Foreign asset or overseas cash flow value fluctuates with the exchange rate changes. We know from statistics that a regression analysis of the asset value (P) versus the spot exchange rate (S) will offer the following regression equation −
P = a + (b x S) + e
Where, a is the regression constant, b is the regression coefficient, and e is a random error term with a mean of zero. Here, b is a measure of economic exposure, and it measures the sensitivity of an asset’s dollar value to the exchange rate.
The regression coefficient is the ratio of the covariance between the asset value and the exchange rate, to the variance of the spot rate. It is expressed as −
b = Cov (P, S)Var (S)
Economic Exposure – Numerical Example
A U.S. company (let us call it USX) has a 10% stake in a European company – say EuroStar. USX is concerned about a decline in the Euro, and as it wants to maximize the Dollar value of EuroStar. It would like to estimate its economic exposure.
USX thinks the probabilities of a stronger and/or weaker Euro is equal, i.e., 50–50. In the strong-Euro scenario, the Euro will be at 1.50 against the Dollar, which would have a negative impact on EuroStar (due to export loss). Then, EuroStar will have a market value of EUR 800 million, valuing USX’s 10% stake at EUR 80 million (or $120 million).
In the weak-Euro scenario, currency will be at 1.25; EuroStar would have a market value of EUR 1.2 billion, valuing USX’s 10% stake will be equal to $150 million.
If P represents the value of USX’s 10% stake in EuroStar in Dollar terms, and S represents the Euro spot rate, then the covariance of P and S is −
Cov (P,S) = –1.875
Var (S) = 0.015625
Therefore, b = –1.875 ÷ (0.015625) = – EUR 120 million
USX’s economic exposure is a negative EUR 120 million, which is equivalent to saying that the value of its stake in EuroStar decreases as the Euro gets stronger, and increases as the Euro weakens.