A U.S. company holds an asset in France and faces the subsequent scenario:
|
|
State 1
|
State 2
|
State 3
|
State 4
|
|
Probability
|
25%
|
25%
|
25%
|
25%
|
|
Spot rate
|
$.30/FF
|
$.25/FF
|
$.20/FF
|
$.18/FF
|
|
P*
|
FF1500
|
FF1400
|
FF1300
|
FF1200
|
|
P
|
$450
|
$350
|
$260
|
$216
|
In the above table, P* is the French franc price of the asset held by the U.S. company and P is the dollar price of the asset.
(a) Calculate the exchange exposure faced by the U.S. Company
(b) What is the variance of the dollar price of this asset if the U.S. Company remains unhedged against this exposure.
(c) In case the U.S. Company hedges against this exposure using the forward contract, what is the variance of the dollar value of the hedged position?
Answer: (a)
E(P) = .25(.30+.25+.20+.18) = $.2325
E(P) = .25(450+350+260+216) = $319
Var(S) = .25[(.30-.2325)2+(.25-.2325)2+(.2-.2325)2+(.18-.2325)2]
= .0022
Cov(P,S) = .25[(450-319)(.30-.2325)+(350-319)(.25-.2325)
(260-319)(.20-.2325)+(216-319)(.18-.2325)]
= 4.18
b = Cov(P,S)/Var(S) = 4.18/.0022 = FF1,900.
(b) Var(P) = .25[(450-319)2+(350-319)2+(260-319)2+(216-319)2]
= 8,053($)2.
(c) Var(P) - b2Var(S) = 8053-(1900)2(.0022) = 111($)2.
The meaning of this is that most of the volatility of the dollar value of the French asset can be removed by hedging exchange risk.