Lesson 1 of 3 6–9% of the exam

By Daniil Tarakanov Updated Oct 21, 20262027 curriculum

Futures price at inception and how daily settlement changes value

At inception a futures contract is priced like a forward, and both are worth zero. A forward's gain or loss builds up until expiry. A futures contract pays its gain or loss every day through the margin account, so right after each settlement its value is back to zero.

8 min cram, 32 min full read. Based on the 2027 CFA® Program Level I curriculum, Derivatives, Learning Module 6. Also part of the 2026 curriculum, so it applies to the November 2026 exam too.

Tailor this to you: take the self-assessment

Before this: Pricing and Valuing Forward Contracts and FRAs, Forwards, Futures, Swaps, Options and Credit Derivatives

On the exam

Compare the value and price of forward and futures contracts

Compare the value and price of forward and futures contracts. Expect: the futures price at inception, the value right after daily settlement, the day's variation margin, and which contract can carry a large unpaid gain or loss mid-life.

How deeply to learn each part

Know the idea: Understand it in general. It frames other topics, but you will not calculate with it.
Use it: Understand it well enough to solve a question with it. Recognize when it applies.
Memorize: Learn it by heart. The exam will not give it to you.

You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.

You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.

What is the futures price at inception?

The futures price at inception is found the same way as a forward price: no-arbitrage compounding of the spot price at the risk-free rate, adjusted for income and costs of holding the underlying. Nothing is paid to enter, so the contract’s value at inception is zero for both buyer and seller, exactly as for a forward.

Futures price at inception Memorize

f_0(T) = \left[S_0 - PV_0(I) + PV_0(C)\right](1 + r)^{T}

Income $I$ (dividends, coupons) lowers the price and costs $C$ (storage, insurance) raise it. A futures price that sits well below this level may signal a convenience yield from holding the physical asset.

Rearrange itFutures price at inception: solve for any input

The question asks for

A commodity trades at 8,500.00. The present value of income from holding it is 0.00 and of storage costs is 40.00. The risk-free rate is 4.00%. The no-arbitrage futures price for delivery in 0.5 years is closest to:

Spot price, S₀PV of income, PV₀(I)PV of costs, PV₀(C)Risk-free rate, r (annual)%Time to expiry, T (years)

f_{0} (T) = [S_{0} - P V_{0} (I) + P V_{0} (C)] (1 + r)^{T}

(8,500.00 − 0.00 + 40.00) × (1 + 0.04)^0.5 = 8,540.00 × 1.019804 = 8,709.13

Futures price, f₀(T)8,709.13

On your calculator

1.04y^x0.5=×(8500+40)=8709.13

y^x power

8500ENTER40+ENTER1.04ENTER0.5y^x×8709.13

ENTER enter (on the HP, puts the number on the stack) · y^x power

For an underlying that is a portfolio (an index) or involves two currencies, the curriculum uses continuous compounding.

Futures price, continuous compounding Use it

f_0(T) = S_0\,e^{rT}

What is a forward worth during its life?

The forward price $F_0(T)$ is fixed when the contract is signed. The contract’s forward value changes as the spot price moves: it is the spot price less the present value of the fixed price still to be paid.

Forward value during the life Use it

V_t(T) = S_t - F_0(T)(1 + r)^{-(T-t)}

Nothing is paid until expiry. A forward that is well in the money for one party is an unpaid claim on the other, which is why forwards carry credit risk and futures do not accumulate it.

How does daily settlement work?

Futures are marked to market every day. The mark to market (MTM) is the change in the contract’s value since the last mark. Under daily settlement the exchange pays that gain from the loser’s margin account to the winner’s, and the contract is re-set to the new settlement price. The payment is called variation margin.

Daily variation margin on a long futures position Use it

VM_t = (f_t - f_{t-1}) \times \text{size} \times N

After the payment, the value reset to zero is complete: the contract is worth nothing at the new price, and tomorrow’s value will be only tomorrow’s move. The short’s variation margin is the same amount with the opposite sign.

