If the interest rate for the next 6 months for the US$ is 1.5% (annual compounding). The interest rate for the € is 2% (annual compounding). The spot price of the € is US $ 1.665. The forward price is expected to be US$ 1.664. Please determine correct forward price and recommend an arbitrage strategy.
Solution
According to Interest Rate Parity theory
F/S = 1+ iA / 1 + iB
Where F = Forward Rate
S = Spot Rate
iA = $ Interest Rate for 6 months
= 1.5% for 6 months
iB = € Interest Rate for 6 months
= 2 % for 6 months
After 6 Months
F/1,000 = 1.015/1.02 , Therefore F = 1.6568
Because the forward price is higher than the model price, we will sell the forward contract. If transaction costs could be covered, we would buy the € in the spot market at $1.665 and sell it in the forward market at $1.664. We would earn interest at the foreign interest rate of 2 percent. By selling it forward, we could then convert back to dollars at the rate of $1.664. In other words, $1.665 would be used to buy 1 unit of the €, which would grow to 1.02 units (the 2 percent € rate). Then 1.02 € would be converted back to 1.02($1.664) = $1.69728. This would be a return of $1.69728/$1.665 – 1 = 0.019387 or 1.94 percent, which is better than the US rate.
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