The UK riskfree interest rate is 05 and the US riskfree inte

The UK risk-free interest rate is 0.5% and the US risk-free interest rate is 0.25%. If the spot exchange rate (US direct) is 1.6077, what is:

a. The 6-month forward rate?

b. The 3-year forward rate?

c. If the 3-year forward rate is actually 1.62, how can an arbitrage profit be obtained? How much arbitrage profit?

Solution

a) 6 month forward rate = Spot rate * ( 1+ US domsttic interst rate * Months/12)/( 1+ UK domsttic interst rate * Months/12) = 1.6077 * ( 1 + 0.25% * 6/12)/( 1+ 0.5% *6/12) = 1.6057

b) 3 month forward contract = Spot rate * ( 1+ US domsttic interst rate * Months/12)/( 1+ UK domsttic interst rate * Months/12) = 1.6077 * ( 1 + 0.25% * 3/12)/( 1+ 0.5% *3/12) = 1.6067

c) By enetring into a3 month forwrd contract the exchange rate of 1.6067 can be booked for use in futuere datye at the fixed predicided exchange rate. So so using forward contract UK pounds can be bought for $1.6067 and then UK pound would be sold for 1.62. This ensures an arbitrage profit,

The arbitrage profit = 1.62 - 1.6067 = 0.0133$

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