Rearrange itDaily settlement of a long futures position: solve for any input

The question asks for

A trader is long 1 futures contract of 25 units each. The settlement price moves from 8,412.50 to 8,384.00. The day's variation margin credited to (positive) or debited from (negative) the margin account is closest to:

Previous settlement priceNew settlement priceUnits per contractNumber of contracts

V M = (f_{t} - f_{t - 1}) \times u \times N

(8,384.00 − 8,412.50) × 25 × 1 = -712.50

Day's variation margin (long)-712.50

On your calculator

8384−8412.5=×25×1=-712.5

8384ENTER8412.5−25×1×-712.5

ENTER enter (on the HP, puts the number on the stack)

Loading the interactive

Switch between the two contracts on the same price path. The forward view builds one large unpaid value; the futures view pays daily bars and returns its value to zero each evening, yet the cash paid in total ends close to the forward’s.

Forward and futures side by side

Same underlying, same expirythe price at inception is the same; the cash flows are not

Forward Memorize private OTC contract
- Price F₀(T) is fixed for life
- Value S_t − F₀(T)(1 + r)^−(T−t), builds up
- Cash paid once, at expiry
- Credit exposure grows with the unpaid value
Futures Memorize standardized, exchange-traded, margined
- Price re-set daily to the settlement price
- Value zero right after each daily settlement
- Cash paid every day, via variation margin
- Credit exposure limited to one day of moves

Exam tip Price and value are different things. A futures price changes daily; a futures value is zero after each settlement.

Do the total gains differ?

The cumulative MTM gain or loss over the whole life is approximately the same for a futures contract and a comparable forward. The contracts differ in when the cash moves, not in how much moves in total.

Worked example Copper, four months in

The position is 25 tonnes of copper agreed at f₀ = F₀ = USD 8,668.33, with two months left. Spot is now USD 8,300 and r = 4%.

Forward value per tonne = 8,300 − 8,668.33 × 1.04^−(2/12) = −USD 311.85. For 25 tonnes: −USD 7,796, owed at expiry.
The futures price is now 8,300 × 1.04^(2/12) = USD 8,354.43. Paid so far through the margin account: (8,354.43 − 8,668.33) × 25 = −USD 7,847.50.
The futures value is zero; the forward value is −7,796. The two totals are close. The difference is two months of interest: the futures cash has already been paid, while the forward value is a present value of a payment due at expiry (−7,796 × 1.04^(2/12) ≈ −7,848).

Forward value on your calculator

1.04y^x(2÷12)+|-=×8668.33= 8611.85
+|-+8300= -311.85

y^x power · +|- change sign

1.04ENTER2ENTER12÷CHSy^x8668.33× 8611.85
CHS8300+ -311.85

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · y^x power

Go deeper Why the two totals are not exactly equal

Futures gains and losses arrive during the life and earn or cost interest, while the forward’s value is a single present value. The last lesson in this module shows how the sign of that interest effect depends on whether the futures price moves with interest rates.

Go deeper Credit consequences

A forward can carry a large unpaid exposure to the counterparty, which is why over-the-counter (OTC) dealers often ask for collateral. A futures position cannot: the clearing house settles each day, so the most that can be unpaid is one day’s move, and a missed margin call closes the position out.

Memorize this

MemorizeForward versus futures: price and value

	Forward	Futures
Value at inception	0	0
Price during life	$F_0(T)$ never changes	new settlement price each day
Value during life	$S_t - F_0(T)(1+r)^{-(T-t)}$	0 after daily settlement
Gain or loss paid	once, at expiry	every day (variation margin)
Total gain or loss	$S_T - F_0(T)$	about the same, paid in instalments

Memory hook Inception: same price, both zero. After that, "futures reset, forwards accumulate".

Know it cold Futures value right after settlement = 0. Variation margin = (new settlement price − old) × size × contracts; sign flips for a short. At expiry the futures price converges to spot.

