Payoff of a forward contract
1. The idea
A forward contract fixes today the price at which one side will buy a share from the other on a set date, the delivery date. That price is the delivery price. The buyer holds the long position and the seller the short position. Unlike an option, a forward is an obligation for both sides. The delivery price agreed in a new forward is today’s forward price: the price at which the forward costs nothing to enter. So a forward’s payoff is also its profit:
\[ \begin{aligned} \text{buyer:}\quad \text{payoff} &= S_T - K,\\ \text{seller:}\quad \text{payoff} &= K - S_T, \end{aligned} \]
where \(S_T\) is the share price at delivery and \(K\) the delivery price. The two payoffs add up to $0. Unlike an option’s payoff, a forward’s payoff can be negative: neither side can walk away.
2. Try it
If an answer is wrong, we will see what went wrong and how to fix it.
3. Both sides on one chart
In the question, we agreed to buy at $50, and the share is worth $56 at delivery. We pay $50 for a share worth $56, so our payoff is $6. The seller has to sell a share worth $56 for $50, so the seller’s payoff is −$6.
Now move the share price at delivery and watch both lines. They cross at the delivery price, where neither side gains.
The chart has two cases:
- Above the $50 delivery price. The buyer gains, and the seller loses the same amount.
- Below $50. The buyer must still pay $50, so the buyer loses and the seller gains.
4. One worked example, then your turn
The worked example is the seller’s side, with the share price below the delivery price.
Now both sides with hints, one step at a time.
And one on your own.
5. Practice
Each question has new numbers, as the buyer or as the seller. You master the skill when you get three right in a row, with at least one right answer when the share price ends above the delivery price and one when it ends below. You can always open the solution, but then that question does not count.
6. Coming back to it
When you have mastered a skill, it comes back on the start page for a short review after 1 day. After each right answer the next review comes later: after 3, 7, 14 and then 30 days. After a wrong one, the reviews start again at 1 day.
This skill: