Question

The current Dollar-Pound exchange rate is 1.60 dollars per British Pound. The U.S. and British risk-free interest rates (annualized, continuously compounded) are 5% and 7.5%, respectively. Answer the following questions.

A. What is the no arbitrage forward price of the British Pound for a 6-month forward contract?

B. Suppose the actual forward price is 1.65 dollars per British Pound. Illustrate the arbitrage opportunity.

Answer 1

Forward Rate = ( 1+ Rate in domestic country/ Rate in foreign country)* Spot Rate

Spot Rate= 1.6

Rate in Domestic country= 5% * 6/12 = 2.5%

Rate in foreign Country = 7.5% * 6/12 = 3.75%

Applying values,

= (1+0.025/1+0.0375)*1.6

= 1.58

B) Borrow 1000 USD for 6 months

Convert to pounds= 1000/1.6= 625

Invest 625 Pounds in UK

Amount received on investment after 6 months = 625+ 3.75%*625

=648.4375

Convert to USD= 648.4375*1.65= 1069.92

Money to repaid at the end of 6 months = 1600*2.5%+1600= 1640

Arbitrage gain = 1069.92- 1040= $29.92