Problem $9\mathrm{.}3$

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\mathrm{.}40$ per pound. 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\mathrm{.}60$ per pound. You

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

Required:

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$-1.$ How would you hedge this exposure?

c$-2.$ If you hedge, what is the variance of the pound value of the hedged position?