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

2) Let as compute the necessary parameter

E(P) = (0.6)(($2800)+(0.4)($2250)=$1680++$900=$2580

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.

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. You have a negative exposure! As the pound gets stronger (weaker) against the dollar , the dollar value of your British holding goes down (Up).

4)Consequence of hedging.

Hedging is a technique utilized to reduce risk, but it’s important to keep in mind that nearly every hedging practice will have its own downsides. First, as indicated above, hedging is imperfect and is not a guarantee of future success, nor does it ensure that any losses will be mitigated. Rather, investors should think of hedging in terms of pros and cons. Do the benefits of a particular strategy outweigh the added expense it requires? Because hedging will rarely if ever result in an investor making money, it’s worth remembering that a successful hedge is one that only prevents losses.