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.

(1)   Calculate the variance of the dollar value of your property

(2) Calculate your exposure to the exchange risk

(3)   Calculate the variance of the dollar value of your property that is attributable to the exchange rate uncertainty.

(4) Examine the consequence of hedging.

Answer 1

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Answer:

1)

Let us compute the necessary parameter values:

E(P) = (.6)($2800)+(.4)($2250) = $1680+$900 = $2,580

E(S) = (.6)(1.40)+(.4)(1.5) = 0.84+0.60 = $1.44

Var(S) = (.6)(1.40-1.44)^2 + (.4)(1.50-1.44)^2

          = .00096+.00144 = .0024.

2)

Cov(P,S) = (.6)(2800-2580)(1.4-1.44)+(.4)(2250-2580)(1.5-1.44)

             = -5.28-7.92 = -13.20

b = Cov(P,S)/Var(S) = -13.20/.0024 = -£5,500.

we get a negative exposure As the pound gets stronger (weaker) against the dollar, the dollar value of your British holding goes down (up).

3)

b.Var(S) =(-5500)^2(.0024) =72,600($)

4)

Buy £5,500 forward. By doing so, you can eliminate the volatility of the dollar value of your British asset that is due to the exchange rate volatility