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CFA Level I Exam · Interest Rate Risk and Return

Money Duration and Price Value of a Basis Point (PVBP)

Updated 7 October 2026 · Fact-checked

Money duration is a bond's annual modified duration multiplied by its full market value. It estimates the currency price change per unit change in yield. PVBP is money duration × 0.0001, the approximate currency change for a one basis point yield move. Find the position value, multiply by modified duration, then scale by the yield change.

Understand Money Duration and Price Value of a Basis Point

Modified duration is a percentage measure. It tells you that a bond with a modified duration of 6 falls about 6% if its yield rises by 1 percentage point. That is useful for comparing bonds, but a portfolio manager also needs to know how many dollars or euros are at risk.

Money duration converts the percentage measure into currency. You multiply annual modified duration by the full price of the position (flat price plus accrued interest, times the amount held). The result is the approximate currency change in value for a change in yield of 1.00, that is, 100 percentage points. In practice you multiply it by a much smaller yield change.

The price value of a basis point (PVBP) is the currency change in the bond's value when its yield changes by one basis point (0.01%). You can get it two ways. Either multiply money duration by 0.0001, or reprice the bond at a yield 1 bp lower and 1 bp higher and take half the difference. The second method is more exact because it captures some curvature. PVBP is also called basis point value (BPV) or DV01.

Money duration and PVBP are additive across holdings, because they are currency amounts. A portfolio's PVBP is the sum of the PVBPs of its bonds. This makes PVBP the standard tool for sizing hedges: you match the PVBP of the hedge to the PVBP of the position.

These are first-order estimates. They work well for small yield changes and are less accurate for large ones, where convexity matters. For a bond with positive convexity, the duration estimate overstates the loss when yields rise and understates the gain when yields fall.

Key formulas to remember

Money duration (MoneyDur)
MoneyDur = Annual modified duration × Full price of the position
Use the full price (flat price + accrued interest) times the par amount held, divided by 100 if the price is quoted per 100 par. The result is in the currency of the bond.
Approximate price change using money duration
ΔPV ≈ −MoneyDur × Δy
Enter Δy as a decimal (25 bps = 0.0025). The sign is negative: yields up, value down. Add the convexity term for large moves.
PVBP from money duration
PVBP ≈ MoneyDur × 0.0001
This is the currency change for a 1 bp yield change.
PVBP from repricing
PVBP = (PV₋ − PV₊) ÷ 2
PV₋ is the value at yield minus 1 bp, PV₊ at yield plus 1 bp. Do not forget to divide by 2.
Portfolio PVBP
PVBP(portfolio) = Σ PVBP of each holding
PVBP and money duration add across holdings, assuming a parallel yield shift. Modified durations combine as value-weighted averages.

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

Use this sequence for any question on money duration or PVBP. Most errors come from using the wrong price or the wrong yield-change scale.

  1. 1Identify what the question wants: money duration, PVBP, or an estimated price change for a given yield move.
  2. 2Find the market value of the position: full price per 100 par ÷ 100 × par amount held. Use the full price, not the flat price, if accrued interest is given.
  3. 3Identify the duration. If you are given Macaulay duration, convert it first: modified duration = Macaulay duration ÷ (1 + periodic yield).
  4. 4Compute money duration = modified duration × position value.
  5. 5For PVBP, multiply money duration by 0.0001. If the question gives prices at yield ± 1 bp, use (PV₋ − PV₊) ÷ 2 instead.
  6. 6For a price change, convert basis points to decimals (divide by 10,000) and apply ΔPV ≈ −MoneyDur × Δy. Make the sign negative for a yield rise.
  7. 7For a portfolio, calculate each holding's PVBP or money duration and add them.
  8. 8Check the size and sign. A PVBP should be tiny compared with the position value, roughly duration × 0.01% of it.

Quickest way: PVBP as duration × value × 0.0001

When to use it: Use this when the question gives modified duration and a position value. At about 90 seconds per question, it avoids repricing the bond.

  1. Write position value = par × price ÷ 100.
  2. Multiply by modified duration, then by 0.0001. On a BA II Plus, key 6.2 × 5225000 × 0.0001 = to get 3,239.50.
  3. For a price change of x bps, multiply the PVBP by x. This avoids decimal conversion errors.
  4. Eliminate options by magnitude: PVBP must be about duration × value ÷ 10,000, so options that are off by a factor of 10, 100 or 10,000 are wrong.
  5. If prices at ±1 bp are given, subtract, halve, then scale to the par amount.

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

  • Forgetting to divide by 2 when computing PVBP from the two repriced values

    The difference PV₋ − PV₊ covers a 2 bp range, but students read it as a 1 bp move.

