Suppose you are a British venture capitalist holding a major stake in an e-comme
ID: 2758827 • Letter: S
Question
Suppose you are a British venture capitalist holding a major stake in an e-commerce start-up in Silicon Valley. As a British resident, you are concerned with the pound value of your U.S. equity position. Assume that if the American economy booms in the future, your equity stake will be worth $1,000,000, and the exchange rate will be $1.40/ . If the American economy experiences a recession, on the other hand, your American equity stake will be worth $500,000, and the exchange rate will be $1.60/ . You assess that a boom and a recession are equally likely to happen. Estimate your exposure to the exchange risk (i.e., find the coefficient b)Explanation / Answer
(a) Estimate your exposure to the exchange risk Boom Recession Probabability 50.00% 50.00% Asset Value (P) in dollars $1,000,000 $500,000 Spot Exchange Rate (s) $1.4 $1.6 Asset Value (P) in pounds £714,285.71 £312,500 Spot Exchange Rate (s) in Pounds £0.71 £0.63 Expected Return on Spot Rate (Es) in pounds = ((0.50)/(1.40) + (0.50)/(1.60) £0.67 per dollar Expected Return on Asset value in in pounds E(P) = (0.50)*(714,285) + (0.50)*(312,500) £513,392.86 per dollar Variance of spot rate (V(s) V(s) = .50/(.71-0.67)^2 +.50/(.63-.67)^2 0.0020 Cov(P,S) =.50(714,285-513,392)(.71 -.67)+.50(312500-513392)(.63-.67) 8968.4311 b = Cov(P,S)/Var(S) = 8968.43/.0020 $4,500,000