Forward and futures side by side

Same underlying, same expirythe price at inception is the same; the cash flows are not

Forward Memorize private OTC contract
- Price F₀(T) is fixed for life
- Value S_t − F₀(T)(1 + r)^−(T−t), builds up
- Cash paid once, at expiry
- Credit exposure grows with the unpaid value
Futures Memorize standardized, exchange-traded, margined
- Price re-set daily to the settlement price
- Value zero right after each daily settlement
- Cash paid every day, via variation margin
- Credit exposure limited to one day of moves

Futures price at inception

f_0(T) = \left[S_0 - PV_0(I) + PV_0(C)\right](1 + r)^{T}

Quick example

A grain trades at 640 and storage costs have a present value of 8. With r = 5% and a three-month contract, f₀ = (640 + 8) × 1.05^0.25 = 655.95.

On your calculator

1.05y^x0.25=×648= 655.95

y^x power

1.05ENTER0.25y^x648× 655.95

ENTER enter (on the HP, puts the number on the stack) · y^x power

Futures price, continuous compounding

f_0(T) = S_0\,e^{rT}

Quick example

An index stands at 2,400 and the continuously compounded rate is 2.4%. For T = 0.75, f₀ = 2,400 × e^0.018 = 2,443.59.

On your calculator

0.024×0.75=2NDe^x×2400= 2443.59

2ND second function (the shifted label above a key) · e^x e to the power x

0.024ENTER0.75×ge^x2400× 2443.59

ENTER enter (on the HP, puts the number on the stack) · g blue shift key · e^x e to the power x

Forward value during the life

V_t(T) = S_t - F_0(T)(1 + r)^{-(T-t)}

Quick example

A forward was agreed at 1,250. Three months before expiry spot is 1,275 and r = 2%. V = 1,275 − 1,250 × 1.02^−0.25 = 31.17 per unit, unpaid until expiry.

On your calculator

1.02y^x0.25+|-=×1250= 1243.83
+|-+1275= 31.17

y^x power · +|- change sign

1.02ENTER0.25CHSy^x1250× 1243.83
CHS1275+ 31.17

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · y^x power

Daily variation margin on a long futures position

VM_t = (f_t - f_{t-1}) \times \text{size} \times N

Quick example

Long 6 contracts of 40 units. The settlement price falls from 207.10 to 205.30. The long pays (205.30 − 207.10) × 40 × 6 = −432.

On your calculator

205.3−207.1=×40×6= -432

205.3ENTER207.1−40×6× -432

ENTER enter (on the HP, puts the number on the stack)

How it is asked

Value after daily settlement

Immediately after settlement, the value of a long futures position is…

Zero. Trap: the cumulative gain, or S − PV(f₀) (the forward formula).
Day's variation margin

Long 3 contracts of 100 units, settlement price 52.40 → 51.90.

(51.90 − 52.40) × 100 × 3 = −150. Traps: one contract only, wrong sign.
Which contract carries the large unpaid MTM

Mid-life, which of forward and futures can hold a large accumulated value?

The forward. The futures value is reset to zero each day.
Price at inception with carry

Spot 1,800, PV of storage 15, r = 3%, T = 0.25.

(1,800 + 15) × 1.03^0.25 = 1,828.46. Trap: ignoring the storage cost (1,813.35).

Exam traps

Using S_t − PV(f₀) as the futures value mid-life. That is the forward formula; a futures value is zero after settlement.
Saying forward and futures prices differ at inception when rates are constant. They are the same.
Forgetting that total gain or loss over the life is about the same for both contracts. Only the timing differs.
Mixing up price and value. The futures price changes every day; its value is reset to zero.
Getting the sign wrong for the short. A rising settlement price is a loss for the short.

Checkpoint

6 exam-style questions. About 90 seconds each.

