# Foreign exchange arbitrage opportunity

Assume your return on U.S. dollar bonds is 𝐾$= 5% and the current exchange rate is S(0) =$ 1.6 per £ . Assume your return on British sterling bonds is 𝐾£ = 12%. The Forward price of stock is S(1) = $1.45 per £ with delivery date 1 year therefore there I believe that there is an arbitrage opportunity but need help developing the portfolio at time 0 and time T • There is confusion in the question between stock and exchange rate. Please correct. If there is an arbitrage opportunity, you can buy one kind of bond and sell the other kind of bond with no net cash, then sell the ones you bought and buy the ones you sold a year later and end up with some cash. Compute the future price of a portfolio with one dollar of US bonds and a negative dollar of sterling bonds. Commented May 8, 2017 at 2:57 ## 1 Answer Yes there is an arbitrage opportunity:$\frac{F_{theoretical}}{S_{0}} = \frac{1+0.05}{1+.12} = \frac{1.05}{1.12}F_{theoretical} = 1.5F_{observed} = 1.45\$

Strategy:

Borrow 1 pound and buy dollar at 1.6. Invest 1.6 dollar for a year and get 1.68 dollars and sell dollar and get 1.1586206 pounds at the end of one year. Pay off 1.12 pounds of loan and make riskless profit of 0.0386206 pounds.

Goodluck