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1. 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	$1.20/	$1.10/	$1.00/	$0.90/
P*	1500	1400	1300	1200
P	$1,800	$1,540	$1,300	$1,080

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?

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

Answer

E(S) = .25(1.20 +1.10+1.00+0.90) = $1.05/

E(P) = .25(1,800+1,540+1,300 +1,080) = $1,430

Var(S) = .25[(1.20-1.05)+(1.10-1.05)+(1.00-1.05)+(0.90-1.05)] = .0125

Cov(P,S) = .25[(1,800-1,430)(1.20-1.05) + (1,540-1,430)(1.10-1.05)

(1,300-1,430)(1.00-1.05) + (1,080-1,430)(0.90-1.05)] = 30

b = Cov(P,S)/Var(S) = 30/0.0125 = 2,400.

b) Var(P) = .25[(1,800-1,430)+(1,540-1,430)+(1,300-1,430)+(1,080-1,430)] = 72,100($)

(c) Var(P) - bVar(S) = 72,100 - (2,400)(0.0125) = 100($)

This means that most of the volatility of the dollar value of the French asset can be removed by

hedging exchange risk. The hedging can be achieved by selling 2,400 forward.

Please give explanation to above answer.