Question

Suppose that you hold a piece of land in the City of London that you may want to sell in one year. As a U.S. resident, you are concerned with the dollar value of the land. Assume that, if the British economy booms in the future, the land will be worth £2,000 and one British pound will be worth $1.40. If the British economy slows down, on the other hand, the land will be worth less, i.e., £1,500, but the pound will be stronger, i.e., $1.50/£. You feel that the British economy will experience a boom with a 60% probability and a slow-down with a 40% probability.
Required:
a. Estimate your exposure b to the exchange risk.
b. Compute the variance of the dollar value of your property that is attributable to the exchange rate uncertainty.
c. Discuss how you can hedge your exchange risk exposure and also examine the consequences of hedging.

Answer 1

Answer and Explanation:

(A) E(P) = (0.6) × ($2800) + (0.4) × ($2250)

= $1680+$900

= $2,580

E(S) = (0.6) × (1.40)+(0.4) × (1.5)

= 0.84 + 0.60

= $1.44

Var(S) = (0.6)(1.40 - 1.44)² + (.4)(1.50 - 1.44)²

= .00096+.00144

= 0.0024.

Cov(P,S) = (0.6)(2800-2580)(1.4-1.44) + (0.4)(2250-2580)(1.5-1.44)

= -5.28-7.92

= -13.20

b = Cov(P,S)/Var(S)

= -13.20/.0024

= -£5,500.

there is a negative exposure.  as the pound gets stronger/weaker against the dollar the dollar value of british holding goes higher.

(B)  b²Var(S) = (-5500)²(.0024) = 72,600($)²

(C). i would Buy 5,500 forward to hedge exchange risk exposure. By doing this, i can eliminate the volatility of the dollar value of your British asset that is due to the volatility of the exchange rate