Lesson 2 of 3 11–14% of the exam

By Daniil Tarakanov Updated Oct 21, 20262027 curriculum

Money duration and PVBP

Money duration converts modified duration into currency: annualized modified duration times the full price, or the market value of the position. The price value of a basis point (PVBP) is the currency change in price for a 1 bp change in yield.

8 min cram, 30 min full read. Based on the 2027 CFA® Program Level I curriculum, Fixed Income, Learning Module 11. 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: Interest Rate Risk and Return, Bond Valuation: Prices and Yields

On the exam

Define, calculate, and interpret modified duration, money duration, and the price value of a basis point (PVBP)

Define, calculate and interpret money duration and PVBP. Expect: a currency loss on a stated position for a given yield change, and PVBP from two bumped prices. Wrong options use par instead of market value or forget the divide-by-2.

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 money duration?

Modified duration is a percentage, which is awkward for a trader who wants to know how many euros are at stake. Money duration fixes that by multiplying annualized modified duration by the bond’s full price. Per 100 of par it uses the full price per 100. For a position it uses the market value of the holding, never the par amount. In the US the same idea is called dollar duration .

Money duration Memorize

\text{MoneyDur} = \text{AnnModDur} \times PV^{Full}

Multiply money duration by the yield change and you have the estimated change in value, in currency.

Estimated change in value Memorize

\Delta PV^{Full} \approx -\text{MoneyDur} \times \Delta y

InteractiveMoney duration and PVBP: duration in currency

Try this 0 of 3

With the worked example, turn on the par-value comparison
Set the yield change to exactly +1 bp
Find the smallest whole-bp rise that loses at least EUR 100,000

Par value heldEURFull price per 100Modified duration (annual)

Yield change+25 bp

Par value vs market value

Market value (full)EUR 19,016,540

Money durationEUR 95,256,511

Estimated change, +25 bpEUR −238,141

PVBP ≈ BPV (per 1 bp)EUR 9,526

Rise that loses EUR 100,00010.5 bp

A +25 bp move costs about EUR 238,141: 25 × the PVBP of EUR 9,526.

Show working

Market value = par × full price ÷ 100 = 20,000,000 × 95.0827 ÷ 100 = EUR 19,016,540.

Money duration = ModDur × market value = 5.00914 × 19,016,540 = EUR 95,256,511. Per 100 of par: 5.00914 × 95.0827 = 476.28.

Estimated change = −money duration × ΔYield = −95,256,511 × 0.0025 = EUR −238,141.

Basis point value = money duration × 0.0001 = EUR 9,526 per bp (per 100 of par: 0.04763). The PVBP, found by repricing as (PV₋ − PV₊) ÷ 2 at ±1 bp, is almost exactly the same figure (the tiny gap is convexity).

Loss budget: 100,000 ÷ 9,525.65 = 10.50 bp.

Market value, money duration and the change

20000000×95.0827÷100=19,016,540.00, market value
×5.00914=95,256,511.18, money duration
×0.0025=238,141.28, the estimated loss

20000000ENTER95.0827×100÷19,016,540.00, market value
5.00914×95,256,511.18, money duration
0.0025×238,141.28, the estimated loss

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

PVBP and the loss budget

95256511.18×0.0001=9,525.65, PVBP
100000÷9525.65=10.50 bp

95256511.18ENTER0.0001×9,525.65, PVBP
100000ENTER9525.65÷10.50 bp

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

Money duration is modified duration with a currency sign on it; PVBP is the same thing for one basis point.

Worked example Bond K per 100 of par, and on a EUR 20 million position

Bond K (6 years, 5% annual coupon, 6% yield) has a full price of 95.0827 and an annualized modified duration of 5.009.

Per 100 of par. Money duration = 5.009 × 95.0827 = 476.28. For a 25 bp rise, the change in present value (ΔPV) ≈ −476.28 × 0.0025 = −1.191 per 100 of par.

On a position. An investor holds EUR 20,000,000 of par. The market value is 20,000,000 × 0.950827 = EUR 19,016,540. With the unrounded duration 5.00914, money duration = 5.00914 × 19,016,540 = EUR 95,256,511. A 25 bp rise gives an estimated loss of 95,256,511 × 0.0025 = EUR 238,141.

