Money, Banking, and International Financeܲ=ߙ+ߚ∙ܵ+ߝ (24)
We can estimate the regression equation easily, and we calculate by using Equation 25.
Covariance measures the variation of the asset’s price to the exchange rate while the variance
shows the variation of the exchange rate. Consequently, two factors influence : the fluctuations
in the exchange rate and the sensitivity of the asset’s price to changes in the exchange rate.
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You, for example, own and rent out a condominium in Europe. You hire a property
manager who can vary the rent, ensuring someone always rents and occupies the property. We
keep the example simple and assume you receive 1,8 00 €, 2,000 €, or 2,2 00 € per month in cash
for rent, shown in Table 1. We refer to each rent as a state, and each rent could occur with a 1/3
probability. We also forecasted the exchange rate for each state, which is S. Then we calculated
the asset’s price, P, in U.S. dollars by multiplying that state’s rent by the exchange rate.
Table 1. Renting out your Condo for Case 1
State Probability Rent (€) Exchange Rate (S) Rent (P)
1 1/3 1, 800 € $1.00 / 1 € $1,800
2 1/3 2,000 € $1.25 / 1 € $2,5 00
3 1/3 2,2 00 € $1.5 0 / 1 € $3,300We calculate 800 for in this case. A positive indicates your cash rent varies with the
exchange rate fluctuations, and you have a potential economic exposure. Did you notice, as the
euro appreciated, the rent in dollars also increased? You could buy a forward contract for 800 €
at a contract price of $1.25 per 1 € to hedge against the exchange rate risk. This example works
out nicely because we evenly spaced out the exchange rates, and the middle exchange rate
determines the forward contract price.
In Table 2, we show is the correct hedge for Case 1. The Forward Price is the exchange
rate in the forward contract while the Exchange Rate is the spot exchange rate for a state. We
purchased a forward contract with a price of $1.25 per euro. If State 1 occurs, we gain from the
exchange rate because the euro depreciated against the U.S. dollar. By exchanging 800 € into
dollars, we gain $200, and we compute it in the Yield column in Table 2. If State 2 occurs, the
forward rate equals the spot rate, so we neither gain nor lose anything. Finally, if State 3 occurs,
the euro appreciated against the U.S. dollar, so we lose $200 on the forward contract. Since each
state is likely to occur, we, on average, break even by buying the forward contract.
We continue with the same example. However, your rents have changed in Table 3. In Case
2, you could receive 1,667.67 €, 2,000 €, or 2,500 € per month in cash, and any rent is equally
likely. Although your rent fluctuates greatly, the exchange moves in the opposite direction of the
rent. Do you notice when you calculate the rent in dollars, the rent amounts equal the same