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.
A forward is set up so that neither side pays the other to enter. The forward price is chosen to make that true. Value at start = 0. Later, as the spot price moves, the contract gains value for one side and loses it for the other. Forward value for the long side after the start = Spot price now − PV of the forward price. At inception that equals zero, because the forward price is exactly what the spot price grows to.
A harder one
A long forward was struck at 100. With three months left, the forward price for delivery on that same date is now 106 and the discount factor for three months is 0.99. What is the value of the long position per unit?
- 5.94 - correct
- 6.00Why not: The undiscounted gain. The six is received in three months, so it must be brought back to today.
- 106Why not: The current forward price itself, not the gain against the contracted price of 100.
The long position agreed to buy at 100. The market now says delivery on the same date costs 106. So at delivery the long gains 106 − 100 = 6. But that 6 arrives in three months, and money later is worth less than money now, so we discount it. Value of long forward = (New forward price − Old contract price) × Discount factor = (106 − 100) × 0.99 = 6 × 0.99 = 5.94. The 6.00 answer forgets to discount, and 106 is just the price, not the gain.
The hardest tier
Why must the price of a forward contract be distinguished from its value?
- Because the forward price keeps changing while the value stays at zeroWhy not: Reversed. The delivery price is fixed at initiation, and it is the value that moves away from zero as the market changes.
- Because the value of a forward always equals the delivery price agreed at the startWhy not: The delivery price is the amount agreed at the start, such as 100, while the value is zero at the start and then changes.
- Because the price is fixed at the start but the value starts at zero and then changes - correct
Forward price is the delivery price fixed when the deal is made, and it never changes for that contract. Forward value is what the contract is worth today, and it starts at zero because no money is paid at the start. Value of long forward = (New forward price − Contract price) × Discount factor. Example: a forward struck at 100 has price 100 and value 0 on day one. If the market forward price later rises to 106, the price is still 100, but the long position is worth about 6 before discounting.
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