Question

Suppose you are a U.S. based company and exports goods from the United Kingdom. In 90 days, you expect to receive payment for a shipment of goods from the UK worth 100,000 British pounds (settlement). The US risk free discrete rate is 2.6% and the UK risk free discrete rate is 4.0%, and the current FX spot rate is $1.23 per pound.

A. You expect the UK pound currency to decrease against the US dollar over next 90 days. Please explain, whether you should buy or short a forward contract on the FX currency to hedge the foreign exchange risk?

B. What is the no-arbitrage profit “Interest Rate Parity” forward price to enter a forward contract expiring in 90 days?

C. After 30 days since the US company entered into a forward contract agreement the FX spot price for USD per pound is now, $1.19 per pound. The US risk free and UK risk free interest rates have stayed the same. What is the value of the US company’s position in the Forward contract at this 30-day mark of the 90-day forward contract?

D. At expiration of the forward contract (at 90 days), assuming forward price agreed was “Interest Rate Parity” price, and the USD per pound currency spot price is $1.23 per pound, what is the value of the US Company’s forward contract position?

Answer 1

A) The company exports goods to the United Kingdom and is expected to receive payment for a shipment of goods. Because the company expects the UK pound currency to decline over next 90 days, so there is a risk to the U.S. company that the value of the UK pound to decline and so it will receive fewer U.S. dollars on conversion. To hedge this risk, the company should into a contract to sell UK pounds forward so as to hedge foreign exchange risk.

B) S₀ (Current spot rate) = $1.23

T (time) = 90/365

r (U.S. risk free rate) = 2.6%

r^f (UK risk free rate) = 4%

Therefore, no-arbitrage price to enter a forward contract expiring in 90 days:

= $1.2259

C) S_t = $1.19

T = 90/365

t = 30/365

T - t = 60/365

r (U.S. risk free rate) = 2.6%

r^f (UK risk free rate) = 4%

= -$0.0384

This represents a gain to the short position of the US company (holding the short forward position) of $0.0384 per UK pound

D) S_t = $1.23

T = 90/365

t = 90/365

T - t = 0/365

r (U.S. risk free rate) = 2.6%

r^f (UK risk free rate) = 4%

= $0.0041

This represents a gain to the short position of the US company (holding the short forward position) of $0.0384 per UK pound