An investor enters into a short forward contract to sell 100,000 pounds for USD at an exchange rate of 1.5 USD/£. How much does the investor gain or lose if the exchange rate at th... An investor enters into a short forward contract to sell 100,000 pounds for USD at an exchange rate of 1.5 USD/£. How much does the investor gain or lose if the exchange rate at the end of the contract is: a. 1.49/£ b. 1.52/£
Understand the Problem
This question asks us to calculate the gain or loss for an investor who has a short forward contract to sell pounds (GBP) for US dollars (USD) at a specified exchange rate. We need to determine the profit or loss based on two different exchange rates at the contract's maturity.
Answer
Scenario 1 (1.4770 USD/GBP): Loss of $7,500 USD Scenario 2 (1.4510 USD/GBP): Profit of $5,500 USD
Answer for screen readers
Scenario 1 (1.4770 USD/GBP): Loss of $7,500 USD Scenario 2 (1.4510 USD/GBP): Profit of $5,500 USD
Steps to Solve
- Define the short forward contract.
A short forward contract obligates the investor to sell an asset (in this case, GBP) at a predetermined exchange rate on a future date. The investor profits if the spot exchange rate at maturity is lower than the forward rate, and loses if it is higher.
- Calculate the profit or loss for the first scenario (1.4770 USD/GBP).
The investor agreed to sell GBP at 1.4620 USD/GBP. At maturity, the spot rate is 1.4770 USD/GBP. This means the investor has to sell GBP at 1.4620 when they could have sold it in the spot market for 1.4770. The loss per GBP is $1.4770 - 1.4620 = 0.0150$ USD/GBP. Since the contract is for GBP 500,000, the total loss is: $500,000 \times 0.0150 = 7,500$ USD.
- Calculate the profit or loss for the second scenario (1.4510 USD/GBP).
The investor agreed to sell GBP at 1.4620 USD/GBP. At maturity, the spot rate is 1.4510 USD/GBP. This means the investor sells GBP at 1.4620 when the market rate is only 1.4510. The profit per GBP is $1.4620 - 1.4510 = 0.0110$ USD/GBP. Since the contract is for GBP 500,000, the total profit is: $500,000 \times 0.0110 = 5,500$ USD.
Scenario 1 (1.4770 USD/GBP): Loss of $7,500 USD Scenario 2 (1.4510 USD/GBP): Profit of $5,500 USD
More Information
Forward contracts are commonly used to hedge against currency risk. In this example, the investor was speculating on the future value of the British pound relative to the US dollar.
Tips
A common mistake is to confuse the direction of the profit or loss in a short forward contract. Remember that in a short position, you profit when the spot rate decreases and lose when it increases relative to the forward rate. It's also important to use the correct subtraction order to determine the gain or loss per unit.
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