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CFA Level I Exam · Yield-Based Bond Convexity and Portfolio Properties

Money Duration and Price Value of a Basis Point

Updated 7 October 2026 · Fact-checked

Money duration is modified duration multiplied by the bond's full price, so it shows the approximate currency change in price per 100% change in yield. PVBP is money duration × 0.0001, the approximate currency price change for a 1 basis point yield change. Compute them from modified duration and price.

Understand Money Duration and Price Value of a Basis Point

Duration measures tell you the percentage price change for a yield change. But a portfolio manager often wants the answer in currency: how many dollars do I gain or lose if yields move? Money duration answers this.

Money duration = annual modified duration × full price of the bond (including accrued interest). It is the approximate currency price change for a 100% (1.00) change in yield. That is a huge move, so it is rarely used directly. You scale it down.

The price value of a basis point (PVBP), also called BPV or DV01, is the currency price change when the yield changes by one basis point (0.01%). It equals money duration × 0.0001. You can also compute it exactly: price at yield minus 1 bp, minus price at yield plus 1 bp, divided by 2.

Both measures are positions in currency terms, so they depend on the size of the holding. A bond with the same modified duration but a higher price, or a bigger par amount held, has a larger money duration. Modified duration is a percentage measure and ignores size.

Like duration, these are linear estimates. For large yield changes they are less accurate because they ignore convexity. A bond price falls when yield rises, so the sign of the change is opposite to the yield move.

Key formulas to remember

Money duration
MoneyDur = ModDur × Full price (PV^Full)
Use the full price, with accrued interest, and the position size you are asked about (for example, price per 100 par times par amount ÷ 100).
Price value of a basis point
PVBP = MoneyDur × 0.0001
Same as approximate currency change for a 1 bp yield move. Quoted as a positive number.
Exact PVBP
PVBP = (PV₋ − PV₊) ÷ 2
PV₋ is the price with yield down 1 bp, PV₊ with yield up 1 bp.
Estimated currency price change
ΔPV ≈ −MoneyDur × Δyield
Δyield in decimals (0.0050 for 50 bps). Add a convexity term for large moves.
Modified duration link
ModDur = MacDur ÷ (1 + y/m)
y is the annual yield, m is the periods per year. Needed when the question gives Macaulay duration.

How to solve Money Duration and Price Value of a Basis Point questions

Use this sequence for any question on money duration or PVBP.

  1. 1Identify what you are given: modified duration, Macaulay duration, or prices at shifted yields.
  2. 2If you have Macaulay duration, convert it to modified duration by dividing by (1 + y/m).
  3. 3Find the full price of the position in currency, including accrued interest and the amount held.
  4. 4Money duration = modified duration × full price.
  5. 5PVBP = money duration × 0.0001, or use (PV₋ − PV₊) ÷ 2 if prices are given.
  6. 6For a yield change Δy, multiply: price change ≈ −money duration × Δy (convert bps to decimals).
  7. 7Check the sign: yields up means price down. Then compare the answer with the three options, which are ordered smallest to largest.

Quickest way: Shortcut: PVBP from price and duration

When to use it: When the question gives modified duration and price and asks for the change per basis point or for a small yield move.

  1. Multiply price × modified duration × 0.0001 to get PVBP.
  2. For a move of n bps, multiply PVBP by n.
  3. Give the direction: down if yield rises, up if yield falls.
  4. Eliminate options with the wrong sign or off by a factor of 100 or 10,000.

Common mistakes in Money Duration and Price Value of a Basis Point

  • Using clean price instead of full price

    Quoted prices are usually clean, and students forget accrued interest.

    Fix: Add accrued interest whenever the question gives it. Money duration is based on the full price.

  • Forgetting to multiply by 0.0001 for PVBP

    Money duration is often mistaken for the answer, but it refers to a 100% yield change.

    Fix: Always scale: PVBP = money duration × 0.0001.

  • Plugging in Macaulay duration directly

    Both are called duration and look similar.

    Fix: Divide Macaulay duration by (1 + y/m) first to get modified duration.

  • Ignoring the position size

    Students compute on a price per 100 par and stop.

    Fix: Multiply by par amount ÷ 100 when the holding is larger, such as a €5 million position.

  • Getting the sign wrong

    PVBP is quoted as a positive number, but price changes are negative when yields rise.

    Fix: State the direction: a yield increase lowers price, a decrease raises it.

Worked examples

Example 1

A bond has a modified duration of 6.50 and a full price of $104.20 per $100 par. An investor holds $2,000,000 par. Estimate the PVBP of the position.

Show the solution
  1. Position full value = 104.20 ÷ 100 × 2,000,000 = $2,084,000.
  2. Money duration = 6.50 × 2,084,000 = $13,546,000.
  3. PVBP = 13,546,000 × 0.0001 = $1,354.60.

Answer: PVBP ≈ $1,354.60 per basis point.

Example 2

A bond has a Macaulay duration of 7.20, a yield of 4.00% with semiannual compounding, and a full price of €98.00 per €100 par. Estimate the price change per €100 par if the yield rises by 25 bps.

Show the solution
  1. Modified duration = 7.20 ÷ (1 + 0.04/2) = 7.20 ÷ 1.02 = 7.0588.
  2. Money duration = 7.0588 × 98.00 = 691.76.
  3. Δyield = 0.0025.
  4. Price change ≈ −691.76 × 0.0025 = −1.7294.

Answer: The price falls by about €1.73 per €100 par.

Exam tips

  • Check whether the question gives modified or Macaulay duration before calculating.
  • Watch the unit of price: per 100 par or the whole position.
  • Check magnitude: PVBP should be roughly one ten-thousandth of price × duration, so reject options off by powers of ten.
  • On a calculator, store the money duration and multiply by the basis points, which saves time on multi-part items.

Practice questions from Yield-Based Bond Convexity and Portfolio Properties

Money Duration and Price Value of a Basis Point: frequently asked questions

What is the difference between money duration and modified duration?

Modified duration gives the approximate percentage price change for a 1% yield change. Money duration gives the approximate currency change, because it multiplies modified duration by the full price.

Is PVBP the same as DV01 or BPV?

Yes, they all describe the approximate currency price change for a 1 basis point yield change. The CFA curriculum uses PVBP.

Does PVBP use clean or full price?

It is based on full price, which includes accrued interest. Using the clean price understates the figure.

Why is PVBP only an estimate?

The price-yield relationship is curved, and duration is a straight-line approximation. For 1 bp the error is tiny, but for large yield changes you need a convexity adjustment.