Question

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

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

Homework Answers

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.
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