Lesson 1 of 4 6–9% of the exam

By Daniil Tarakanov Updated Oct 20, 20262027 curriculum

Forward price vs forward value: at initiation, during the life, at expiry

The forward price is the fixed price written in the contract. The forward's value is what the position is worth today: zero at initiation, then the spot price minus the present value of the forward price, and at expiration simply the spot price minus the forward price.

8 min cram, 32 min full read. Based on the 2027 CFA® Program Level I curriculum, Derivatives, Learning Module 5. 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: Arbitrage, Replication and the Cost of Carry

On the exam

Explain how the value and price of a forward contract are determined at initiation, during the life of the contract, and at expiration

Explain how the value and price of a forward contract are determined at initiation, during the life and at expiration. Expect a numeric value-during-the-life question (long or short) and a concept question on price versus value.

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 difference between a forward’s price and its value?

The forward price and the forward value are two different numbers, and the exam checks that you can tell them apart. The price is the rate written into the contract. The value is what the position is worth right now.

	Forward price, F₀(T)	Forward value, V_t(T)
What it is	The price agreed today for exchange at T	The gain or loss if the contract were settled now
At initiation	Set so the contract is fair	Zero
After initiation	Never changes	Moves with the spot price, time and rates
Same for both sides?	Yes	Equal and opposite: the long’s gain is the short’s loss

The value is a mark to market (MTM) figure. It measures the gain or loss for a counterparty if the contract were settled immediately. Over-the-counter forwards usually settle only at maturity, so the MTM is a paper gain or loss until then. Futures pay it out daily.

The long forward at the three dates that matter

Value of a long forward, Vthe price F₀(T) is the same at every date; only the value moves

Initiation (t = 0) Memorize V₀(T) = 0; F₀(T) set by no arbitrage
During the life (t) Memorize V_t(T) = S_t − F₀(T)(1 + r)^−(T−t)
Expiration (T) Memorize V_T(T) = S_T − F₀(T); the settlement amount

What is a forward worth at initiation?

The value at initiation is zero for both sides. The forward price is chosen so that neither party gains or loses at the start, which is why no cash changes hands. For an asset with no income or costs, no arbitrage fixes that price at the spot price compounded at the risk-free rate.

Forward price, no income or costs Use it

F_0(T) = S_0(1 + r)^T

Value at initiation Memorize

V_0(T) = 0

The same equation tells you the risk-free rate that the two prices imply.

What is a forward worth at expiration?

The value at expiration is the settlement amount. At T the spot price and the forward price are both prices for immediate exchange, so nothing is left to discount.

Value at expiration Memorize

V_T(T) = S_T - F_0(T) \quad \text{(long)}, \qquad F_0(T) - S_T \quad \text{(short)}

Outcome at T	Long	Short
S_T above F₀(T)	Gain	Loss
S_T below F₀(T)	Loss	Gain
S_T equals F₀(T)	Zero	Zero

The long buys at F₀(T) something worth S_T. If S_T is higher, the long gains. The short is on the other side of the same trade.

What is a forward worth during its life?

The value during the life is the gain or loss at time t if the contract were closed now. The long effectively owns the asset, worth S_t, and owes the forward price at T. What it owes is not F₀(T) in today’s money. It is the present value of the forward price , discounted at the risk-free rate over the remaining time T − t.

Value during the life, long position Memorize

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

Value during the life, short position Memorize

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

Worked example Six months into a one-year forward

An asset with no income or costs trades at USD 150 and r = 3%. A one-year forward is agreed.

Initiation: F₀(1) = 150 × 1.03 = USD 154.50, and V₀ = 0.
After six months the spot price is USD 158. The present value of the forward price over the remaining half year is 154.50 × 1.03^−0.5 = 152.23.
Long value = 158 − 152.23 = USD 5.77. Short value = −USD 5.77.
At expiration, if the spot price ends at USD 149: long value = 149 − 154.50 = −USD 5.50.

