Assume that: the present dollar-vs-pound exchange rate is 1.33 USD/GBP; the one-

Question

Assume that: the present dollar-vs-pound exchange rate is 1.33 USD/GBP; the one- year risk-free return for GBP is RGPB 1.017; and the one-year risk-free return for USD is RUSD = 1.006. (a) What is the theoretical one-year forward exchange rate? (b) Suppose the one-year forward exchange rate available in the marketplace is 1.40 USD/GBP. This is more than the theoretical forward exchange rate, so an arbi trage is possible. Describe a risk-free strategy for making money in this situation. How much does it gain, using a forward contract to buy or sell 100 GBP?

Explanation / Answer

Solution:

Spot Rate = 1.33USD/GBP

Interest rate in Britain = 1.7% ( Since one year return is 1.017 , So 1.017-1 = 0.017)

Interest rate in USA = 0.6% ( Since one year return is 1.006 , So 1.006-1 = 0.006)

Now, Using interest rate Parity formula

Forward rate = Spot rate * (1+ interest rate in USA)/ (1+ interest rate in Britain)

Forward rate = 1.33 * 1.006/1.017 = 1.315615

So theoretical forward rate = 1.315615 or 1.3156

Part B )

If One year forward rate that is available in the market then we can sell this because it is higher than the calculated theoretical value of 1.315615.

We will sell the one year forward contract for 1.40 and after one year we can cover our position by buying at 1.315615

Earning per GBP = 1.40-1.315615 = 0.084385

Total earning after selling 100 GBP = 100* 0.084385 = 8.4385 USD

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