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

Question 59

Multiple Choice

Find an effective hedge financial hedge if a U.S.firm holds an asset in Great Britain and faces the following scenario:
 State 1 Probability 25% Spotrate $2.20/£P£3,000P$6,600 State 2 State 350%25%$2.00/£$1.80/££2,250£2,000$5,000$3,600\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 = Cov(P,S) VAR(S) \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 = 1500.02\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( \$ 2.20 - \$ 2.00 ) ^ { 2 } + 0.50 ($2.00$2.00) 2( \$ 2.00 - \$ 2.00 ) ^ { 2 } + 0.25 ($1.80$2.00) 2( \$ 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
Which of the following is the most effective hedge financial hedge?


A) Sell £7,500 forward at the 1-year forward rate,F1($/£) ,that prevails at time zero.
B) Buy £7,500 forward at the 1-year forward rate,F1($/£) ,that prevails at time zero.
C) Sell £2,500 forward at the 1-year forward rate,F1($/£) ,that prevails at time zero.
D) 0.25 × £3,000 + 0.50 × £2,500 + 0.25 × £2,000 = £2,500

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