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Consider a Dutch investor with 1,000 euros to place in a bank deposit in either the Netherlands (home country) or Great Britain (foreign country). The (one-year) interest rate on bank deposits is 2.00% in Britain and 4.04% in the Netherlands. The (one-year) forward euro–pound exchange rate is 1.575 euros per pound and the spot rate is 1.5 euros per pound. Answer the following questions, using the exact equations for UIP and CIP as necessary. b. What is the (riskless) euro-denominated return on British deposits for this investor using forward cover? c. Is there an arbitrage opportunity here? Explain why or why not. Is this an equilibrium in the forward exchange rate market? d. If the spot rate and interest rates are as stated previously, what should be the equilibrium forward rate, according to CIP? e. Suppose the forward rate takes the value given by your answer to (d). Calculate the forward premium on the British pound for the Dutch investor (where exchange rates are in euros per pound). Is it positive or negative? Why do investors require this premium/discount in equilibrium? f. If UIP holds, what is the expected depreciation of the euro against the pound over one year? g. Based on your answer to (f), what is the expected euro–pound exchange rate one year ahead?

Question

Consider a Dutch investor with 1,000 euros to place in a bank deposit in either the Netherlands (home country) or Great Britain (foreign country). The (one-year) interest rate on bank deposits is 2.00% in Britain and 4.04% in the Netherlands. The (one-year) forward euro–pound exchange rate is 1.575 euros per pound and the spot rate is 1.5 euros per pound. Answer the following questions, using the exact equations for UIP and CIP as necessary.

b. What is the (riskless) euro-denominated return on British deposits for this investor using forward cover?

c. Is there an arbitrage opportunity here? Explain why or why not. Is this an equilibrium in the forward exchange rate market?

d. If the spot rate and interest rates are as stated previously, what should be the equilibrium forward rate, according to CIP?

e. Suppose the forward rate takes the value given by your answer to (d). Calculate the forward premium on the British pound for the Dutch investor (where exchange rates are in euros per pound). Is it positive or negative? Why do investors require this premium/discount in equilibrium?

f. If UIP holds, what is the expected depreciation of the euro against the pound over one year?

g. Based on your answer to (f), what is the expected euro–pound exchange rate one year ahead?

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Solution

b. The riskless euro-denominated return on British deposits for this investor using forward cover can be calculated as follows:

First, convert the 1,000 euros to pounds using the spot rate: 1,000 euros / 1.5 euros per pound = 666.67 pounds.

Then, calculate the amount of pounds the investor will have after one year by applying the British interest rate: 666.67 pounds * 1.02 (2% interest rate) = 680.00 pounds.

Finally, convert this amount back to euros using the forward rate: 680.00 pounds * 1.575 euros per pound = 1,071 euros.

So, the riskless euro-denominated return on British deposits for this investor using forward cover is 1,071 euros - 1,000 euros = 71 euros.

c. There is no arbitrage opportunity here because the return on the British deposit with forward cover (71 euros) is less than the return on the Dutch deposit (1,000 euros * 1.0404 = 1,040.40 euros). This is an equilibrium in the forward exchange rate market because the returns on the two investments are equal when the risk of exchange rate changes is hedged using the forward market.

d. According to Covered Interest Parity (CIP), the equilibrium forward rate should be equal to the spot rate multiplied by the ratio of the interest rates in the two countries. So, the equilibrium forward rate should be: 1.5 euros per pound * (1.0404 / 1.02) = 1.53 euros per pound.

e. The forward premium on the British pound for the Dutch investor is the percentage difference between the forward rate and the spot rate. If the forward rate is 1.53 euros per pound, the forward premium is: (1.53 - 1.5) / 1.5 * 100% = 2%. This premium is positive, which means that investors require a higher return for investing in British deposits to compensate for the risk of the pound depreciating against the euro.

f. If Uncovered Interest Parity (UIP) holds, the expected depreciation of the euro against the pound over one year is the difference between the interest rates in the two countries, which is 4.04% - 2.00% = 2.04%.

g. Based on the expected depreciation of the euro, the expected euro–pound exchange rate one year ahead is the current spot rate multiplied by the ratio of 1 plus the interest rates in the two countries, which is: 1.5 euros per pound * (1.02 / 1.0404) = 1.47 euros per pound.

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