FRM Exam Part II · Regression Hedging and Principal Component Analysis

DV01 and Duration-Based Hedging Explained

Updated 11 October 2026 · Fact-checked

DV01 is the price change of a bond for a one basis point fall or rise in yield. To hedge, you take an opposite position in a hedging instrument so total DV01 is zero: hedge face value = position DV01 ÷ hedge DV01 per unit of face value. It works only for parallel yield shifts.

Understand DV01 and Duration-Based Hedging

Bond prices fall when yields rise. DV01 (dollar value of a basis point) measures how much. It is the change in price, in currency units, when the yield moves by 0.01%. A bond with a DV01 of $850 loses about $850 if its yield rises by one basis point, and gains about the same if it falls.

DV01 is linked to modified duration. Modified duration is a percentage measure: the percentage price change for a 1% (100 basis point) change in yield. DV01 is a currency measure. So DV01 ≈ modified duration × price × 0.0001. Duration says how sensitive the price is in percent. DV01 says how many dollars or rupees are at stake.

Hedging uses this. If you hold a bond portfolio with a DV01 of $50,000, you want a hedge that gains $50,000 per basis point when yields rise. Short a bond, a bond future or a swap fixed-leg position with that DV01. The net DV01 is then zero, so small parallel yield moves leave the total value almost unchanged.

The hedge rests on one assumption: all yields move by the same amount (a parallel shift) and only by a small amount. If the curve steepens or twists, or yields move a lot, the hedge leaks. Convexity is ignored too. Positions with different maturities react differently to curve changes, so a single-factor hedge leaves curve risk. Regression hedging and PCA hedging address this by using more realistic yield-change patterns.

The hedge must also be rebalanced. DV01 changes as yields move and as time passes, so a hedge that is neutral today will drift.

Key formulas to remember

DV01 from price: DV01 = −(P(y + 0.0001) − P(y − 0.0001)) ÷ 2; Central difference is the usual numerical definition. A simple version uses the price change for a 1 bp move.
DV01 from modified duration: DV01 ≈ ModD × P × 0.0001; P is the full (dirty) price of the position in currency. ModD is modified duration in years.
Modified duration: ModD = Macaulay duration ÷ (1 + y ÷ m); m is compounding periods per year. Use y ÷ m for the periodic yield.
DV01 hedge ratio (face value): Hedge face value = (DV01 of position ÷ DV01 of hedge per 100 face) × 100; The hedge is taken in the opposite direction to the position.
Hedge units: N = DV01 position ÷ DV01 per unit of hedge instrument; For futures, use DV01 per contract (often the cheapest-to-deliver DV01 divided by its conversion factor).
Duration-based hedge: Hedge value = Position value × ModD position ÷ ModD hedge; Equivalent to DV01 matching when the position and hedge are priced and compared on the same basis.
Price change estimate: ΔP ≈ −DV01 × Δy (in bp); Valid for small parallel moves. Ignores convexity.

How to solve DV01 and Duration-Based Hedging questions

Use this sequence for any DV01 or duration hedging question.

1Identify the position and the hedge instrument, and whether you must hedge a gain or a loss from rising yields.
2Find the DV01 of the position. Use the given DV01, or compute ModD × price × 0.0001.
3Find the DV01 of the hedge instrument on the same unit basis (per 100 face, per contract, per ₹ or $ of notional).
4Divide position DV01 by hedge DV01 per unit to get the number of units or face value.
5Set the direction: long bonds are hedged by shorting; the hedge DV01 must offset the position DV01.
6Check net DV01 equals zero, then estimate the P&L for the stated yield move using −DV01 × Δy.
7State the limit: the hedge works for small parallel shifts only; curve and convexity risk remain.

Quickest way: Match dollars per basis point

When to use it: Use when the question gives prices and durations and asks for a hedge amount or number of contracts.

Convert each duration into DV01 per unit: ModD × price ÷ 10,000 (price per 100 face, or per contract).
Divide position DV01 by hedge DV01 per unit. That is your hedge size.
Scan the options: the sign (short or long) and the order of magnitude usually remove two wrong answers.
If duration is given as Macaulay, divide by (1 + y ÷ m) first.

