A U. S. firm holds an asset in Great Britain and faces the following scenario:
State 1 State 2 State 3
Probability 25% 50% 25%
Spot rate $ 2.50 /£ $ 2.00 /£ $ 1.60 /£
P* £ 1,800 £ 2,250 £ 2,812.50
P $4,500 $4,500 $4,500

Which of the following would be an effective hedge?
A) Buy £2,500 forward at the 1-year forward rate, F1($/£), that prevails at time zero.

B) Sell £25,000 forward at the 1-year forward rate, F1($/£), that prevails at time zero.

C) Sell £2,278.13 forward at the 1-year forward rate, F1($/£), that prevails at time zero.

D) none of the options

C) Sell £2,278.13 forward at the 1-year forward rate, F1($/£), that prevails at time zero.

Explanation:

given data

                     State 1           State 2               State 3

Probability      25%            50%                      25%

Spot rate      $ 2.50 /£    $ 2.00 /£            $ 1.60 /£

P*                   £ 1,800       £ 2,250             £ 2,812.50

P                     $4,500          $4,500               $4,500

solution

company holds portfolio in pound. so to get hedge, they will sell that of the same amount.

we get here average value of the portfolio that is

The average value of the portfolio = £ (0.25*1800 + 0.5*2250 + 0.25*2812.5)

The average value of the portfolio = 2278.13

so correct option is C) Sell £2,278.13 forward at the 1-year forward rate, F1($/£), that prevails at time zero.