Suppose you are a British venture capitalist holding a major stake in an e-comme

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

Prob = 0.70

P*= $1,000,000

S = $1.40

P = £714,300

Prob = 0.30

P*= $500,000

S = $1.60

P = £312,500

E(S) = (0.70)/(1.40) + (0.30)/(1.60) = £0.688/$

E(P) = (0.70)*(714,300) + (0.30)*(312,500) = £593,760/$

Var(S) = 0.00167

Cov(P,S) = 7,535

b = Cov(P,S)/Var(S) = 7,535/0.00167 = 4,511,976 ($)

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