1Immediately after the daily settlement, the value of a long futures position is:
2A trader is long two soybean futures contracts of 5,000 bushels each. The settlement price moves from USD 11.84 to USD 11.69 a bushel. The day's variation margin is closest to:
3A metal trades at EUR 2,000 with a risk-free rate of 3%. It has no storage costs or income. The one-year futures price is closest to:
4Halfway through the life of otherwise identical contracts, which one most likely carries a large accumulated value that has not yet been paid?
5A forward was agreed at 940. With four months to expiry the spot price is 962 and the risk-free rate is 3%. The value of the long forward per unit is closest to:
6A trader is short 4 futures contracts of 50 units each. The settlement price rises from 318.60 to 320.15. The day's variation margin is closest to:

Key takeaways

At inception the futures price equals the forward price and both contracts are worth zero.
A forward's value builds up and is paid at expiry; a futures contract is settled daily and its value resets to zero.
Daily variation margin = (new settlement price − previous) × size × contracts, with the sign reversed for the short.
The total gain or loss over the life is about the same for both; only the timing differs.

Futures price at inception

f_0(T) = \left[S_0 - PV_0(I) + PV_0(C)\right](1 + r)^{T}

Quick example

A grain trades at 640 and storage costs have a present value of 8. With r = 5% and a three-month contract, f₀ = (640 + 8) × 1.05^0.25 = 655.95.

On your calculator

1.05y^x0.25=×648= 655.95

y^x power

1.05ENTER0.25y^x648× 655.95

ENTER enter (on the HP, puts the number on the stack) · y^x power

Futures price, continuous compounding

f_0(T) = S_0\,e^{rT}

Quick example

An index stands at 2,400 and the continuously compounded rate is 2.4%. For T = 0.75, f₀ = 2,400 × e^0.018 = 2,443.59.

On your calculator

0.024×0.75=2NDe^x×2400= 2443.59

2ND second function (the shifted label above a key) · e^x e to the power x

0.024ENTER0.75×ge^x2400× 2443.59

ENTER enter (on the HP, puts the number on the stack) · g blue shift key · e^x e to the power x

Forward value during the life

V_t(T) = S_t - F_0(T)(1 + r)^{-(T-t)}

Quick example

A forward was agreed at 1,250. Three months before expiry spot is 1,275 and r = 2%. V = 1,275 − 1,250 × 1.02^−0.25 = 31.17 per unit, unpaid until expiry.

On your calculator

1.02y^x0.25+|-=×1250= 1243.83
+|-+1275= 31.17

y^x power · +|- change sign

1.02ENTER0.25CHSy^x1250× 1243.83
CHS1275+ 31.17

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · y^x power

Daily variation margin on a long futures position

VM_t = (f_t - f_{t-1}) \times \text{size} \times N

Quick example

Long 6 contracts of 40 units. The settlement price falls from 207.10 to 205.30. The long pays (205.30 − 207.10) × 40 × 6 = −432.

On your calculator

205.3−207.1=×40×6= -432

205.3ENTER207.1−40×6× -432

ENTER enter (on the HP, puts the number on the stack)

All Derivatives formulas, every lesson

Practice exam-style questions on Pricing and Valuing Futures Contracts

Next lesson Interest rate futures: the 100 minus rate convention

Questions about this lesson?

Where this comes back

Pricing and Valuing Interest Rate Swaps Derivatives
Convexity and Portfolio Duration Fixed Income
Introduction to Risk Management Portfolio Construction

Questions candidates ask

What is the difference between futures price and futures value?

The price is the level the contract trades at and is re-set every day to the settlement price. The value is what the position is worth to its holder. Right after daily settlement the value is zero, because the day's gain or loss has just been paid in cash.

Why is a futures contract's value zero after daily settlement?

The exchange credits or debits the gain or loss to the margin account each day and re-sets the contract to the new settlement price. A new contract at the market price is worth nothing, so the value starts again at zero. A forward is not settled, so its value accumulates.

Are futures prices the same as forward prices?

At inception, yes: both equal the spot price compounded at the risk-free rate, adjusted for income and costs. Later their cash flows differ, and the last lesson in this module explains why the two prices can drift apart slightly.

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