A U.S.firm holds an asset in Israel and faces the following scenario:
$\begin{array}{l}\begin{array} { l } &\text { State 1}\\\text { Probability } & 25 \% \\\text { Spotrate } & \$ 0.30 / LS \\P^{*} & LS 2,000 \\P & \$ 600\end{array}\begin{array} { l } \text { State 2}&\text { State 3}\\50 \% & 25 \% \\\$ 0.20/LS & \$ 0.15 / LS \\£ 5,000 & £ 3,000 \\\$ 1,000 & \$ 4,50\end{array}\end{array}$
where,
P^* = Israeli shekel (IS) price of the asset held by the U.S.firm
P = Dollar price of the same asset
The "exposure" (i.e.,the regression coefficient beta) is
Hint: Calculate the expression $\frac { \operatorname { Cov } ( P , S ) } { \operatorname { VAR } ( S ) }$ .

Question

A U.S.firm holds an asset in Israel and faces the following scenario:

\begin{array}{l}\begin{array} { l } &\text { State 1}\\\text { Probability } & 25 \% \\\text { Spotrate } & \$ 0.30 / LS \\P^{*} & LS 2,000 \\P & \$ 600\end{array}\begin{array} { l } \text { State 2}&\text { State 3}\\50 \% & 25 \% \\\$ 0.20/LS & \$ 0.15 / LS \\£ 5,000 & £ 3,000 \\\$ 1,000 & \$ 4,50\end{array}\end{array}

where,
P^* = Israeli shekel (IS) price of the asset held by the U.S.firm
P = Dollar price of the same asset
The "exposure" (i.e.,the regression coefficient beta) is
Hint: Calculate the expression

\frac { \operatorname { Cov } ( P , S ) } { \operatorname { VAR } ( S ) }

.

Quizplus · Accepted Answer

Using the given data, we need to calculate the covariance of P and S and the variance of S.
Cov(P,S) = (0.25*(2000-600)*(0.30-0.20) + 0.5*(5000-600)*(0.20-0.20) + 0.25*(3000-600)*(0.15-0.20) + 0.5*(4500-600)*(0.15-0.20)) = -1360
Var(S) = (0.25*(0.30-0.20)^2 + 0.5*(0.20-0.20)^2 + 0.25*(0.15-0.20)^2) = 0.0025
Therefore, the exposure (beta) = Cov(P,S)/Var(S) = -1360/0.0025 = -52,631.6
Hence, the answer is A.

A USFirm Holds an Asset in Israel and Faces the Following