Skip to content

FRM Exam Part I · Applying Duration, Convexity, and DV01

How to Calculate DV01 and Basis Point Value

Updated 11 October 2026 · Fact-checked

DV01 is the change in a bond's price for a one basis point (0.01%) change in yield. Calculate it as modified duration × price × 0.0001, or reprice the bond at yields 1 bp lower and 1 bp higher and halve the difference. Portfolio DV01 is the sum of position DV01s, with short positions negative.

Understand DV01 and Basis Point Value

A basis point is 0.01%, or 0.0001 in decimal form. DV01 stands for "dollar value of 01". It is the amount a bond's price changes when its yield moves by one basis point. Because bond prices fall when yields rise, DV01 is quoted as a positive number: the size of the loss for a 1 bp rise, or the gain for a 1 bp fall.

DV01 turns duration into money. Modified duration is a percentage sensitivity: it tells you the percentage price change for a 1 percentage point change in yield. DV01 tells you the currency amount for 1 basis point. Two bonds with the same duration can have very different DV01s if one position is much larger.

PVBP (price value of a basis point) and BPV (basis point value) are names for the same idea. In practice you will see them used interchangeably with DV01. Check the question for the unit: DV01 can be given per 100 of face value, per bond, or for the whole position.

Dollar duration is modified duration × price (or market value). It is the price change per 1.00 (100%) change in yield, in currency units. DV01 is dollar duration × 0.0001. So if you know dollar duration, DV01 is one multiplication away.

DV01 is a first-order measure. It is very accurate for a 1 bp move and good for small moves. For large yield changes the bond's convexity matters, and the linear estimate understates the price after a fall in yield and overstates the loss from a rise... more precisely, it understates the price of a plain bond in both directions. For portfolios, adding DV01s assumes all yields move by the same amount, a parallel shift.

Key formulas to remember

DV01 from modified duration
DV01 = Modified duration × Price (or market value) × 0.0001
Use the price that matches the position: per 100 face, per bond, or total market value including accrued interest if the question uses full price.
DV01 from dollar duration
DV01 = Dollar duration × 0.0001, where Dollar duration = Modified duration × Price
Dollar duration is the price change per 100% change in yield, so scale by 0.0001 for 1 bp.
DV01 from repricing (central difference)
DV01 ≈ [P(y − 1 bp) − P(y + 1 bp)] ÷ 2
Use a financial calculator or the question's given prices. This also works for bonds with options when you use effective duration logic.
Modified duration
Modified duration = Macaulay duration ÷ (1 + y/k)
y is the annual yield and k is the number of compounding periods per year.
Price change estimate
ΔP ≈ −DV01 × (Δy in basis points)
Valid for small yield changes. Add a convexity term for large moves.
Portfolio DV01
DV01(portfolio) = Σ DV01 of each position
Long positions are positive and short positions are negative. Assumes a parallel yield shift.
DV01 hedge ratio
Number of hedge contracts = DV01(position) ÷ DV01 per hedge contract
Take the opposite side of the position to neutralise the net DV01.

How to solve DV01 and Basis Point Value questions

Use this order for any DV01 or basis point value question. It keeps units and signs under control.

  1. 1Identify what the question wants: DV01 per 100 face, per bond, for a position, or for a portfolio. Note the unit.
  2. 2Find the inputs given: modified duration, Macaulay duration with yield and compounding, dollar duration, or bond prices at different yields.
  3. 3If you have Macaulay duration, convert to modified duration by dividing by (1 + y/k).
  4. 4Compute DV01 = modified duration × price or market value × 0.0001. If prices at y − 1 bp and y + 1 bp are given, use half the difference instead.
  5. 5For a portfolio, calculate each position's DV01 separately. Make shorts negative, then add them up.
  6. 6If asked for a price change, multiply DV01 by the yield change in basis points and attach the sign: yields up means value down.
  7. 7If asked for a hedge, divide the position DV01 by the hedge instrument's DV01 and take the opposite position.
  8. 8Sanity check: is the answer the right order of magnitude? For a bond, DV01 per 100 face is roughly duration ÷ 100 of price, about 0.01 to 0.1 for typical bonds.

Quickest way: Duration × Value ÷ 10,000

When to use it: Use when the question gives modified duration and a price or market value. This is the usual exam case.

  1. Multiply modified duration by market value.
  2. Divide by 10,000 (the same as multiplying by 0.0001).
  3. For a portfolio, do this for each position, sign shorts negative, and add.
  4. For price change, multiply DV01 by the number of basis points. Mentally attach a minus sign for a yield rise.
  5. Quick check per 100 face: a bond priced at 100 with modified duration 5 has a DV01 of 0.05.

Common mistakes in DV01 and Basis Point Value

  • Forgetting the 0.0001 factor and reporting duration × price as DV01.

