A U.S.firm holds an asset in Great Britain and faces the following scenario:
$\begin{array}{l}\begin{array} { l } &\text { State 1}\\\text { Probability } & 25 \% \\\text { Spotrate } & \$ 2.20 / £ \\P^{*} & £ 1,800 \\P & \$ 4,500\end{array}\begin{array} { l } \text { State 2}&\text { State 3}\\50 \% & 25 \% \\\$ 2.00/£ & \$ 1.60 / £ \\£ 2,250 & £ 2,812.50 \\\$ 4,500 & \$ 4,500\end{array}\end{array}$
where,
P^* = Pound sterling 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 Great Britain and faces the following scenario:

\begin{array}{l}\begin{array} { l } &\text { State 1}\\\text { Probability } & 25 \% \\\text { Spotrate } & \$ 2.20 / £ \\P^{*} & £ 1,800 \\P & \$ 4,500\end{array}\begin{array} { l } \text { State 2}&\text { State 3}\\50 \% & 25 \% \\\$ 2.00/£ & \$ 1.60 / £ \\£ 2,250 & £ 2,812.50 \\\$ 4,500 & \$ 4,500\end{array}\end{array}

where,
P^* = Pound sterling 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 calculate the variance of the exchange rate, we first need to calculate the expected exchange rate:

E(S) = (0.25 x 2.20) + (0.50 x 2.00) + (0.25 x 1.60) = 1.95

Next, we calculate the deviations from the expected exchange rate and their probabilities:

Deviation State 1: 2.20 - 1.95 = 0.25

Probability of State 1: 0.25

Deviation State 2: 2.00 - 1.95 = 0.05

Probability of State 2: 0.50

Deviation State 3: 1.60 - 1.95 = -0.35

Probability of State 3: 0.25

We square the deviations and multiply them by their probabilities:

(0.25^2 x 0.25) + (0.05^2 x 0.50) + (-0.35^2 x 0.25) = 0.0100 + 0.0025 + 0.0894 = 0.1019

Therefore, the variance of the exchange rate is 0.1019.

The best choice is B because it is the only option that calculates the correct variance of the exchange rate.

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