At time zero you enter a short position in a forward contract on 1 share of the stock XYZ at the forward price of 10.00. Moreover, you buy one exotic derivative, with the same maturity as the forward contract, which pays to the holder exactly one share of the stock if the product S(0)×S(T) of the price today and the price at maturity is above 100.00, and which pays the holder exactly zero if that product is below 100.00. The today's stock price is 10.00 and today’s selling price of one derivative of this kind is 6.00. Assume that, after those trades are put in place, the initial capital you have (need) is invested (borrowed) at zero interest rate. In your answer, use minus sign for a loss.
Enter your total profit or loss if at maturity the price of one stock share is 12.00:
>> Enter your total profit or loss if at maturity the price of one stock share is 6.00:
To calculate the total profit or loss at maturity, let's analyze the two scenarios separately:
1. Price at maturity is 12.00:
- For the short position in the forward contract, you would need to buy back the stock at the market price of 12.00 to fulfill your obligation. This results in a loss of (12.00 - 10.00) = -2.00.
- As you entered a short position in the exotic derivative, it would pay zero because the product S(0)×S(T) = 10.00 × 12.00 = 120.00 is not above 100.00. So there is no profit or loss from the derivative.
- The initial investment or borrowing at zero interest rate is not relevant for this scenario, as it has no impact on the final outcome.
Total profit or loss = Loss from the forward contract + Profit/Loss from the exotic derivative
= -2.00 + 0
= -2.00
2. Price at maturity is 6.00:
- For the short position in the forward contract, you would need to buy back the stock at the market price of 6.00 to fulfill your obligation. This results in a profit of (10.00 - 6.00) = 4.00.
- As you entered a short position in the exotic derivative, it would pay one share of the stock since the product S(0)×S(T) = 10.00 × 6.00 = 60.00 is below 100.00. Therefore, the profit from the derivative is (1 × 6.00) - 6.00 = 0.
- Again, the initial investment or borrowing at zero interest rate does not affect the final outcome.
Total profit or loss = Profit from the forward contract + Profit/Loss from the exotic derivative
= 4.00 + 0
= 4.00
So, the total profit or loss is:
- If the price at maturity is 12.00: -2.00
- If the price at maturity is 6.00: 4.00
To determine the total profit or loss at maturity, we need to consider the payoff from both the short position in the forward contract and the exotic derivative.
Let's break down the calculations:
1. Short position in the forward contract:
The profit or loss from the forward contract depends on the difference between the forward price and the price at maturity.
- If the price at maturity is higher than the forward price (12.00 > 10.00), you would incur a loss equal to the difference between the two prices. So the loss from the forward contract would be (12.00 - 10.00) = -2.00 (minus sign denotes loss).
- If the price at maturity is lower than the forward price (6.00 < 10.00), there would be no loss from the forward contract as you have already sold the stock at a higher price.
2. Payoff from the exotic derivative:
The derivative pays off only if the product of the price today and the price at maturity (S(0)×S(T)) is above 100.00. Otherwise, the payoff is zero.
- If the price today and at maturity multiplied together is above 100.00, you would receive one share of the stock, resulting in a profit. Therefore, the profit from the exotic derivative would be +1.00 (as the stock is valued at 12.00).
- If the product of the two prices is below 100.00, the payoff from the exotic derivative is zero.
3. Net profit or loss:
To calculate the net profit or loss, we need to subtract the initial investment in the exotic derivative, which was bought at a price of 6.00.
Now let's calculate the total profit or loss for each scenario:
- If the price of one stock share is 12.00:
- Loss from the forward contract: -2.00
- Profit from the exotic derivative: +1.00
- Net profit or loss: (-2.00) + 1.00 - 6.00 = -7.00 (minus sign denotes loss)
Therefore, if the price of one stock share is 12.00, the total profit or loss would be -7.00.
- If the price of one stock share is 6.00:
- Loss from the forward contract: 0 (no loss incurred)
- Payoff from the exotic derivative: 0 (no payoff received)
- Net profit or loss: 0 - 6.00 = -6.00 (minus sign denotes loss)
Therefore, if the price of one stock share is 6.00, the total profit or loss would be -6.00.