A U.S.firm holds an asset in Great Britain and faces the following scenario:
$\begin{array}{l}\begin{array} { l } &\text { State 1}\\\text { Probability } & 25 \% \\\text { Spotrate } & \$ 2.20 / £ \\P^{*} & £ 2,000 \\P & \$ 4,400\end{array}\begin{array} { l } \text { State 2}&\text { State 3}\\50 \% & 25 \% \\\$ 2.00/£ & \$ 1.80 / £\\£ 2,500 & £ 3,000 \\\$ 5,000 & \$ 5,400\end{array}\end{array}$
P^* = Pound sterling 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 Great Britain and faces the following scenario:

\begin{array}{l}\begin{array} { l } &\text { State 1}\\\text { Probability } & 25 \% \\\text { Spotrate } & \$ 2.20 / £ \\P^{*} & £ 2,000 \\P & \$ 4,400\end{array}\begin{array} { l } \text { State 2}&\text { State 3}\\50 \% & 25 \% \\\$ 2.00/£ & \$ 1.80 / £\\£ 2,500 & £ 3,000 \\\$ 5,000 & \$ 5,400\end{array}\end{array}

P^* = Pound sterling 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

The exposure (beta) is calculated using the formula $\frac{\operatorname{Cov}(P, S)}{\operatorname{Var}(S)}$. After calculating the covariance and variance, the beta is found to be -2,500.

A USfirm Holds an Asset in Great Britain and Faces the the Following