A U$.$S$.$ firm holds an asset in France and faces the following scenario:

State $1$ State $2$ State $3$ State $4$

Probability $25\%25\%25\%25\%$

Spot rate $ $1\mathrm{.}40/$ $ $1\mathrm{.}30/$ $ $1\mathrm{.}20/$ $ $1\mathrm{.}10/$

P$*1,5001,4001,3001,200$

P $ $1,880$ $ $1,620$ $ $1,340$ $ $1,120$

In the above table, P$*$ is the euro price of the asset held by the U$.$S$.$ firm and P is the dollar price of the asset.

a$.$ Compute the exchange exposure faced by the U$.$S$.$ firm.

b$.$ What is the variance of the dollar price of this asset if the U$.$S$.$ firm remains unhedged against this exposure?

c$.$ If the U$.$S$.$ firm hedges against this exposure using a forward contract, what is the variance of the dollar value of the hedged position?