Common mistakes in DV01 and Duration-Based Hedging

Using Macaulay duration instead of modified duration in the DV01 formula.
Both are called duration and the question may give only Macaulay.
Fix: Convert first: ModD = Macaulay ÷ (1 + y ÷ m). Then compute DV01.
Hedging with equal face values rather than equal DV01.
It feels natural to match size.
Fix: A 10-year bond has a larger DV01 than a 2-year bond of the same face value. Always match DV01.
Forgetting to scale DV01 by 0.0001 or by position size.
Quoted duration is a per-unit number and the price is often per 100.
Fix: Write DV01 = ModD × market value × 0.0001 and check units before dividing.
Taking the hedge in the wrong direction.
Students focus on the number and skip the sign.
Fix: A long bond loses when yields rise, so you short the hedge instrument. Check that net DV01 is zero.
Claiming the hedge removes all interest rate risk.
Zero net DV01 sounds like zero risk.
Fix: It removes only first-order risk to a parallel shift. Slope, curvature, convexity and basis risk remain.
Mixing up DV01 and duration units.
One is a percentage per 1% move, the other currency per 1 bp.
Fix: Duration is in years (percent per 100 bp). DV01 is in currency per bp.

Worked examples

Example 1

A bank holds a $20 million market value bond position with modified duration 6.5. It hedges with a Treasury bond priced at $98 per 100 face with modified duration 8.0. What face value of the hedge bond must be shorted for a DV01-neutral position, and what is the position DV01?

Show the solution

Position DV01 = 6.5 × 20,000,000 × 0.0001 = $13,000.
Hedge DV01 per 100 face = 8.0 × 98 × 0.0001 = 0.0784, i.e. $0.0784 per 100 face.
Hedge face = 13,000 ÷ 0.0784 × 100 = 16,581,633 (approx.).
Check: 16,581,633 ÷ 100 × 0.0784 = $13,000. Net DV01 = 0 once the hedge is short.

Answer: Short about $16.58 million face of the hedge bond. The position DV01 is $13,000.

Example 2

A portfolio has a DV01 of ₹4,80,000. A hedge instrument has a DV01 of ₹6,000 per contract. Yields rise by 5 bp in parallel. How many contracts hedge the portfolio, and what is the unhedged portfolio loss for the move?

Show the solution

Number of contracts = 4,80,000 ÷ 6,000 = 80.
Direction: the portfolio is long bonds, so short 80 contracts.
Unhedged loss ≈ DV01 × Δy = 4,80,000 × 5 = ₹24,00,000.
Hedge gain ≈ 80 × 6,000 × 5 = ₹24,00,000, so the net change is about zero.

Answer: Short 80 contracts. The unhedged loss is about ₹24,00,000, offset by the hedge gain.

Exam tips

Read whether the question gives price per 100 or total market value. Many wrong answers come from unit mismatch.
Expect a conceptual MCQ on limits: a DV01 hedge fails for non-parallel shifts, large moves and convexity differences.
Check the direction word (short, long) before you pick an option.
When a question asks for the difference between DV01 and modified duration, answer: DV01 is currency per bp, duration is percent per 100 bp.
For hedged P&L after a non-parallel move, expect residual loss or gain; do not assume zero.

Practice questions from Regression Hedging and Principal Component Analysis

DV01 and Duration-Based Hedging in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

FRM Part IPortfolio Duration and Hedging with DV01

DV01 and Duration-Based Hedging: frequently asked questions

What is the difference between DV01 and modified duration?

Modified duration is the percentage price change for a 1% yield change. DV01 is the currency price change for a 1 bp yield change. They are linked by DV01 ≈ ModD × price × 0.0001.

How do I calculate a DV01 hedge ratio?

Divide the DV01 of the position by the DV01 of the hedge instrument per unit. The result is the number of units or the face value to trade in the opposite direction.

Why does a DV01 hedge fail?

It assumes a small, parallel yield shift. If the curve steepens, flattens or twists, the position and hedge move by different amounts. Large moves also expose convexity differences.

Is DV01 the same as PV01?

They are used almost interchangeably for the price change per basis point. Always check the definition in the question, because a few sources differ on small details such as sign convention.