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? Multiple Choice

$83,500

$61,800

$216,960

$100,200

None of the options.

Answer 1

We need to understand what the question is asking.

Covered interest rate parity predicts the expected future spot exchange rate. If the given future exchange rate is different, then there is an arbitrage opportunity. So we first need to calculate the exchange rate predicted by the covered interest rate parity equation:

F($/£) = Spot x 1 + ius F($/ £) = 1.2 x F($/ £) = $1.16 1.04 1.07

However the given rate is $1.26 so there is an arbitrage opportunity

• We can borrow USD 1000000 @ 4 interest
• Convert the same to Pound @ $1.2 per pound, so we will have Pound 833333.33
• On this we will get an interest of 7% so after one year we will have Pound 833333.33 x 1.07 = 891666.67
• Simultaneously we will enter into a forward contract to convert the pounds back to USD after one year at the rate of $1.26 per pound
• We will convert it back at $1.26 when in market the actual spot rate will be only $1.16 so we will get $0.10 extra per pound
• We will have 891666.67 x 1.26 = USD 1123500
• We will return the 1000000 that we had borrowed plus the interest @4% on the same, so total we will return 1040000
• So we will be left with 1123500-1040000 = 83500

So the correct option is 83500