Step 2 and 3 on your calculator

1.03y^x0.5+|-=×154.5= 152.23
+|-+158= 5.77

y^x power · +|- change sign

1.03ENTER0.5CHSy^x154.5× 152.23
CHS158+ 5.77

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

Rearrange itForward value during the life: solve for any input

The question asks for

A forward was agreed at a price of 154.50. With 0.5 years left the spot price is 158.00 and the risk-free rate is 3.00%. The asset pays no income and has no costs. The value of the long position is closest to:

Spot price now, S_tForward price, F₀(T)Risk-free rate, r (annual)%Time remaining, T − t (years)

V_{t} (T) = S_{t} - F_{0} (T) (1 + r)^{- (T - t)}

158.00 − 154.50 × (1 + 0.03)^−0.5 = 158.00 − 152.23 = 5.77

Value of the long position, V_t(T)5.77

On your calculator

1.03y^x0.5+|-=×154.5=152.2334
+|-+158=5.7666

y^x power · +|- change sign

1.03ENTER0.5CHSy^x154.5×152.2334
CHS158+5.7666

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

InteractiveForward price vs forward value over the life

Try this 0 of 3

Slide today all the way to expiry
Before expiry, drag the spot at today's date to exactly the forward price
Partway through the life, raise the rate today above the starting rate

Today, t6 months

Spot at initiation S₀

Risk-free rate at initiation r3%

Rate today (from t on)3%

Spot path (drag the dots or type)

At 3 monthsAt 6 monthsAt 9 monthsAt expiry S_T

Forward price F₀(T), fixed154.50

PV of F₀(T) at t152.23

Long value V_t+5.77

Blue: spot path. Dashed: the forward price, which never moves. Purple: the PV of the forward price, rising to meet it at expiry. The bar at today is the long's value.

The long is worth +5.77. The long owns the asset in effect (158.00) and owes 154.50 in 6 months, worth 152.23 today. The short holds the mirror image.

Show working

Price at initiation: F₀(T) = S₀ × (1 + r)^T = 150.00 × 1.03¹ = 154.50. Value at initiation: 0.

During the life (t = 6 months, 6 months left): PV of F₀(T) = 154.50 × 1.03^−0.5 = 152.23

Long V_t = S_t − F₀(T)(1 + r)^{−(T − t)} = 158.00 − 152.23 = +5.77; short = −5.77.

Traps: ignoring the discounting gives +3.50; discounting over the full term T gives +8.00.

The forward price on your calculator

1.03y^x1=×150=154.50, the forward price

y^x power

150ENTER1.03ENTER1y^x×154.50, the forward price

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

The long's value today

1.03y^x0.5=1/x×154.5=152.23, PV of F₀(T)
+|-+158=+5.77, long value

y^x power · 1/x reciprocal · +|- change sign

158ENTER154.5ENTER1.03ENTER0.5y^x÷−+5.77, long value

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

The price is locked; the value is the spot price minus what you still owe, in today's money.

The present value of the forward price starts at the spot price on the day the contract is agreed, S₀, and drifts up toward F₀(T) at the risk-free rate as expiration nears. Where the spot price sits relative to that line decides who is ahead.

Who gains: compare S_t with the present value of the forward price

S_t against F₀(T)(1 + r)^−(T−t)gain for one side is exactly the loss for the other

S_t above it Memorize long: MTM gain; short: MTM loss
S_t below it Memorize long: MTM loss; short: MTM gain
S_t equal to it Memorize no gain or loss for either side

What moves the value?

Three things move V_t(T) after initiation, and the exam asks about each.

The spot price. A jump in S_t moves the long’s value one for one. Right after initiation the PV of the forward price still equals S₀, so a jump from USD 150 to USD 165 gives the long 165 − 150 = USD 15.
Time. The present value of the forward price grows toward F₀(T) as expiration nears. With the spot price unchanged, the long’s value drifts down and the short’s drifts up.
The interest rate. A higher rate lowers the present value of the forward price. That helps the long and hurts the short.

Worked example Rates rise, long position

A fund is long a one-year forward agreed at F₀(T) = 210.00. Four months later (eight months left) the spot price is 207 and the risk-free rate is 3.5%. How does the fund’s MTM change if the rate rises to 5.0% with the spot price unchanged?

At 3.5%: 207 − 210.00 × 1.035^−(8/12) = 207 − 205.24 = 1.76 gain.
At 5.0%: 207 − 210.00 × 1.05^−(8/12) = 207 − 203.28 = 3.72 gain.

The higher rate lowers the present value of the forward price, which is what the long still owes. The long’s gain grows by 1.96, and the short loses the same amount.

Step 2 on your calculator

1.05y^x(8÷12)=1/x×210= 203.28
+|-+207= 3.72

y^x power · 1/x reciprocal · +|- change sign

1.05ENTER8ENTER12÷y^x1/x210× 203.28
CHS207+ 3.72

ENTER enter (on the HP, puts the number on the stack) · y^x power · 1/x reciprocal · CHS change sign

Exam tip Whenever a question says “during the life”, discount the forward price over T − t, not T.

