Question

The U.S. interest rate is 4.0% per annum. The U.K. interest rate is 7.0% per annum. S($/£) = $1.2; F($/£) = $1.26. How much can an investor earn with a $1,000,000 covered interest arbitrage?

Answer 1

Solution:

Forward price in one year according to the existing spot prices and interest rate should be:

Forward ($/£) rate = Spot ($/£) rate * [(1+ US interest rate) / (I +UK interest rate)] = 1.2 * [1.04/1.07] = $1.16635

Existing F($/£) = $1.26 (given)

The existing forward rate is higher than what it should be according to the existing interest rates in these nations. So, we should sell pounds after one year using this forward rate and buy the required amount of pounds in spot market. This way we will make profit higher than the ecisting risk free rate in US but without taking any risk.

Following transactions are required for earning this covered interest arbitrage:

• Use $1,000,000 to buy £ today at the existing spot rate of S($/£) = $1.2.
• So, we will have 1000000/1.2 = £833,333.333
• We can invest £833,333.333 at UK interest rate of 7% to have £833,333.333*1.07 = £891,666.6667 after 1 year.
• Enter into a forward contract that to sell £891,666.6667 in 1-year at existing forward rate of F($/£) = $1.26.
• After one year, settle the forward contract by selling £891,666.6667 at the contracted rate of F($/£) = $1.26, which would give us 891,666.6667 * 1.26 = $1,123,500.
• If we would have invested $1,000,000 at US interest rate of 1.04 then we would have accumulated $1,000,000 * 1.04 =$1,040,000.
• But using forward contract and covered interest arbitrage we have earned $1,123,500 - $1,040,000 = $83,500 more without taking any risk.

By investing $1,000,000 and using covered interest arbitrage we are able to earn $1,123,500, that is $1,123,500 - $1,040,000 = $83,500 profit over risk free rate without taking any risk.