Strategic Financial Management · Forwards and Futures

Forward Contract Features and Pricing Using Cost of Carry

Updated 11 October 2026 · Fact-checked

A forward contract is a private agreement to buy or sell an asset at a fixed price on a future date. Its fair price comes from cost of carry: spot price plus financing and storage costs, minus income from the asset. Under continuous compounding, F = S × e^(rT). Compute it step by step.

Understand Forward Contracts: Features and Pricing

A forward contract is an over-the-counter agreement between two parties. One agrees to buy and the other to sell an asset on a fixed future date at a price fixed today. This price is the forward price. No one pays the full price today. The contract is settled on the delivery date, either by delivering the asset or by paying the cash difference.

Key features: it is customised (asset, quantity, date and price are negotiated), it is not traded on an exchange, it is not marked to market daily, and it carries counterparty (credit) risk because either side can default. It is usually held until maturity, and closing it early is hard. The long party agrees to buy. The short party agrees to sell.

The forward price is not a forecast of the future spot price. It is fixed by no-arbitrage. Suppose you want the asset at time T. You can buy it today by borrowing money and hold it until T. That costs the spot price plus interest, plus storage and insurance, minus any income you receive. This total is the cost of carry. If the forward price differs from this, a risk-free profit (arbitrage) is possible.

For a financial asset with no income, the forward price is the spot price grown at the risk-free rate. If the asset pays income, such as a dividend or coupon, you subtract the future value of that income. If it has a dividend yield, you subtract the yield from the rate. For a commodity, you add storage cost. Where the asset gives a benefit from holding it, such as a convenience yield, you subtract that benefit.

The value of an existing forward is different from its forward price. At the start, the value is nil. Later, the value of a long position is the present value of the difference between the current forward price and the price originally agreed.

Key rules to remember

Forward price, simple interest, no income: F = S × (1 + r × T); S = spot price, r = annual risk-free rate, T = time in years. Use when the question says simple interest or gives a period of months.
Forward price, annual compounding: F = S × (1 + r)^T; Use when the question says compounded annually.
Forward price, continuous compounding: F = S × e^(rT); Use when the question says continuously compounded.
Forward price with known income: F = (S − PV of income) × (1 + r)^T; Or F = S × (1 + r)^T − FV of income. Income may be dividends or coupons. Discount or compound each amount from its own date.
Forward price with dividend yield: F = S × e^((r − q)T); q = continuous dividend yield. With a discrete annual yield q, the exact form is F = S × [(1 + r) ÷ (1 + q)]^T. Otherwise use the form the question specifies. The approximation F ≈ S × (1 + r − q)^T is used only when the question specifies it.
Forward price with storage cost (commodity): F = (S + PV of storage costs) × (1 + r)^T; Storage and insurance are added. Convenience yield, if given, is subtracted.
Value of long forward: Value = (F_new − F_old) ÷ (1 + r)^(remaining T); F_new is the current forward price for the same maturity. F_old is the agreed price. Equivalent: Value = S − PV of income − [F_old ÷ (1 + r)^(remaining T)].
Implied repo rate: Implied r = [(F + FV of income) ÷ S − 1] × (12 ÷ months); For an asset with no income, FV of income is zero and this becomes (F ÷ S − 1) × (12 ÷ months). It is on a simple-interest basis. Compare it with your borrowing rate: if the implied repo rate is higher, buying spot with borrowed money and selling the forward (cash and carry) gives a profit.

How to solve Forward Contracts: Features and Pricing questions

Use this order for any forward pricing question. It keeps the compounding basis and the cash flows right.

1Identify the asset: commodity, share, index, bond or currency. This decides which costs and income apply.
2Note the spot price, the time to maturity in years, and the rate. Convert months into years, for example 3 months = 0.25.
3Check the compounding basis: simple, annual or continuous. Use the matching formula.
4List every income and cost during the contract life, with dates. Dividends and coupons reduce the price. Storage and insurance increase it.
5Bring income or costs to a common date. Either deduct the present value from spot or add the future value to the forward. Be consistent.
6Compute the theoretical forward price.
7Compare it with the quoted forward price. If quoted is higher, sell forward and buy spot (cash and carry). If quoted is lower, buy forward and short the asset (reverse cash and carry).
8Write the arbitrage profit or the final price clearly with the unit and a one-line conclusion.

Quickest way: Spot grown at the net cost of carry

When to use it: Use for objective questions and short numerical parts where there are one or two simple cash flows.

