S.firm holds an asset in Great Britain and faces the following scenario: $\begin{array} { l c c c } & \text { State } 1 & \text { State } 2 & \text { State } 3 \\\text { Probability } & 25 \% & 50 \% & 25 \% \\\hline \text { Spot rate } & \$ 2.20 / £ & \$ 2.00 / £ & \$ 1.80 / € \\P ^ { * } & £ 3,000 & £ 2,500 & £ 2,000 \\P & \$ 6,600 & \$ 5,000 & \$ 3,600 \\\hline\end{array}$ P^* = Pound sterling price of the asset held by the U.S.firm P = Dollar price of the same asset
The CFO runs a regression of the form $P = a + b \times S + e$ .
The regression coefficient beta is calculated as b = $\operatorname { Cov } ( P , S )$
$\operatorname { Var } ( S )$ Where $\begin{aligned}\operatorname { Cov } ( P , S ) = & 0.25 \times ( \$ 6,600 - \$ 5,050 ) \times ( \$ 2.20 - \$ 2.00 ) \\+ 0.50 \times ( \$ 5,000 - \$ 5,050 ) \times ( \$ 2.00 - \$ 2.00 ) & + 0.25 \times ( \$ 3,600 - \$ 5,050 ) \times ( \$ 1.80 - \$ 2.00 ) \\\operatorname { Cov } ( P , S ) = & 77.50 + 0 + 72.50 \\\operatorname { Cov } ( P , S ) = & 150 \\b = \frac { 150 } { 0.02 } = 7,500\end{aligned}$ The variance of the exchange rate is calculated as: $\begin{array} { l } \mathrm { E } ( S ) = 0.25 \times \$ 2.20 + 0.50 \times \$ 2.00 + 0.25 \times \$ 1.80 = \$ .55 + \$ 1 + \$ .45 = \$ 2.00 \\\operatorname { VAR } ( S ) = 0.25 ( \$ 2.20 - \$ 2.00 ) ^ { 2 } + 0.50 ( \$ 2.00 - \$ 2.00 ) ^ { 2 } + 0.25 ( \$ 1.80 - \$ 2.00 ) ^ { 2 } = 0.01 + 0 + 0.01 \\= 0.02\end{array}$ The expected value of the investment in U.S.dollars is:
E[P] = 0.25 * $6,600 + 0.50 * $5,000 + 0.25 * $3,600 = $5,050
Which of the following is the most effective hedge financial hedge?

Question

S.firm holds an asset in Great Britain and faces the following scenario:

\begin{array} { l c c c } & \text { State } 1 & \text { State } 2 & \text { State } 3 \\\text { Probability } & 25 \% & 50 \% & 25 \% \\\hline \text { Spot rate } & \$ 2.20 / £ & \$ 2.00 / £ & \$ 1.80 / € \\P ^ { * } & £ 3,000 & £ 2,500 & £ 2,000 \\P & \$ 6,600 & \$ 5,000 & \$ 3,600 \\\hline\end{array}

P^* = Pound sterling price of the asset held by the U.S.firm P = Dollar price of the same asset
The CFO runs a regression of the form

P = a + b \times S + e

.
The regression coefficient beta is calculated as b =

\operatorname { Cov } ( P , S )

\operatorname { Var } ( S )

Where

\begin{aligned}\operatorname { Cov } ( P , S ) = & 0.25 \times ( \$ 6,600 - \$ 5,050 ) \times ( \$ 2.20 - \$ 2.00 ) \\+ 0.50 \times ( \$ 5,000 - \$ 5,050 ) \times ( \$ 2.00 - \$ 2.00 ) & + 0.25 \times ( \$ 3,600 - \$ 5,050 ) \times ( \$ 1.80 - \$ 2.00 ) \\\operatorname { Cov } ( P , S ) = & 77.50 + 0 + 72.50 \\\operatorname { Cov } ( P , S ) = & 150 \\b = \frac { 150 } { 0.02 } = 7,500\end{aligned}

The variance of the exchange rate is calculated as:

\begin{array} { l } \mathrm { E } ( S ) = 0.25 \times \$ 2.20 + 0.50 \times \$ 2.00 + 0.25 \times \$ 1.80 = \$ .55 + \$ 1 + \$ .45 = \$ 2.00 \\\operatorname { VAR } ( S ) = 0.25 ( \$ 2.20 - \$ 2.00 ) ^ { 2 } + 0.50 ( \$ 2.00 - \$ 2.00 ) ^ { 2 } + 0.25 ( \$ 1.80 - \$ 2.00 ) ^ { 2 } = 0.01 + 0 + 0.01 \\= 0.02\end{array}

The expected value of the investment in U.S.dollars is:
E[P] = 0.25 * $6,600 + 0.50 * $5,000 + 0.25 * $3,600 = $5,050
Which of the following is the most effective hedge financial hedge?

Quizplus · Accepted Answer

Selling F1F1F1S1F1F1F107,500 forward at the 1-year forward rate will help the firm lock in a price of $7,500 for each pound sterling it will receive in the future. This will hedge the firm against the potential depreciation of the pound sterling, therefore, protecting the dollar value of the asset held by the firm.

Sfirm Holds an Asset in Great Britain and Faces the Following