PS08__Answers_ - EC 340 Spring 2011 Problem Set 8 1. There...

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Unformatted text preview: EC 340 Spring 2011 Problem Set 8 1. There are three currencies: U.S. dollars ($), British pounds (£), and European euros (€). The three exchange rates are: $2 = £1, $0.75 = €1, and €3 = £1 Show how an arbitrageur who begins with dollars can make a profit in this situation. Suppose you start with $2. Buy £1. Then exchange £1 for €3. Finally, €3 = $2.25 (since every euro exchanges for 75 cents). 2. There are three currencies: U.S. dollars ($), British pounds (£), and European euros (€). The three exchange rates are: $2 = £1, $0.75 = €1, and €3 = £1 Show how an arbitrageur who begins with pounds can make a profit in this situation. Suppose you start with £1 and exchange it for €3. Use the €3 to buy $2.25. Since each pound costs only 2 dollars, $2.25 will purchase more than 1 pound, making a profit. 3. There are three currencies: U.S. dollars ($), British pounds (£), and European euros (€). The three exchange rates are: $2 = £1, $0.75 = €1, and €3 = £1 Show how an arbitrageur who begins with euros can make a profit in this situation. Start with €1 and buy $0.75. Use the $0.75 to buy £0.375 (each pound costs $2, so 75 cents only buys a fraction of a pound…to find the fraction, divide $0.75 by $2). Finally, exchange £0.375 for €1.125 euros (each pound buys 3 euros, so 0.375 pounds buys 3*0.375 euros). 4. Suppose that the spot rate for the euro is $1.40 and the forward rate is $1.47. Is the euro selling forward at a discount or at a premium? Calculate the size of the discount or premium. The euro is selling forward at a premium since the forward euro is more expensive than the spot euro. The size of the premium is ($1.47 ‐ $1.40)/$1.40 = 0.05. 5. Suppose that the U.S. interest rate is 4 percent and the Canadian interest rate is 5 percent. What is the implied forward premium or discount on the Canadian dollar? The covered interest parity condition is U.S. interest rate = Canadian interest rate + forward premium on Canadian dollar So: .04 = .05 + forward premium on Canadian dollar Forward premium on Canadian dollar = 0.04 – 0.05 = ‐0.01. Since the “premium” is negative, we say that the Canadian dollar is selling forward at a discount. 6. Suppose that the U.S. interest rate is 3 percent and the German interest rate is 1 percent. What is the expected rate of appreciation or depreciation of the euro based on uncovered interest parity? The uncovered interest parity condition is U.S. interest rate = German interest rate + expected appreciation of the euro So: .03 = .01 + expected appreciation of the euro Expected appreciation of the euro = 0.03 – 0.01 = ‐0.02. The expectation is that the euro will appreciate by 2 percent relative to the dollar. ...
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This note was uploaded on 11/11/2011 for the course EC 340 taught by Professor Ballie during the Spring '10 term at Michigan State University.

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