Question

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

State	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?

Note C* refers to GPB Cash flow and C refers to the USD equivalent using the spot rate

Answer 1

a.)

State	Probability	Spot Rate	C*	C	Proceeds from Fwd. contract	Dollar value of hedged position
State 1	40%	$2.50/£	£2,000	2000 x 2.50 = $5000
State 2	60%	$2.30/£	£2,500	2500 x 2.30 = $ 5750

b.) Approximate Exposure in terms of Dollar can be calculated as below –

5000 x 0.40 + 5750 x 0.60 = $ 5450

c.)

State	Probability	Spot Rate	C*	C	Proceeds from Fwd. contract	Dollar value of hedged position
State 1	40%	$2.50/£	£2,000	2000 x 2.50 = $5000	2..45 x 2000 = $ 4900
State 2	60%	$2.30/£	£2,500	2500 x 2.30 = $ 5750	2.45 x 2500 = $ 6125

d)

State	Probability	Spot Rate	C*	C	Proceeds from Fwd. contract	Dollar value of hedged position
State 1	40%	$2.50/£	£2,000	2000 x 2.50 = $5000	2..45 x 2000 = $ 4900	(2.45 – 2.50) x 2000 = - $ 100
State 2	60%	$2.30/£	£2,500	2500 x 2.30 = $ 5750	2.45 x 2500 = $ 6125	(2.45 – 2.30) x 2500 = $ 375

e) Simple average of unhedged cash flows = (5000 + 5750)/2 = $ 5375

Variance = Sum of (x - Mean)^2 = (5000 - 5375)^2 + (5750 - 5375)^2 = $ 281250

f) Simple average = (-100 + 375)/2 = $ 137.50

Variance = Sum of (x - Mean)^2 = (-100 - 137.5)^2 + (375 - 137.5)^2 = $ 112812.5