A U.S. firm holds an asset in Israel and faces the following scenario:
$\begin{array} { l l l l }
\hline & \text { State 1 } & \text { State 2 } & \text { State 3 } \
\hline \text { Probability } & 25 \% & 50 ^ { \circ } \text { o } & 25 \% \
\text { Spot rate } & \$ 0.30 \text { ILS } & \text { \$0.20 ILS } & \$ 0.15 / \text { ILS } \
\text { P* } & \text { ILS2,000 } & \text { ILS5,000 } & \text { ILS3,000 } \
\text { P } & \$ 3,000 & \text { \$2.500 } & \text { \$750 }
\end{array}$
where,
P* = Israeli new shekel (ILS) price of the asset held by the U.S. firm
P = dollar price of the same asset

-The variance of the exchange rate is: (Round your final answer and intermediate calculations to 6 decimal places)

Question

A U.S. firm holds an asset in Israel and faces the following scenario:
$\begin{array} { l l l l } 
\hline & \text { State 1 } & \text { State 2 } & \text { State 3 } \
\hline \text { Probability } & 25 \% & 50 ^ { \circ } \text { o } & 25 \% \
\text { Spot rate } & \$ 0.30 \text { ILS } & \text { \$0.20 ILS } & \$ 0.15 / \text { ILS } \
\text { P* } & \text { ILS2,000 } & \text { ILS5,000 } & \text { ILS3,000 } \
\text { P } & \$ 3,000 & \text { \$2.500 } & \text { \$750 }
\end{array}$
where,
P* = Israeli new shekel (ILS) price of the asset held by the U.S. firm
P = dollar price of the same asset

-The variance of the exchange rate is: (Round your final answer and intermediate calculations to 6 decimal places)

Quizplus · Accepted Answer

To calculate the variance of the exchange rate, we first need to find the mean (average) exchange rate, then use it to calculate the variance.1. Calculate the mean exchange rate:$$ \text{Mean} = (0.25 \times 0.30) + (0.50 \times 0.20) + (0.25 \times 0.15) = 0.075 + 0.10 + 0.0375 = 0.2125 $$2. Calculate the variance:$$ \text{Variance} = \sum (\text{Probability} \times (\text{Spot rate} - \text{Mean})^2) $$$$ = (0.25 \times (0.30 - 0.2125)^2) + (0.50 \times (0.20 - 0.2125)^2) + (0.25 \times (0.15 - 0.2125)^2) $$$$ = (0.25 \times 0.00765625) + (0.50 \times 0.00015625) + (0.25 \times 0.00390625) $$$$ = 0.0019140625 + 0.000078125 + 0.0009765625 $$$$ = 0.00296875 $$Rounded to six decimal places, the variance of the exchange rate is 0.002969.

A US Firm Holds an Asset in Israel and Faces the the Following