Suppose a U.S. firm has an asset in Britain whose local currency price is random. For simplicity, suppose there are only three states of the world. The future local currency price of this British asset (P*) as well as the future exchange rate (S) will be determined, depending on the realized state of the world. State Probability P* S 1 0.50 980 $1.40/ 2 0.30 1,000 $1.50/ 3 0.20 1,070 $1.60/ a. What is the value of asset in $ (P) in the three states? (2 points) b. Calculate the mean of P. (2 points) c. Calculate the variance of P. (2 points) d. Calculate the variance of S. (2 points) e. Calculate the covariance between the dollar value of the asset and the exchange rate Cov(P,S). (2 points) f. Measure the firm's economic exposure based on sensitivities of earnings to exchange rate (beta). (2 points) g. Based on the economic exposure calculated from d, what is the optimal hedging using forward? (2 points) h. Suppose the forward rate is equal to the expected future spot rate from the probability distribution. Now calculate the total USD value (including the value of assets and profit/loss from the forward position) after hedging. (4 points). i. What is the new mean of the value in $ after hedging? (2 points) j. What is the new variance of the value in $ after hedging? (2 points)