Question

A U.S. investor can borrow 1,000,000 or 500,000 GBP. The spot rate is $2.00/GBP, the one year forward rate is $2.02/GBP. The U.S. one year interest rate is 14% and the one year British interest rate is 12%. Determine if there is a covered interest rate arbitrage opportunity, and if so, clearly show each step involved in the arbitrage opportunity. Show the total dollar profit. If you determined that there is no arbitrage opportunity, describe why you made that decision.

Answer 1

Accordin to IRPT

Foward Rate = Spot Rate * (1+Hi) / (1+Fi)

= 2 * (1+0.14) / (1+ 0.12)

= 2 * 1.14 / 1.12

= 2 * 1.0179

= 2.0357

One year forward rate given is 2.02

Arbitrage exists

Borrow 100000 GBP @12%

amount payable after 1 year = GBP 112000

Convert GBP 100000 into USD at spot rate $ 2 /GBP

= 100000 * 2

= $ 200000

Invest $ 200000 @14% for year

= 200000 *14%

= 28000

Total value of $ after 1 year = $ 228000

Convert $ into GBP and repay the loan maturity

= 228000/2.02

= 112871.3

Repay 112000 GBP loan

Arbitrage profit = 112871.3 - 112000

= GBP 817.3

Pls do rate, if the answer is correct and comment, if any further assistance is required.