Question

A U.S. firm holds an asset in Israel and faces the following scenario in Israeli Shaekel (IS):

Probability                                                                                          Case 1                   Case 2                  Case 3

                                                                                                                25%                        50% 25%

Spot Price                                                                                            ($/IS)0.3000        ($/IS)0.2000       ($/IS)0.1500

Israeli Shaekel price of asset held by U.S. Firm    IS2000                   IS5000                   IS3000  

U.S. Dollar price of the same asset   $600     $1000                    $450

What is the Exposure (Regression Coefficient Beta) Coefficient?

Hint: Calculate the expression : covariance of the U.S. dollar price of the Israeli asset divided by the variance of the ($/Israeli Shaekel) exchange rate.

Answer 1

1.Computation of Exposure Coefficient:

a. Cov(P,S) = 0.25 × ($600 – $762.50) × ($0.30 – $0.2125) + 0.50× ($1000 – $762.50) × ($0.20 – $0.2125) + 0.25($450 – $762.50)*($0.15 – $0.2125)= -3.5547 - 1.4844 + 4.8828

Cov(P,S)= -0.1563

b. VAR(S) = 0.25($0.30 – $0.2125)2+ 0.50($0.20 – $0.2125)2+ 0.25($0.15 – $0.2125)2= 0.001914 + 0.000078 + 0.000976= 0.002968

Exposure Coefficient = Cov(P,S) / Variance(P) = -0.1563 / 0.002968

Exposure Coefficient = Cov(P,S) / Variance(P) = -52.6316