Assume that you hold a piece of land in the City of London that you may wish to sell in one year. Like a U.S. resident, we are concerned along with the dollar value of the land. Suppose that, if the British economy booms in the future, the valuation of the land is £2,000 and one British pound will be worth $1.40. If the British economy slows down, alternatively, the land will be worth less, that is £1,500, but the pound will be stronger, that is $1.50/£. You feel that the British economy will understand a boom with a 60% possibility and a slow-down with a 40% probability.
(a) Measure your exposure b to the exchange risk.
(b) Calculate the variance of the dollar value of your property which is attributable to the exchange rate uncertainty.
(c) Explain how you can hedge your exchange risk exposure and as well examine the consequences of hedging.
Solution: (a) Let us calculate 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 = $1.44
Var(S) = (.6)(1.40-1.44)2 + (.4)(1.50-1.44)2
= .00096+.00144 = .0024.
Cov(P,S) = (.6)(2800-2580)(1.4-1.44)+(.4)(2250-2580)(1.5-1.44)
= -5.28-7.92 = -13.20
b = Cov(P,S)/Var(S) = -13.20/.0024 = -£5,500.
You comprise a negative exposure! As the pound gets stronger (weaker) against the dollar, the dollar value of your British holding goes down(up).
(b) b2Var(S) = (-5500)2(.0024) =72,600($)2
(c) Buy £5,500 forward. By doing this, you can remove the volatility of the dollar value of your British asset that is because of the exchange rate volatility.