A U.S.firm holds an asset in Great Britain and faces the following scenario:
$\begin{array}{l}\begin{array} { l } &\text { State 1}\\\text { Probability } & 25 \% \\\text { Spotrate } & \$ 2.20 / £ \\P^{*} & £ 3,000 \\P & \$ 6,600\end{array}\begin{array} { l } \text { State 2}&\text { State 3}\\50 \% & 25 \% \\\$ 2.00/£ & \$ 1.80 / £ \\£ 2,500 & £ 2,000 \\\$ 5,000 & \$ 3,600\end{array}\end{array}$
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^{*} & £ 3,000 \\P & \$ 6,600\end{array}\begin{array} { l } \text { State 2}&\text { State 3}\\50 \% & 25 \% \\\$ 2.00/£ & \$ 1.80 / £ \\£ 2,500 & £ 2,000 \\\$ 5,000 & \$ 3,600\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

The variance of the exchange rate is calculated as:$$\sigma^2 = \sum_{i=1}^n p_i (s_i - \bar{s})^2$$where:* $\sigma^2$ is the variance of the exchange rate* $p_i$ is the probability of state $i$* $s_i$ is the spot rate in state $i$* $\bar{s}$ is the expected spot rateIn this case, the expected spot rate is:$$\bar{s} = \sum_{i=1}^n p_i s_i = 0.25 \times 2.20 + 0.50 \times 2.00 + 0.25 \times 1.80 = 2.00$$Therefore, the variance of the exchange rate is:$$\sigma^2 = 0.25 \times (2.20 - 2.00)^2 + 0.50 \times (2.00 - 2.00)^2 + 0.25 \times (1.80 - 2.00)^2 = 0.02$$

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