CFA Level I Exam · Pricing and Valuation of Futures Contracts

How to Value a Forward Contract Over Time

Updated 7 October 2026 · Fact-checked

A forward contract's value is the present value of the gain or loss from locking in its price. At initiation it is zero. During its life, long value = spot price (less PV of carry benefits plus PV of costs) minus PV of the forward price. At expiration, long value = spot price − forward price.

Understand Valuation of Forward Contracts Over Time

A forward contract has a forward price, which is the fixed price agreed at initiation for delivery at expiration. The value of the contract is a different thing. Price is the number written in the contract and never changes. Value is what the contract is worth to each party today, and it changes as the market moves.

At initiation, no cash changes hands, so the value is zero to both sides. The forward price is set so that this is true. That is the no-arbitrage idea: neither party gets a free gain on day one.

After initiation, the spot price moves and time passes. Suppose the spot price rises. The long holds a contract to buy at the old, lower forward price, so the long gains and the short loses. Forwards are a zero-sum game, so the short's value is always the negative of the long's value.

To value the contract, compare two ways of buying the asset at time T: pay today's no-arbitrage forward price for T, or pay the original forward price. The difference at T is the gain. You then discount that difference back to today at the risk-free rate. If the asset pays income, such as dividends, you subtract the present value of that income from spot. If it has storage costs, you add their present value.

At expiration, there is no time left to discount and no carry left. The long's value is simply spot price minus the forward price. The long receives that amount if it is positive, and pays it if it is negative.

Key formulas to remember

Value at initiation: V₀(T) = 0 for both long and short; The forward price F₀(T) is set so that neither party pays anything at the start.
Value of long during the life (no carry): Vₜ(T) = Sₜ − F₀(T) ÷ (1 + r)^(T − t); Asset with no income or costs. T − t is the remaining time in years. The short's value is −Vₜ(T).
Value of long during the life (with income and costs): Vₜ(T) = [Sₜ − PVₜ(benefits) + PVₜ(costs)] − F₀(T) ÷ (1 + r)^(T − t); Use only the benefits and costs still to come after time t. Benefits such as dividends reduce value for the long; costs such as storage increase it.
Equivalent form using the current forward price: Vₜ(T) = [Fₜ(T) − F₀(T)] ÷ (1 + r)^(T − t); Fₜ(T) is the no-arbitrage forward price for the same expiration, calculated at time t.
Value at expiration: V_T(T) = S_T − F₀(T) for the long; F₀(T) − S_T for the short; No discounting. The values are equal in size and opposite in sign.
Short position: Value of short = −(value of long); A forward is zero-sum between the two counterparties.

How to solve Valuation of Forward Contracts Over Time questions

Use the same sequence for any question on valuing a forward after initiation. Work out the long first, then flip the sign for the short if needed.

1Identify the time point: initiation, during the life, or expiration. If initiation, the value is zero and you are done.
2Write down the original forward price F₀(T), the current spot Sₜ, the risk-free rate r, and the remaining time T − t in years.
3List any income or costs still to come, such as dividends, coupons or storage. Ignore any that have already been paid.
4Find the present value of those remaining benefits and costs, discounting at r for the time until each payment.
5Compute the adjusted spot: Sₜ − PV(benefits) + PV(costs).
6Discount the original forward price: F₀(T) ÷ (1 + r)^(T − t).
7Subtract: long value = adjusted spot − discounted forward price. Switch the sign for the short.
8Check the sign against intuition. If spot has risen since initiation, the long should show a gain.

Quickest way: Compare the old and new forward prices

When to use it: Use when the question gives or lets you easily compute the current forward price for the same expiration, or when no carry cash flows are involved.

Get the new forward price for the remaining term: Fₜ(T).
Subtract the original price: Fₜ(T) − F₀(T). This is the gain to the long at time T.
Discount that difference over the remaining time at r.
Eliminate options: if the market has gone up, the long's value must be positive. This removes one or two options at once.
For the short, change the sign.