Using par instead of market value would overstate the exposure by about 5%: the exam sets that as a wrong option.

The position, step by step

20000000×0.950827= 19,016,540
×5.00914= 95,256,511
×0.0025= 238,141, the estimated loss

20000000ENTER0.950827× 19,016,540
5.00914× 95,256,511
0.0025× 238,141, the estimated loss

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

Rearrange itMoney duration: solve for any input

The question asks for

A position has a market value of 19,016,540.00 and an annualized modified duration of 5.00914. Its money duration is closest to:

Annualized modified durationFull price or position market value

MoneyDur = AnnModDur \times P V^{F u l l}

5.00914 × 19,016,540.00 = 95,256,511.18

Money duration95,256,511.18

On your calculator

5.00914×19016540=

5.00914ENTER19016540×

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

Rearrange itCurrency change from money duration: solve for any input

The question asks for

A position has a money duration of 95,256,511.00. If the yield changes by +25 bp, the estimated change in its value is closest to:

Money durationYield change (basis points)

Δ P V^{F u l l} \approx - MoneyDur \times Δ y

−95,256,511.00 × 0.0025 = -238,141.28

Estimated change in value-238,141.28

On your calculator

95256511×0.0025=+|-

+|- change sign

95256511ENTER0.0025×CHS

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Exam tip The yield change goes in as a decimal and the value in as market value. Check both before you multiply.

What is the price value of a basis point?

The price value of a basis point (PVBP) is the change in a bond’s full price for a 1 bp change in yield. Instead of using a duration figure, you reprice the bond a basis point down and a basis point up, take the difference and halve it.

Price value of a basis point Memorize

PVBP = \frac{PV_- - PV_+}{2}

$PV_-$ and $PV_+$ are the full prices at a yield 1 bp lower and 1 bp higher. Halving is needed because the two prices lie 2 bp apart; you want the change for one. PVBP is a price in currency per 100 of par, not a percentage. It is also called PV01, and in the US DV01 .

Worked example Bond K's PVBP, and what it means for EUR 20 million

At a yield of 5.99% the full price is 95.13032. At 6.01% it is 95.03506.

PVBP = (95.13032 − 95.03506) ÷ 2 = 0.09526 ÷ 2 = 0.04763 per 100 of par.

For the EUR 20 million position, 0.04763% of the par amount is 0.0004763 × 20,000,000 = EUR 9,526 per basis point. At that rate a loss of EUR 100,000 takes about 10.5 bp.

Reprice, subtract, halve

2NDCLR TVM with P/Y set to 1
6N
5PMT
100FV
5.99I/Y
CPTPV −95.13032
6.01I/Y
CPTPV −95.03506
95.13032−95.03506=÷2= 0.04763
×200000= 9,526 for EUR 20 million of par

2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · PMT payment · FV future value · I/Y interest rate per year (per period when P/Y is 1) · CPT compute · PV present value

fCLEAR FIN
6n
5PMT
100FV
5.99i
PV −95.13032
6.01i
PV −95.03506
95.13032ENTER95.03506−2÷ 0.04763
200000× 9,526 for EUR 20 million of par

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · PMT payment · FV future value · i interest rate per period · PV present value · ENTER enter (on the HP, puts the number on the stack)

Rearrange itPrice value of a basis point: solve for any input

The question asks for

A bond's full price is 95.13032 at a yield 1 bp lower and 95.03506 at a yield 1 bp higher. Its PVBP per 100 of par is closest to:

Full price at yield − 1 bp, PV₋Full price at yield + 1 bp, PV₊

P V B P = \frac{P V _{-} - P V _{+}}{2}

(95.13032 − 95.03506) ÷ 2 = 0.04763

PVBP (per 100 of par)0.0476

On your calculator

95.13032−95.03506=÷2=

95.13032ENTER95.03506−2÷

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

The same number is available from duration. The basis point value (BPV) is money duration times one basis point, 0.0001.

Basis point value Use it

BPV = \text{MoneyDur} \times 0.0001

For Bond K, 476.28 × 0.0001 = 0.04763, the same figure as the repricing method, reached from duration instead.