Go deeper Credit risk follows the value

A counterparty to an over-the-counter forward faces the other side’s credit risk only while its own value is positive. If V_t(T) is positive for the long, the short owes it money and could default. Dealers measure that exposure from the same MTM formula.

Go deeper Closing out early with an offsetting forward

Instead of waiting, a party can enter an offsetting forward at today’s price. The two forward prices lock in a difference that is paid at T. The present value of that difference is the value of the original forward today.

Memorize this

MemorizeValue of a forward at each date (no income or costs)

When	Long	Short
Initiation, $t=0$	$0$	$0$
During the life, $t$	$S_t - F_0(T)(1+r)^{-(T-t)}$	$F_0(T)(1+r)^{-(T-t)} - S_t$
Expiration, $T$	$S_T - F_0(T)$	$F_0(T) - S_T$

Memory hook Long = what you hold (spot) minus what you owe (the forward price, in today's money). Short is the mirror. At $t=0$ the two sides cancel; at $T$ nothing is left to discount.

Know it cold Discount $F_0(T)$ only over the remaining time $T-t$ . Price is fixed; value starts at zero and moves.

The long forward at the three dates that matter

Value of a long forward, Vthe price F₀(T) is the same at every date; only the value moves

Initiation (t = 0) Memorize V₀(T) = 0; F₀(T) set by no arbitrage
During the life (t) Memorize V_t(T) = S_t − F₀(T)(1 + r)^−(T−t)
Expiration (T) Memorize V_T(T) = S_T − F₀(T); the settlement amount

Who gains: compare S_t with the present value of the forward price

S_t against F₀(T)(1 + r)^−(T−t)gain for one side is exactly the loss for the other

S_t above it Memorize long: MTM gain; short: MTM loss
S_t below it Memorize long: MTM loss; short: MTM gain
S_t equal to it Memorize no gain or loss for either side

Forward price, no income or costs

F_0(T) = S_0(1 + r)^T

Quick example

A share trades at 80 and r = 3%. The nine-month forward price is 80 × 1.03^0.75 = 81.79.

On your calculator

1.03y^x0.75=×80= 81.7933

y^x power

1.03ENTER0.75y^x80× 81.7933

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

Value at initiation

V_0(T) = 0

Quick example

Entering a forward at the no-arbitrage price costs nothing and is worth zero to both sides.

Value at expiration

V_T(T) = S_T - F_0(T) \quad \text{(long)}, \qquad F_0(T) - S_T \quad \text{(short)}

Quick example

Forward agreed at 1,250 and spot ends at 1,190. Long: 1,190 − 1,250 = −60. Short: +60.

On your calculator

1190−1250= -60

1190ENTER1250− -60

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

Value during the life, long position

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

Quick example

Forward agreed at 46.00, spot now 44.50, r = 5%, 0.4 years left. PV of the forward price = 46 × 1.05^−0.4 = 45.11. Value = 44.50 − 45.11 = −0.61.

On your calculator

1.05y^x0.4+|-=×46= 45.11
+|-+44.5= -0.61

y^x power · +|- change sign

1.05ENTER0.4CHSy^x46× 45.11
CHS44.5+ -0.61

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

Value during the life, short position

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

Quick example

Same contract from the short side: 45.11 − 44.50 = +0.61. The short gains exactly what the long loses.

On your calculator

1.05y^x0.4+|-=×46−44.5= 0.61

y^x power · +|- change sign

1.05ENTER0.4CHSy^x46×44.5− 0.61

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

How it is asked

Value of the long partway through

Forward agreed at 74.00, one year; after three months spot is 75.60 and r = 3%. Long value?

75.60 − 74.00 × 1.03^−0.75 = 3.22. Traps: 1.60 (no discounting), 3.76 (discounted over the full year).
Value of the short

Short forward at 320, six months left, spot 312, r = 3%.

320 × 1.03^−0.5 − 312 = 3.31. Trap: the long's sign (−3.31).
Price and value at initiation

Which is zero at initiation, the price or the value?

Value is zero; the price is set by no arbitrage. Trap: saying the price is zero.
Interest rates rise, spot unchanged

What happens to the long and the short?