Common mistakes in Valuation of Forward Contracts Over Time

Treating the forward price and the forward value as the same thing.
Both are called 'forward' and both are quoted in currency units.
Fix: Remember: price is fixed in the contract, value changes over time and is zero at initiation.
Forgetting to discount the original forward price.
At expiration the formula is simply S − F, so students carry that form into the mid-life case.
Fix: During the life, always divide F₀(T) by (1 + r)^(T − t). Only at expiration is there no discounting.
Subtracting dividends or income already paid.
Students include every cash flow listed in the question.
Fix: Include only cash flows that occur after time t. Past payments are already reflected in the spot price.
Using the wrong sign for income and costs.
Memorizing the formula without the logic behind it.
Fix: Income reduces the long's adjusted spot because the long does not receive it. Storage costs increase it. Think from the long's side.
Using the full term instead of the remaining time.
The original contract term is stated first in the question.
Fix: Use T − t, the time left. Draw a quick timeline if the question is unclear.
Giving the short the same sign as the long.
Rushing at the final step.
Fix: The short's value is always the negative of the long's. Check this before choosing an option.

Worked examples

Example 1

A 1-year forward on a non-dividend-paying stock was initiated at a forward price of 105. Six months later the stock trades at 110 and the risk-free rate is 4% per year (annual compounding). What is the value of the long position, to the nearest 0.01? Options: A) 2.58, B) 7.04, C) 8.05.

Show the solution

Remaining time T − t = 0.5 years. No income or costs.
Discount the original forward price: 105 ÷ (1.04)^0.5.
(1.04)^0.5 = 1.019804, so 105 ÷ 1.019804 = 102.9610.
Long value = 110 − 102.9610 = 7.0390, which rounds to 7.04.
Check the sign: the spot price is above the discounted forward price, so the long should be positive. This fits all three options, so rely on the calculation.

Answer: B) 7.04

Example 2

A 9-month forward on a stock was initiated at a forward price of 52.00. Three months later the stock price is 55.00. The stock pays a dividend of 1.00 in two months' time. The risk-free rate is 3% per year (annual compounding). What is the value of the short position? Options: A) −2.77, B) −2.24, C) 2.24.

Show the solution

Remaining time T − t = 6 months = 0.5 years.
PV of dividend: the dividend is in 2 months, so PV = 1.00 ÷ (1.03)^(2/12). (1.03)^(0.16667) = 1.004939, so PV = 0.99509.
Adjusted spot = 55.00 − 0.99509 = 54.00491.
Discounted original forward price = 52.00 ÷ (1.03)^0.5. (1.03)^0.5 = 1.014889, so 52.00 ÷ 1.014889 = 51.2372.
Long value = 54.00491 − 51.2372 = 2.7677, which rounds to 2.77.
Short value = −2.77.

Answer: A) −2.77. The long's value is positive because the spot price rose, so the short's value must be negative. This removes option C at once.

Exam tips

Look for the words 'value', 'price' and 'initiation'. Initiation always means value is zero, so no calculation is needed.
Use direction as an elimination tool. If spot is above the discounted forward price, the long is positive and the short is negative. This often removes two options immediately.
Check which cash flows are still to come. Questions often include a dividend that has already been paid as a trap.
Keep the remaining time in years. Convert months by dividing by 12 before you raise (1 + r) to a power.
On the TI BA II Plus, compute powers with: 1.04 [yˣ] 0.5 [=]. Use the memory keys to hold intermediate results and avoid rounding early.

Practice questions from Pricing and Valuation of Futures Contracts

Valuation of Forward Contracts Over Time in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Valuation of Forward Contracts Over Time: frequently asked questions

What is the difference between the value of a forward and the price of a forward?

The forward price is the fixed delivery price agreed at the start. The value is what the contract is worth today to one party. The price stays constant, while the value starts at zero and moves with the market.

What is the value of a forward contract at expiration?

For the long, it is the spot price at expiration minus the forward price. For the short, it is the forward price minus the spot price. The two values are equal in size and opposite in sign.

Why is the value of a forward zero at initiation?

The forward price is set using no-arbitrage pricing so that the contract has no advantage to either side. Because no cash is exchanged at the start, both parties have a value of zero.

How does a dividend affect the value of a long forward?

Dividends still to be paid before expiration reduce the long's value. The long does not receive them, so you subtract their present value from the spot price when valuing the contract.