Assume 1 year interest rate on risk free securities in the united states is 10 %

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Explanation / Answer

We will use interest rate parity equation to arrive at the forward exchange rate for 12 months hence, by using the formula: Forward Rate = Spot Rate * (1+ rdomestic) / (1+ rother) ; where r is the interest rate in domestic and other country. Now we are give Spot Rate (S) is 1GBP = 1.50 USD or 1USD = 0.6667 GBP, rUSD = 10% and rGBP = 6%. Hence Forward Rate (F) = 1.50 * (1+10%) / (1+6%) = 1.5566

Theoretically, for a no arbitrage condition to be satisfied, the forward exchange rate should be equal to the future spot rate every day of the year because in case of a mismatch, traders will be able to profit from possible arbitrage. However even if there is an arbitrage, the subsequent transaction flow to profit from the arbitrage will change the demand supply dynamics such that the future spot prices are in line with the forward rate.

We can see with an example - let us calculate the forward price after 3 months using the interest rate parity:

F3 month = 1.50 * (1+10%/4) / (1+6%/4) = 1.5148 (rounded to 4 decimals). Now if the future spot price at this time is 1.52, then a trader can do the following:

Hence, the forward exchange rate should be equal to the future spot rates every day of the year.

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