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 variance of the exchange rate is:

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 variance of the exchange rate is:

Quizplus · Accepted Answer

To find the variance of the exchange rate, we need to first calculate the expected exchange rate and then calculate the variance using the formula:

Variance = Σ (Xi - E(X))^2 x P(Xi)

where Xi = exchange rate for state i, E(X) = expected exchange rate, and P(Xi) = probability of state i occurring.

Using the given information, we can calculate the expected exchange rate as:

E(X) = 0.25 x 0.30 + 0.5 x 0.20 + 0.25 x 0.15 = 0.2125

Now, we can use the formula to calculate the variance as:

Variance = (0.30 - 0.2125)^2 x 0.25 + (0.20 - 0.2125)^2 x 0.5 + (0.15 - 0.2125)^2 x 0.25 = 0.002969

Therefore, the answer is B.

As for the best choice for the U.S. firm, it depends on their objective and risk tolerance. State 1 offers the highest dollar price for the asset, but also has the highest exchange rate risk. State 3 offers the lowest exchange rate risk, but also the lowest dollar price for the asset. State 2 may offer a balance between risk and reward. The U.S. firm should consider their overall portfolio and make a decision based on their specific circumstances.

A USFirm Holds an Asset in Israel and Faces the Following