Rearrange itBasis point value from money duration: solve for any input

The question asks for

A bond has a money duration of 476.28. Its basis point value is closest to:

Money duration (per 100 of par or for the position)

B P V = MoneyDur \times 0.0001

476.28 × 0.0001 = 0.047628

Basis point value (same unit)0.0476

On your calculator

476.28×0.0001=

476.28ENTER0.0001×

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

Go deeper Why repricing and BPV differ slightly, and how traders use PVBP

Repricing at ±1 bp averages the gain and the loss, which cancels most of the curvature, so it differs from the duration-based BPV only far out in the decimals. For large moves the difference is convexity, covered in the next module.

PVBP is additive across positions: the money values simply add, whereas percentage durations need weights. That is why desks quote risk in PVBP or DV01. To hedge, a trader sizes an offsetting futures position so that its DV01 equals the bond position’s DV01. See the Derivatives topic for the contracts. PVBP by repricing also works for bonds whose cash flows change with yields, because it only needs two prices.

How do the four yield duration measures compare?

Which yield duration measure answers which question

Yield duration measuresall assume certain cash flows and a move in the bond’s own yield

Macaulay duration Memorize a time in years: the horizon where price and reinvestment risk offset
Modified duration Memorize a percentage: % price change for a yield change
Money duration Memorize a currency amount for the position, per unit of yield
PVBP Memorize a currency amount per 1 bp, found by repricing

Measure	What it is	Answers
Macaulay duration	PV-weighted average time to cash flows, in years	The horizon at which price and reinvestment risk offset
Modified duration	Macaulay ÷ (1 + r per period)	The % price change for a yield change
Money duration	ModDur × full price or position value	The currency change for a yield change
PVBP	(PV₋ − PV₊) ÷ 2 at ±1 bp	The currency change for a 1 bp change

All four assume certain cash flows, a change in the bond’s own yield and an instantaneous move, so that no time passes. Duration measures that drop those assumptions come in later modules.

Memorize this

MemorizeMoney duration and PVBP

Measure	Formula	Unit
Money duration	AnnModDur × full price (or position value)	currency
Value change	−MoneyDur × Δy	currency
PVBP	(PV₋ − PV₊) ÷ 2 at ±1 bp	currency per 100 par
BPV	MoneyDur × 0.0001	currency per bp

Memory hook Money duration is modified duration with a currency sign on it; PVBP is the same thing for one basis point.

Know it cold Always full price or market value, never par. PVBP, PV01 and DV01 are the same idea. PVBP is a price, not a percentage.

Which yield duration measure answers which question

Yield duration measuresall assume certain cash flows and a move in the bond’s own yield

Macaulay duration Memorize a time in years: the horizon where price and reinvestment risk offset
Modified duration Memorize a percentage: % price change for a yield change
Money duration Memorize a currency amount for the position, per unit of yield
PVBP Memorize a currency amount per 1 bp, found by repricing

Money duration

\text{MoneyDur} = \text{AnnModDur} \times PV^{Full}

Quick example

A holding of USD 10,000,000 par is priced at 98.00 (market value 9,800,000) with an annualized modified duration of 6.10. Money duration = 6.10 × 9,800,000 = USD 59,780,000.

On your calculator

10000000×0.98×6.1= 59,780,000

10000000ENTER0.98×6.1× 59,780,000

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

Estimated change in value

\Delta PV^{Full} \approx -\text{MoneyDur} \times \Delta y

Quick example

The same position, with a money duration of 59,780,000, and a yield rise of 15 bp: −59,780,000 × 0.0015 = −USD 89,670.

On your calculator

59780000×0.0015=+|- −89,670

+|- change sign

59780000ENTER0.0015×CHS −89,670

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Price value of a basis point

PVBP = \dfrac{PV_- - PV_+}{2}

Quick example

A bond is priced at 100.0562 at a yield 1 bp lower and 99.9438 at a yield 1 bp higher. (100.0562 − 99.9438) ÷ 2 = 0.0562 per 100 of par.

On your calculator

100.0562−99.9438=÷2= 0.0562

100.0562ENTER99.9438−2÷ 0.0562

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

Basis point value

BPV = \text{MoneyDur} \times 0.0001

Quick example

A position has a money duration of 59,780,000. Its basis point value is 59,780,000 × 0.0001 = USD 5,978 per basis point.

On your calculator

59780000×0.0001= 5,978

59780000ENTER0.0001× 5,978

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

How it is asked

Currency loss on a position

CAD 4,000,000 par, full price 102.40, AnnModDur 6.30, yield +25 bp. Estimated loss?

