Let the expected pound return on a U.K. equity be 15%, and let its volatility be 20%. The volatility of the dollar/pound exchange rate is 10%.
a. Graph the (approximate) volatility of the dollar return on the U.K. equity as a function of the correlation between the U.K. equity's return in pounds and changes in the dollar/pound exchange rate.
b. Suppose the correlation between the U.K. equity return in pounds and the exchange rate change is 0. What expected exchange rate change would you need if the U.K. equity investment is to have a Sharpe ratio of 1.00?
(Assume that the risk-free rate is 0 for a U.S. investor.)
Does this seem like a reasonable expectation?