Find an effective hedge financial hedge if a U.S.firm holds an asset in Great Britain and faces the following scenario:
$\begin{array}{l}\begin{array} { l } &\text { State 1}\\\text { Probability } & 25 \% \\\text { Spotrate } & \$ 2.20 / £ \\P^{*} & £ 3,000 \\P & \$ 6,600\end{array}\begin{array} { l } \text { State 2}&\text { State 3}\\50 \% & 25 \% \\\$ 2.00/£ & \$ 1.80 / £ \\£ 2,250 & £ 2,000 \\\$ 5,000 & \$ 3,600\end{array}\end{array}$
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 × S + e
The regression coefficient beta is calculated as b = $\frac { \operatorname { Cov } ( P , S ) } { \operatorname { VAR } ( S ) }$ Where
Cov(P,S) = 0.25 × ($6,600 - $5,050) × ($2.20 - $2.00) + 0.50 × ($5,000 - $5,050) × ($2.00 - $2.00) + 0.25 × ($3,600 - $5,050) × ($1.80 - $2.00) Cov(P,S) = 77.50 + 0 + 72.50
Cov(P,S) = 150
B = $\frac { 150 } { 0.02 }$ = 7,500
The variance of the exchange rate is calculated as
E(S) = 0.25 × $2.20 + 0.50 × $2.00 + 0.25 × $1.80
= $.55 + $1 + $.45
= $2.00
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
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 = $5,050
Suppose that you implement your hedge at F₁($/£) = $2/£.Your cash flows in state 1,2,and 3 respectively will be

Question

Find an effective hedge financial hedge if 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 / £ \\£ 2,250 & £ 2,000 \\\$ 5,000 & \$ 3,600\end{array}\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 × S + e
The regression coefficient beta is calculated as b =

\frac { \operatorname { Cov } ( P , S ) } { \operatorname { VAR } ( S ) }

Where
Cov(P,S) = 0.25 × ($6,600 - $5,050) × ($2.20 - $2.00) + 0.50 × ($5,000 - $5,050) × ($2.00 - $2.00) + 0.25 × ($3,600 - $5,050) × ($1.80 - $2.00) Cov(P,S) = 77.50 + 0 + 72.50
Cov(P,S) = 150
B =

\frac { 150 } { 0.02 }

= 7,500
The variance of the exchange rate is calculated as
E(S) = 0.25 × $2.20 + 0.50 × $2.00 + 0.25 × $1.80
= $.55 + $1 + $.45
= $2.00
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
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 = $5,050
Suppose that you implement your hedge at F₁($/£) = $2/£.Your cash flows in state 1,2,and 3 respectively will be

Quizplus · Accepted Answer

To hedge the U.S. firm's asset holding in Great Britain, the CFO can use a forward contract to sell British pounds and lock in a specific exchange rate. The hedge ratio for the contract can be calculated as the beta of the regression between the dollar price of the asset and the exchange rate, which is 7,500. The forward rate to sell pounds for dollars would be calculated as follows: F₁ = \$2.20 / £ × (1 + 7,500 × 0.02) / (1 + 0.02) = \$2 / £ This forward rate can be used to sell pounds at a fixed exchange rate of $2 per pound, regardless of the spot rate at the time of the transaction. In state 1, the spot rate is $2.20 per pound. The U.S. firm's asset is worth £3,000, which is worth $6,600 at the spot rate. With the hedging contract in place, the U.S. firm would sell £3,000 for $6,000, and gain $100 from the appreciation of the pound to $2. In state 2, the spot rate is $2 per pound. The U.S. firm's asset is worth £2,250, which is worth $5,000 at the spot rate. With the hedging contract in place, the U.S. firm would sell £2,250 for $4,500, and not gain or lose anything due to the spot rate staying constant. In state 3, the spot rate is $1.80 per pound. The U.S. firm's asset is worth £2,000, which is worth $3,600 at the spot rate. With the hedging contract in place, the U.S. firm would sell £2,000 for $4,000, and gain $400 from the appreciation of the pound to $2. Therefore, the cash flows in state 1, 2, and 3 would be $5,100, $5,000, and $5,100, respectively. The correct answer is A.

Find an Effective Hedge Financial Hedge If a U P* = Pound Sterling Price of the Asset Held by an Asset

Find an Effective Hedge Financial Hedge If a U P^* = Pound Sterling Price of the Asset Held by an Asset