PV of F₀ falls, so the long gains, the short loses.

Exam traps

Discounting the forward price over the full term T instead of the remaining time T − t.
Using S_t − F₀(T) during the life. That is the expiration formula; before expiry the forward price must be discounted.
Saying the forward price changes after initiation. It is fixed; only the value moves.
Sign errors for the short. The short's value is the long's value with the sign flipped.

Checkpoint

5 exam-style questions. About 90 seconds each.

1A one-year forward was agreed at F₀(T) = CHF 62.00. Three months later the spot price is CHF 63.10 and the risk-free rate is 4%. The asset pays no income and has no costs. The value of the long position is closest to:
2A trader is short a forward agreed at F₀(T) = 500 with six months to expiration. The spot price is 485 and the risk-free rate is 2%. The asset pays no income and has no costs. The value of the short position is closest to:
3At initiation of a forward contract, the forward price and the forward value are best described as:
4A portfolio manager is long a forward on an asset with no income or costs. Two months into the contract the spot price has not moved, but the risk-free rate rises by one percentage point. Compared with just before the rate change, the mark-to-market value of the long position has most likely:
5A trader is short a forward agreed at F₀(T) = 840. At expiration the spot price is 872. The value of the short position at expiration is closest to:

Key takeaways

The forward price is fixed at initiation; the value starts at zero and moves with the spot price, time and interest rates.
Long value during the life = S_t minus the present value of F₀(T) over the remaining time T − t. The short is the negative.
At expiration the value is the settlement amount: S_T − F₀(T) for the long.
If rates rise with the spot price unchanged, the present value of the forward price falls: the long gains and the short loses.

Forward price, no income or costs

F_0(T) = S_0(1 + r)^T

Quick example

A share trades at 80 and r = 3%. The nine-month forward price is 80 × 1.03^0.75 = 81.79.

On your calculator

1.03y^x0.75=×80= 81.7933

y^x power

1.03ENTER0.75y^x80× 81.7933

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

Value at initiation

V_0(T) = 0

Quick example

Entering a forward at the no-arbitrage price costs nothing and is worth zero to both sides.

Value at expiration

V_T(T) = S_T - F_0(T) \quad \text{(long)}, \qquad F_0(T) - S_T \quad \text{(short)}

Quick example

Forward agreed at 1,250 and spot ends at 1,190. Long: 1,190 − 1,250 = −60. Short: +60.

On your calculator

1190−1250= -60

1190ENTER1250− -60

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

Value during the life, long position

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

Quick example

Forward agreed at 46.00, spot now 44.50, r = 5%, 0.4 years left. PV of the forward price = 46 × 1.05^−0.4 = 45.11. Value = 44.50 − 45.11 = −0.61.

On your calculator

1.05y^x0.4+|-=×46= 45.11
+|-+44.5= -0.61

y^x power · +|- change sign

1.05ENTER0.4CHSy^x46× 45.11
CHS44.5+ -0.61

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

Value during the life, short position

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

Quick example

Same contract from the short side: 45.11 − 44.50 = +0.61. The short gains exactly what the long loses.

On your calculator

1.05y^x0.4+|-=×46−44.5= 0.61

y^x power · +|- change sign

1.05ENTER0.4CHSy^x46×44.5− 0.61

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

All Derivatives formulas, every lesson

Practice exam-style questions on Pricing and Valuing Forward Contracts and FRAs

Next lesson Valuing a forward when the asset pays income or has costs

Questions about this lesson?

Where this comes back

Valuing a forward when the asset pays income or has costs Pricing and Valuing Forward Contracts and FRAs
Pricing and Valuing Futures Contracts Derivatives
Pricing and Valuing Interest Rate Swaps Derivatives

Questions candidates ask

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

The price is the fixed rate for the future exchange, set at initiation so the contract costs nothing. The value is what the contract is worth to a party right now, if it were closed out. The price never changes; the value starts at zero and moves with the spot price, time and interest rates.

How do you value a forward contract before expiration?

For the long, subtract the present value of the forward price from the current spot price: S_t − F₀(T)(1 + r)^−(T−t), where T − t is the time remaining. The short is the negative. If the asset pays income or has costs, adjust the spot price for them first.

Why is a forward contract worth zero at inception?

Because the forward price is set by no arbitrage: it equals the spot price compounded at the risk-free rate (adjusted for carry). At that price neither side expects to gain, so no money changes hands and the value to both parties is zero.

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