Compare DV01 and effective duration as gauges of price sensitivity, noting how they are alike and how they differ.
The idea
DV01 and effective duration both measure first-order price sensitivity to a small change in yield, and both ignore convexity. They are linked by DV01 = effective duration × price × 0.0001, where the price is the full market value of the position. The difference is the unit. Duration is a percentage sensitivity, quoted in years, so it is independent of position size and lets you compare a cheap bond with an expensive one. DV01 is in currency, so it grows with the position and with price, and DV01s of different positions can simply be added. Two bonds with the same duration have different DV01s if their market values differ, and a bond with a lower duration but a much larger value can carry more DV01. Use duration to compare instruments and DV01 to size hedges and set limits.
Formulas
DV01 from effective duration
DV01 = D × P × 0.0001
- D
- the effective duration
- P
- the full market value of the position, or price per 100 of face
Use market value, not face. Both measures are first-order and ignore convexity.
A practice question
What is the main difference between DV01 and effective duration as measures of price sensitivity?
- DV01 is a currency amount that grows with position size, while duration is a percentage sensitivity independent of size. - correct
- DV01 is a second-order measure and duration is a first-order measure.Why not: Both are first-order measures of price sensitivity; second-order sensitivity is convexity.
- DV01 is stated in years and duration is stated in currency.Why not: Reverses the units: duration is in years (percentage per unit yield) and DV01 is in currency per basis point.
- DV01 applies only to bonds without embedded options, while duration applies to all bonds.Why not: DV01 can be found by repricing for any security; both can handle options when computed by repricing.
Duration = percentage change in price per unit change in yield. DV01 = dollar price change per basis point. They carry the same first-order information in different units.
A harder one
A position has a face value of USD 30 million with a price of 105.20 per 100 of face and an effective duration of 6.8. Its DV01 is closest to:
- USD 20,400Why not: Uses face value instead of market value when converting duration to DV01.
- USD 21,461 - correct
- USD 214,608Why not: Multiplies duration by value and by 0.001, which corresponds to a 10bp change.
- USD 2,146,080Why not: Multiplies duration by value and by 0.01, which corresponds to a 100bp change.
Market value = 30 million x 1.052 = 31.56 million. DV01 = 6.8 x 31,560,000 x 0.0001 = USD 21,461.
The hardest tier
Position X has a market value of USD 50 million and an effective duration of 3. Position Y has a market value of USD 12 million and an effective duration of 10. Which pair of statements is correct?
- X loses more for a parallel rise in yields, while Y has the higher duration. - correct
- Y loses more for a parallel rise in yields, and Y has the higher duration.Why not: Ranks dollar loss by duration, ignoring that X's market value is much larger and gives X the larger DV01.
- X loses more for a parallel rise in yields, and X has the higher duration.Why not: Takes the larger dollar loss to mean higher duration, confusing a dollar measure with a percentage measure.
- Y loses more for a parallel rise in yields, while X has the higher duration.Why not: Reverses both rankings, treating market value as duration and duration as size.
DV01 of X = 3 x 50 million x 0.0001 = 15,000. DV01 of Y = 10 x 12 million x 0.0001 = 12,000. X loses more in dollars, but Y has the higher duration.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
Start free →More in Applying Duration, Convexity, and DV01
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