Question

if a U.S. firm holds an asset in Great Britain and faces the following scenario:

State: Probability	State 1: 25%	State 2: 50%	State 3: 25%
Spot Rate	$2.20/£	$2.00/£	$1.80/£
P*	£3,000	£2,500	£2,000
P	$6,600	$5,000	$3,600

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 is estimated as b=7500
Suppose the firm Sells £7,500 forward at the 1-year forward rate F₁($/£) = $2/£. Total value (i.e., net cash flows from hedging plus asset value) in state 1, 2, and 3 respectively will be

Answer 1

Cash flows from short forward contract = (F - S) * £7,500

Where F is thee forward price = $2/£

S is the spot price after 1 year

Cash flows from change in asset price = P(spot rate) - P ($2.00/£) = P(spot rate) - $5000

Case 1: If S = $2.20/£

Cash flows from short forward contract = ($2.0/£ - $2.20/£) * £7,500 = -$1500

Cash flows from change in asset price = $6600 - $5000 = $1600

Total cashflow = $1600 - -$1500 = $100

Case 2: If S = $2.0/£

Cash flows from short forward contract = ($2.0/£ - $2.0/£) * £7,500 = 0

Cash flows from change in asset price = $5000 - $5000 = 0

Total cashflow = 0 + 0 = 0

Case 3: If S = $1.8/£

Cash flows from short forward contract = ($2.0/£ - $1.8/£) * £7,500 = $1500

Cash flows from change in asset price = $3600 - $5000 = -$1400

Total cashflow = $1500 - -$1400 = $100