Question

A U.S. firm has a subsidiary in Great Britain and faces the following scenario:

	Probability	Spot Rate	C*	C	Proceeds from Fwd. contract	Dollar value of hedged position
State 1	40%	$2.50/£	£2,000
State 2	60%	$2.30/£	£2,500

a. Fill in the dollar value of the cash flow (C) in the table above.

b. Estimate your exposure to exchange rate risk (b).

c. Compute the proceeds from the forward contract if you hedge this exposure. Assume the forward rate is $2.45/£. Fill in the proceeds in the appropriate box in the table above. Use two decimal places in your calculations.

d. Compute the dollar value of the hedged position and fill in the blanks in the table above.

e. Calculate the variance of the un-hedged position.

f. If you hedge, what is the variance of the dollar value of the hedged position?

Answer 1

(a.) Dollar value of the cash flow (C)

State 1 = 2.5 * 2000 = $5000

State 2 = 2.3 * 2500 = $5750

(b.) Exposure to exchange rate risk

= (0.40*5000) + (0.60*5750) = $5450

(c.) Proceeds from the forward contract

State 1 = (2.45 - 2.50)*2000 = ($100) (Firm has to pay $100)

State 2 = (2.45-2.30)*2500 = $375

(d.) Dollar value of the hedged position

State 1 = $5000 - $100 = $4900

State 2 = $5750 + $375 = $6125

Now for (e.) and (f.), Variance,

(e.) Variance of un-hedged position

(f.)

Mean of dollar value of hedged position = (0.40*4900) + (0.6*6125) = $5635

Variance of dollar value of the hedged position