Read off S, r and T. Make T in years.
If there is income, pick one route and stay with it. Route A: subtract the PV of income from S first, then apply the growth factor to (S − PV of income). Route B: apply the growth factor to S first, then deduct the FV of income at the maturity date.
Apply the growth factor: (1 + rT) for simple interest or e^(rT) for continuous. With no income this is S × (1 + rT) or S × e^(rT).
Compare with the quote. Quote above fair means sell the forward and buy the asset with borrowed money. Quote below fair means buy the forward, short the asset and invest the proceeds at the risk-free rate.
Check sense: with no income, the forward price must exceed spot when r is positive.

Common mistakes in Forward Contracts: Features and Pricing

Using T in months in the formula.
The question gives 6 months and students plug in 6.
Fix: Always convert to years first. 6 months = 0.5.
Adding dividends instead of subtracting them.
Students think income increases the price.
Fix: Income from the asset lowers the cost of carry. Subtract its value from the forward price.
Mixing present value and future value of income.
A dividend is deducted from S without discounting, or deducted from F without compounding.
Fix: Either deduct the PV of income from S, or deduct its FV from S(1 + r)^T. Never mix.
Treating the forward price as the expected future spot price.
The word forward sounds like a forecast.
Fix: The forward price is set by arbitrage. It says nothing about where spot will go.
Confusing the forward price with the value of a forward.
Both are called a price in practice.
Fix: At the start the value is zero. Later value is the PV of the gain from the old price against the current forward price.
Choosing the wrong arbitrage direction.
Students memorise the steps without the logic.
Fix: If the quoted forward is too high, sell it and buy the asset with borrowed money. If too low, buy it and short the asset.

Worked examples

Example 1

The spot price of a share is ₹800. It pays no dividend. The risk-free rate is 8% per annum, simple interest. Calculate the fair 6-month forward price. If the quoted 6-month forward is ₹850, state the arbitrage action and the profit per share at maturity.

Show the solution

S = ₹800, r = 8%, T = 6 ÷ 12 = 0.5 year.
Fair F = 800 × (1 + 0.08 × 0.5) = 800 × 1.04 = ₹832.
Quoted price ₹850 is higher than fair ₹832, so the forward is overpriced.
Action: sell the forward at ₹850. Borrow ₹800 and buy the share today.
At maturity: deliver the share and receive ₹850. Repay loan with interest = ₹832.
Profit = 850 − 832 = ₹18 per share.

Answer: Fair forward price = ₹832. Quoted ₹850 is overpriced, so do cash and carry: buy spot with borrowed money and sell forward. Risk-free profit = ₹18 per share.

Example 2

A share trades at ₹500. A dividend of ₹10 is expected in 2 months. The risk-free rate is 12% per annum, compounded monthly. Find the fair price of a 3-month forward on the share. Use monthly compounding at 1% per month and compound the dividend to month 3.

Show the solution

Monthly rate = 12% ÷ 12 = 1%.
Future value of spot over 3 months = 500 × (1.01)^3 = 500 × 1.030301 = ₹515.1505.
Dividend is received at month 2, so it earns interest for 1 month: 10 × 1.01 = ₹10.10.
Fair forward price = 515.1505 − 10.10 = ₹505.0505.
Rounded: ₹505.05.

Answer: The fair 3-month forward price is about ₹505.05. The dividend lowers the price below the no-dividend figure of ₹515.15.

Exam tips

Read the compounding basis first. Examiners often change between simple, annual and continuous across questions, and the answer differs by a few rupees.
Show the cash flows at each date in a short table or list. Marks are given for method even if the final figure differs.
In arbitrage questions, write both legs: the action today and the action at maturity. Then state the profit.
Learn the e^x values you may be given, such as e^0.05, and use them as supplied. Do not recompute from memory.
For MCQs, check direction before calculation. With positive rates and no income, the forward price is above spot. With high income, it can be below spot.

Practice questions from Forwards and Futures

Forward Contracts: Features and Pricing in other exams

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

Forward Contracts: Features and Pricing: frequently asked questions

What is cost of carry in a forward contract?

It is the net cost of holding the asset until the delivery date. It includes interest on the funds used and any storage or insurance, minus income such as dividends. Spot plus cost of carry gives the fair forward price.

How is a forward contract different from a futures contract?

A forward is a private, customised contract settled at maturity with counterparty risk. A futures contract is standardised, traded on an exchange and marked to market daily. A clearing corporation guarantees it.

Is the forward price the same as the expected spot price?

No. The forward price is set by no-arbitrage using spot, interest and carrying costs. The future spot price can turn out higher or lower.

When do I use e^(rT) in a forward price question?

Use it when the question states that interest is continuously compounded. Otherwise use the simple or periodic compounding formula stated in the problem.