.45% Credit = $1,500,000 or £1,000,000. a. (1+I $ ) = 1.02 (1+I £ )(F/S) = (1.0145)(1.52/1.50) = 1.0280 Thus, IRP is not holding exactly.
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b. (1) Borrow $1,500,000; repayment will be $1,530,000. (2) Buy £1,000,000 spot using $1,500,000. (3) Invest £1,000,000 at the pound interest rate of 1.45%; maturity value will be £1,014,500. (4) Sell £1,014,500 forward for $1,542,040 Arbitrage profit will be $12,040 c. Following the arbitrage transactions described above, The dollar interest rate will rise; The pound interest rate will fall; The spot exchange rate will rise; The forward exchange rate will fall. These adjustments will continue until IRP holds. 3. Suppose the current spot rate is $1.8 = £1 (or 0.5556 £/$) on the first of January. By year-end the US CPI is expected to climb from 144 to 150 and the UK CPI from 120 to 130. According to PPP, what is the expected spot rate on December 31?
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