Question

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

State	Probability	FX	Asset value
1	0.15	$1.30/€	€2,000
2	0.25	$1.20/€	€2,500
3	0.60	$1.10/€	€3,000

The exchange exposure β faced by the U.S. firm is closest to

Select one:

a. –$4,400

b. $4,400

c. –$5,400

d. –$3,400

Answer 1

Solution:
	E(S) = 0.15($1.30) + 0.25($1.20) + 0.60($1.10) = $1.16/€
	E(P) = 0.15(€ 2000) + 0.25(€ 2500) + 0.60(€ 3000) = €2,725
	Var(S) = 0.15(1.30-1.16)2 + 0.25(1.20-1.16)2+ 0.60(1.10-1.16)2 = 0.0055
	Cov(P,S) = 0.15(2,000 - 2,725)(1.30 - 1.16) + 0.25(2,500 - 2,725)(1.20 - 1.16) + 0.60(3,000 - 2,725)(1.10-1.16) = -27.38
	b = Cov(P,S)/Var(S) = -27.38/0.0055 = -$4,977.
	Therefore, the exchange exposure β faced by the U.S. firm is closest to (a) - $4,400.