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 the American economy will experience a boom with a 70 percent probability and a recession with a 30 percent probability.

(a) Estimate your exposure to the exchange risk.

(b) Compute the variance of the pound value of your American equity position that is attributable to the exchange rate uncertainty.

(c) How would you hedge this exposure? If you hedge, what is the variance of the pound value of the hedged position?

Solution:

Prob = 0.70P* = $1,000,000S = $1.40P = 714,300

Prob = 0.30P* = $500,000S = $1.60P = 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 (How do you get this)?

Cov(P,S) = 7,535 (How do you get this)?

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

(b)b2Var(S) = (4,511,976)2*(0.00167) = 33,997,738,800

(c)Var(e) = Var(P) - b2Var(S) = 33,903,080,400 - 33,997,738,800 0

You can hedge this exposure by selling $4,511,976 forward.