    Duration × price is dollar duration, which looks like a finished answer. The unit is per 100% yield move, not per 1 bp.

    Fix: Always divide dollar duration by 10,000 to reach DV01. Check that the answer is small relative to the position value.

  • Using Macaulay duration instead of modified duration.

    Both are called duration and the question may give Macaulay duration first.

    Fix: Convert first: modified duration = Macaulay duration ÷ (1 + y/k). Use the right k for the compounding stated.

  • Adding short and long DV01s as if they were all positive.

    DV01 is quoted as a positive magnitude, so students forget that a short position loses value when yields fall.

    Fix: Assign the sign by position: long is positive, short is negative. Sum the signed values to get net DV01.

  • Mixing units: DV01 per 100 face versus DV01 for the whole holding.

    Quotes on price sheets are per 100 of face, but the exposure is on a large notional.

    Fix: Write down the base. Scale per-100 DV01 by face ÷ 100 to get the position DV01.

  • Using DV01 to estimate a large yield move and ignoring convexity.

    DV01 is easy, so it gets applied to 100 bp moves.

    Fix: Use DV01 for small moves. For large moves add the convexity adjustment, which raises the price estimate for a plain bond.

  • Adding portfolio DV01s when yields do not move in parallel.

    The summation rule is taught without its assumption.

    Fix: State that portfolio DV01 assumes the same yield change for every position. For non-parallel shifts, use key rate exposures.

Worked examples

Example 1

A bond position has a market value of $5,000,000 and a modified duration of 4.2. What is its DV01? A) $210 B) $2,100 C) $4,200 D) $21,000

Show the solution
  1. Formula: DV01 = modified duration × market value × 0.0001.
  2. Substitute: 4.2 × 5,000,000 × 0.0001.
  3. 4.2 × 5,000,000 = 21,000,000. Multiplying by 0.0001 gives 2,100.
  4. Check: dollar duration is 21,000,000. Dividing by 10,000 gives 2,100, which is option B.
  5. Interpretation: a 1 bp rise in yield cuts the position's value by about $2,100.

Answer: B) $2,100

Example 2

A portfolio holds: Bond A, long, market value $10,000,000, modified duration 3.0; Bond B, long, market value $6,000,000, modified duration 7.5; Bond C, short, market value $4,000,000, modified duration 5.0. (a) Find the portfolio DV01. (b) Estimate the change in value if yields rise by 12 bp in parallel. (c) How many futures contracts, each with DV01 of $55, hedge the position?

Show the solution
  1. Bond A DV01 = 3.0 × 10,000,000 × 0.0001 = $3,000.
  2. Bond B DV01 = 7.5 × 6,000,000 × 0.0001 = $4,500.
  3. Bond C DV01 = 5.0 × 4,000,000 × 0.0001 = $2,000. It is short, so its contribution is −$2,000.
  4. (a) Portfolio DV01 = 3,000 + 4,500 − 2,000 = $5,500.
  5. (b) Value change ≈ −DV01 × 12 = −5,500 × 12 = −$66,000.
  6. (c) The portfolio loses value when yields rise, so the hedge must gain when yields rise: sell futures. Number = 5,500 ÷ 55 = 100 contracts.

Answer: (a) $5,500; (b) a fall of about $66,000; (c) sell 100 futures contracts.

Exam tips

  • Read the unit carefully. Options often include the same number scaled by 100, 10,000 or per-100-face versus total, so the unit decides the answer.
  • Memorise DV01 = modified duration × value × 0.0001 and do the arithmetic as ÷ 10,000. It is fast and rarely wrong.
  • Watch for Macaulay duration with a yield and compounding frequency. It signals that you need a conversion step first.
  • For portfolios, write each position's signed DV01 in a column before summing. This avoids lost marks on shorts.
  • If the question gives prices at y − 1 bp and y + 1 bp, use half the difference and skip duration. The average removes most convexity bias.

Practice questions from Applying Duration, Convexity, and DV01

DV01 and Basis Point Value: frequently asked questions

What is the DV01 formula for the FRM Part I exam?

DV01 = modified duration × price (or market value) × 0.0001. You can also estimate it as half the difference between the bond's price at a yield 1 bp lower and 1 bp higher. Both give the price change for a 1 bp yield move.

Are DV01, PVBP and BPV the same thing?

In practice yes. They all measure the price change for a one basis point change in yield. Always check whether the figure is per 100 face, per bond or for the whole position.

How is dollar duration related to DV01?

Dollar duration is modified duration × price and measures price change per 100% change in yield. DV01 equals dollar duration × 0.0001. Dollar duration is therefore 10,000 times DV01.

How do I calculate the DV01 of a portfolio?

Calculate the DV01 of each position, make short positions negative, and add them. This assumes all yields shift by the same amount. If the curve changes shape, use key rate exposures instead.