    Fix: Remember that PVBP = (PV₋ − PV₊) ÷ 2. The two prices are 1 bp on each side of the starting yield.

  • Using the flat price instead of the full price for money duration

    Quoted prices exclude accrued interest, so they are the numbers students see first.

    Fix: Use the full price (flat + accrued) whenever accrued interest is given. Money duration measures the value you actually hold.

  • Treating money duration as a percentage or leaving it per 100 par

    Students confuse it with modified duration or stop after multiplying by the per-100 price.

    Fix: Scale to the amount actually held. Money duration is in currency, such as USD or EUR, for the whole position.

  • Converting basis points wrongly, such as using 0.25 for 25 bps

    Mixing percent and decimal forms. 25 bps is 0.25% and 0.0025.

    Fix: Divide basis points by 10,000. Or skip decimals and multiply PVBP by the number of basis points.

  • Getting the sign wrong on the price change

    Students quote the magnitude and ignore direction.

    Fix: Bond prices and yields move in opposite directions. ΔPV ≈ −MoneyDur × Δy, so a yield rise gives a negative change.

  • Averaging portfolio PVBP or money duration instead of adding it

    Portfolio duration is a weighted average, so students apply the same idea to currency measures.

    Fix: Currency risk measures add. Sum the PVBPs. Only the percentage measure, modified duration, is weighted by value.

Worked examples

Example 1

An investor holds USD 5,000,000 par value of a bond quoted at a full price of 104.50 per 100 par. Its annual modified duration is 6.20. The approximate PVBP is closest to: A) USD 3,239.50, B) USD 32,395.00, C) USD 32,395,000.

Show the solution
  1. Position value = 5,000,000 × 104.50 ÷ 100 = USD 5,225,000.
  2. Money duration = 6.20 × 5,225,000 = USD 32,395,000.
  3. PVBP = 32,395,000 × 0.0001 = USD 3,239.50.
  4. Option C is the money duration, not the PVBP. Option B is the money duration × 0.001, a decimal-scaling error.

Answer: A) USD 3,239.50. A one basis point rise in yield lowers the position's value by about USD 3,239.50.

Example 2

A bond with USD 20,000,000 par has a price of 102.4560 per 100 par when its yield is 1 bp lower, and 102.3640 when its yield is 1 bp higher. The PVBP of the position is closest to: A) USD 4,600, B) USD 9,200, C) USD 18,400.

Show the solution
  1. Difference per 100 par = 102.4560 − 102.3640 = 0.0920.
  2. Divide by 2 because the two prices are 1 bp either side: 0.0920 ÷ 2 = 0.0460 per 100 par.
  3. Scale to the position: 0.0460 ÷ 100 × 20,000,000 = USD 9,200.
  4. Option C skips the division by 2. Option A halves the answer a second time.

Answer: B) USD 9,200. The implied money duration is 9,200 ÷ 0.0001 = USD 92,000,000, and a 25 bp yield rise would lower the value by about 25 × 9,200 = USD 230,000.

Exam tips

  • Money duration and PVBP questions are usually short calculations. Check the option magnitudes first; wrong options are often off by factors of 10, 100 or 10,000.
  • Read whether the question gives a price per 100 par or the position value. Scale to the position before applying duration.
  • When prices at yield ± 1 bp are given, the answer uses (PV₋ − PV₊) ÷ 2. Options often include the undivided value as a trap.
  • If the question gives Macaulay duration, convert to modified duration before computing money duration.
  • Remember that these are linear estimates. If a question mentions a large yield change or convexity, expect the answer to need a convexity adjustment.

Practice questions from Interest Rate Risk and Return

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

What is the difference between modified duration and money duration?

Modified duration is a percentage sensitivity of price to yield. Money duration is modified duration times the full value of the position, so it is in currency. Use modified duration to compare bonds and money duration to see how much value is at risk.

How do you calculate the PVBP of a bond?

Multiply the bond's money duration by 0.0001. Alternatively, reprice the bond at yields 1 bp lower and 1 bp higher and compute (PV₋ − PV₊) ÷ 2. Scale the result to the par amount you hold.

Is PVBP the same as BPV or DV01?

They refer to the same idea: the currency change in value for a one basis point change in yield. Use the formula in the curriculum, and read the question to see whether it asks per 100 par or for the whole position.

Can you add PVBPs across bonds in a portfolio?

Yes. PVBP is a currency amount, so the portfolio PVBP is the sum of the individual PVBPs. This relies on yields moving in parallel, which is an assumption for the portfolio estimate.