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 Canadian resident, you are concerned with the Canadian 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 C$2.40. If the British economy slows down, on the other hand, the land will be worth less, say, £1,500, but the pound will be stronger, say $2.50/£. You feel that the British economy will experience a boom with a 60 percent probability and a slowdown with a 40 percent probability.

a) Estimate your exposure to the exchange risk.
b) Compute the variance of the dollar value of your property that is attributable to exchange rate uncertainty.

Answer 1

a) To estimate exposure to exchange risk, consider possible outcomes and their probabilities. b) Variance of property value due to exchange rate uncertainty can be calculated using a formula.

Step-by-step explanation:

a) To estimate your exposure to exchange risk, you need to consider the possible outcomes and their probabilities. In this case, there is a 60% probability of a boom in the British economy and a 40% probability of a slowdown. The value of your property in Canadian dollars will depend on the exchange rate at that time. If the pound is worth C$2.40, your property will be worth £2,000 x C$2.40 = C$4,800. If the pound strengthens to $2.50/£, your property will be worth £1,500 x C$2.50 = C$3,750. Therefore, your exposure to exchange risk is the difference between these two values, which is C$4,800 - C$3,750 = C$1,050.

b) The variance of the dollar value of your property attributable to exchange rate uncertainty can be calculated using the following formula:

Var(X) = P1 * (X1 - E(X))^2 + P2 * (X2 - E(X))^2

Where P1 and P2 are the probabilities of the two outcomes (in this case, boom and slowdown), X1 and X2 are the values of the property in Canadian dollars corresponding to each outcome, and E(X) is the expected value of the property in Canadian dollars.

Using the values from the previous calculations, the variance of the dollar value of your property is:

Var(X) = 0.6 * (C$4,800 - C$1,050)^2 + 0.4 * (C$3,750 - C$1,050)^2 = C$1,317,000