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/.$ 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/.$ You assess that the

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

probability.

$17$

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.