Short Forward Contract Payoff at Maturity Explained

Let’s talk about forward contracts and specifically what happens at the very end, at maturity, if you’re in a short position. Imagine you are a wheat farmer. To plan your finances and reduce uncertainty, you enter into an agreement with a bakery today to sell them a certain amount of wheat in three months at a price fixed today, say $5 per bushel. This agreement is like a forward contract.

In this scenario, you, the farmer, have taken a short position in a forward contract on wheat. “Short position” simply means you have agreed to sell something in the future. You’re obligated to deliver the wheat at the agreed-upon price and date. The bakery, on the other hand, has a “long position” because they have agreed to buy.

Now, fast forward three months to the maturity date of this contract. What determines your payoff, your profit or loss, at this point? It all depends on the actual market price of wheat at that time, which we call the spot price at maturity.

Let’s consider a few scenarios. Remember, you agreed to sell at $5 per bushel.

Scenario 1: Imagine at maturity, the market price of wheat is now $4 per bushel. If you hadn’t entered into the forward contract, you would have to sell your wheat at this lower market price of $4. But because you have a forward contract to sell at $5, you are still going to receive $5 per bushel from the bakery. In this case, you are better off because of the forward contract. Your payoff is positive. Specifically, you’ve effectively sold your wheat for $1 more per bushel than the current market price. We can say your payoff is the agreed price of $5 minus the spot price of $4, which equals $1 per bushel.

Scenario 2: What if, at maturity, the market price of wheat has risen to $6 per bushel? Now, if you hadn’t entered the forward contract, you could sell your wheat on the open market for $6. However, you are obligated to fulfill your forward contract and sell it to the bakery for the agreed price of $5. In this case, you are worse off compared to selling at the higher market price. You’ve lost the opportunity to sell at $6. Your payoff is negative. In this case, it’s the agreed price of $5 minus the spot price of $6, which equals negative $1 per bushel.

Scenario 3: Let’s say the market price at maturity is exactly $5 per bushel, the same as the agreed-upon forward price. In this situation, your payoff is zero. You are neither better nor worse off compared to selling at the market price. The agreed price and the market price are the same, so five dollars minus five dollars equals zero.

So, what’s the general pattern here? For a short position in a forward contract, the payoff at maturity is calculated by taking the agreed-upon forward price and subtracting the spot price of the underlying asset at maturity.

If the spot price at maturity is lower than the agreed-upon forward price, your payoff is positive. You benefit from having locked in a higher selling price.

If the spot price at maturity is higher than the agreed-upon forward price, your payoff is negative. You lose out on the opportunity to sell at the higher market price.

If the spot price at maturity is equal to the agreed-upon forward price, your payoff is zero.

Think of it like this: as the spot price at maturity goes up, your payoff as the short position holder goes down. It’s an inverse relationship. If you were to visualize this payoff profile on a graph, with the spot price on the horizontal axis and the payoff on the vertical axis, you would see a downward sloping straight line. When the spot price is very low, your payoff is high and positive. As the spot price increases, the payoff decreases, eventually becoming negative.

In essence, when you hold a short position in a forward contract, you are betting that the price of the underlying asset will go down, or at least not rise too much, by the time the contract matures. Your maximum potential profit is limited to the agreed-upon forward price if the spot price falls to zero. However, your potential losses are theoretically unlimited if the spot price rises significantly, because there’s no upper limit to how high prices can go. This highlights the importance of understanding and managing the risks associated with forward contracts, especially when taking a short position.