The following 3 cases represent 3 distinct scenarios. In each case, a US firm has an investment in London that has an equal probability (1/3rd) of being worth a certain number of British Pounds, and that valuation is associated with a certain future exchange rate S, shown in USD/GBP. For example, in Case 1, scenarion1, there is a 33.33% chance that the investment will be worth 980 GBP, in which case the exchange rate will be 1.4 USD/GBP. In Case 2, scenario 1 has a 33.33% probability in which case the investment will be worth 1000 GBP and the exchange rate will be 1.4 USD/GBP. To hedge yourself in Case 2, you should: Measuring Currency Exposure: Prob. P* (GBP) S P=SP* A. Case 1 1 0.333333333 980 1.4 1372 Cov(P,S) =34/3 2 0.333333333 1000 1.5 1500 Var (S) .02/3 3 0.333333333 1070 1.6 1712 Mean 1.5 1528 B.Case 2 1 0.333333333 1000 1.4 1400 2 0.333333333 933 1.5 1400 3 0.333333333 875 1.6 1400 Mean 1.5 1400 C. Case 3 1 0.333333333 1000 1.4 1400 Cov(P,S) 20/3 2 0.333333333 1000 1.5 1500 Var (S) .02/3 3 0.333333333 1000 1.6 1600 Mean 1.5 1500