Market value 4,096,000 × 6.30 = 25,804,800; × 0.0025 = CAD 64,512. Par instead of market value gives 63,000.
PVBP from two bumped prices

Full price 96.15; 96.2087 at −1 bp, 96.0913 at +1 bp.

(96.2087 − 96.0913) ÷ 2 = 0.0587. Forgetting the 2 gives 0.1174.
Which measure gives a currency change?

Macaulay, modified, money duration or PVBP?

Money duration (per unit of yield) or PVBP (per bp). Modified duration is a percentage.

Exam traps

Multiplying by par value instead of the market (full) value.
Using the flat price instead of the full price.
Forgetting to divide by 2 in PVBP.
Treating PVBP as a percentage. It is a price, in currency per 100 of par.

Checkpoint

4 exam-style questions. About 90 seconds each.

1An investor holds GBP 5,000,000 par of a bond with a full price of 104.50 and an annualized modified duration of 7.20. If the yield rises by 20 bp, the estimated loss is closest to:
2A bond's full price is 101.20. At a yield 1 bp lower it is 101.2468; at a yield 1 bp higher it is 101.1532. Its PVBP per 100 of par is closest to:
3Which measure most directly tells a portfolio manager the change in a position's value in currency for a given change in yield?
4An investor holds CHF 8,000,000 par of a bond with a full price of 97.25 and an annualized modified duration of 4.10. If the yield rises by 40 bp, the estimated loss in value is closest to:

Key takeaways

Money duration = AnnModDur × full price (or market value).
ΔValue ≈ −MoneyDur × ΔYield, with the yield change as a decimal.
PVBP = (PV₋ − PV₊) ÷ 2 at ±1 bp, and it is almost exactly money duration × 0.0001.
Always market value, never par.

Money duration

\text{MoneyDur} = \text{AnnModDur} \times PV^{Full}

Quick example

A holding of USD 10,000,000 par is priced at 98.00 (market value 9,800,000) with an annualized modified duration of 6.10. Money duration = 6.10 × 9,800,000 = USD 59,780,000.

On your calculator

10000000×0.98×6.1= 59,780,000

10000000ENTER0.98×6.1× 59,780,000

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

Estimated change in value

\Delta PV^{Full} \approx -\text{MoneyDur} \times \Delta y

Quick example

The same position, with a money duration of 59,780,000, and a yield rise of 15 bp: −59,780,000 × 0.0015 = −USD 89,670.

On your calculator

59780000×0.0015=+|- −89,670

+|- change sign

59780000ENTER0.0015×CHS −89,670

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Price value of a basis point

PVBP = \dfrac{PV_- - PV_+}{2}

Quick example

A bond is priced at 100.0562 at a yield 1 bp lower and 99.9438 at a yield 1 bp higher. (100.0562 − 99.9438) ÷ 2 = 0.0562 per 100 of par.

On your calculator

100.0562−99.9438=÷2= 0.0562

100.0562ENTER99.9438−2÷ 0.0562

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

Basis point value

BPV = \text{MoneyDur} \times 0.0001

Quick example

A position has a money duration of 59,780,000. Its basis point value is 59,780,000 × 0.0001 = USD 5,978 per basis point.

On your calculator

59780000×0.0001= 5,978

59780000ENTER0.0001× 5,978

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

All Fixed Income formulas, every lesson

Practice exam-style questions on Modified Duration, Money Duration and PVBP

Next lesson What makes duration higher or lower

Questions about this lesson?

Where this comes back

Convexity and Portfolio Duration Fixed Income
Effective Duration, Key Rate Duration and Empirical Duration Fixed Income
Credit Risk Fixed Income
Introduction to Risk Management Portfolio Construction
Pricing and Valuing Interest Rate Swaps Derivatives

Questions candidates ask

What is money duration?

Modified duration multiplied by the bond's full price or the position's market value. It estimates the currency change in value for a change in yield. In the US it is often called dollar duration.

Is PVBP the same as DV01?

Yes. PVBP, PV01 and DV01 all mean the price change for a 1 bp change in yield.

How do you calculate PVBP?

Reprice the bond at a yield 1 bp lower and 1 bp higher, subtract the second price from the first, and divide by 2.

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