Work out what a forward contract is worth before it matures
The idea
A forward is worth zero at inception because its price is set to make it so. Afterwards it has value to whichever party the market has moved toward. To the long, the value is the present value of the difference between the current forward price for the remaining term and the contracted forward price. This is the central distinction between price and value in forward commitments: the contracted price is fixed for the life of the deal, while the value floats as the market reprices the same delivery date.
Formulas
Value of a forward during its life
Vₜ = Sₜ − F₀ ÷ (1 + r)^(T − t)
- Vₜ
- the value to the long party today
- Sₜ
- the spot price today, part way through the contract
- F₀
- the forward price agreed at the start
- r
- the risk-free rate
- T
- the years from the start to delivery
- t
- the years elapsed
A forward is worth nothing at inception, because F₀ is set to make it so, and moves away from zero as the spot moves. What the long gains the short loses exactly.
A practice question
What is the value of a forward contract at inception?
- Equal to the spot priceWhy not: The spot price is what the asset costs today, not what the contract is worth to either party.
- Zero — correct
- Equal to the forward priceWhy not: The forward price is the agreed amount to be paid later; the contract itself starts worth nothing.
The forward price is chosen precisely so neither party pays the other to enter. Value accrues only as the market moves afterwards.
A harder one
A long forward was struck at 100. With three months left, the forward price for that same date is 106 and the discount factor is 0.99. What is the position worth?
- Approximately 5.94 — correct
- Approximately 6.00Why not: The undiscounted gain. The six is received in three months, so it must be brought back to today.
- Approximately 106Why not: The current forward price itself, not the gain against the contracted price of 100.
The long can now lock in a sale at 106 against an obligation to buy at 100, a gain of 6 at delivery. Discounting to today gives 6 x 0.99 = 5.94.
The hardest tier
Why is the distinction between a forward's price and its value more important than for an option?
- Because forward prices are not observableWhy not: They are quoted in liquid markets and are readily observed.
- Because option values are always zero at inceptionWhy not: An option's value at inception is its premium, which is precisely why the distinction is less confusing there.
- Because forwards have no premium — correct
All of the economics show up as a value that moves away from zero. An option is paid for up front, so its price and its value are the same thing at every moment; a forward costs nothing to enter, and the entire exposure appears as a value that starts at zero and drifts.
In the app: 9 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
Take the free diagnostic →