Suppose a US investor purchases a UK equity. Let the expected pound return on the U.K. equity be 20%, and let its volatility (measured by standard deviation) be 30%. The volatility of the dollar/pound exchange rate is 10%. The risk-free rate in the U.S. (denoted rf) is 2%. 1) Compute the volatility of the dollar return on the U.K. equity when the correlation (denoted as r) between the U.K. equity’s return in pounds and changes in the dollar/pound exchange rate is 0.5. 2) Suppose the correlation between the U.K. equity return in pounds and the exchange rate change is 0.5. What expected exchange rate change would you expect if the U.K. equity investment is to have a Sharpe ratio of 1? 3) If the Sharpe ratio of the U.S. equities is greater than the Sharpe ratio of the U.K. equities, can a US investor benefit from investing abroad? Explain graphically the benefits of international diversification.
