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 $$1,000,000,$ and the exchange rate will be $$\frac{1\mathrm{.}40}{}.$ If the American economy experiences a recession, on the

other hand, your American equity stake will be worth $$500,000,$ and the exchange rate will be $$\frac{1\mathrm{.}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.

Exposure

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

Variance