Dollar Duration (DV01)

What it is

Dollar duration, commonly called DV01 (dollar value of an 01) or money duration, quantifies how much a bond’s price changes in dollar terms for a small change in yield. It converts percentage sensitivity (duration) into a dollar amount, which is useful for measuring and hedging interest-rate risk.

Core formulae

Using modified duration (Dmod):
– Approximate dollar price change ≈ −Dmod × Δy × P
where Δy is the change in yield in decimal form (e.g., 25 bps = 0.0025) and P is the bond price.

Derived measures:
– DV01 (per 1 basis point) = Dmod × P × 0.0001
– Dollar duration for a 1% (100 bps) yield change = Dmod × P × 0.01

If you start from Macaulay duration (DMac) and current yield i:
– Dmod = DMac / (1 + i)
– Dollar change ≈ −(DMac/(1+i)) × Δy × P

Portfolio dollar duration = sum of each position’s dollar duration (or weight × individual dollar durations).

Quick example

Bond price = $1,000, modified duration = 6.
Yield rises by 25 bps (0.0025):
Price change ≈ −6 × 0.0025 × $1,000 = −$15.
So the bond loses about $15 in value.

How managers use it

• Expresses interest-rate exposure in dollars, making hedging and aggregation across positions straightforward.
• Facilitates trading decisions and size of hedges (e.g., how many futures or swaps to use to offset exposure).

Comparison with other duration measures

• Macaulay duration: the weighted average time to receive cash flows (measured in years); useful for immunization and time-weighted metrics.
• Modified duration: Macaulay duration adjusted for yield; measures percent price sensitivity for a 1% yield change.
• Dollar duration (DV01): converts percent sensitivity into an absolute dollar change. It is the practical bridge between duration and portfolio P&L.

Limitations and considerations

• Linear approximation: dollar duration assumes a linear relationship between price and yield. For large yield moves, errors increase; convexity matters.
• Parallel shift assumption: usually assumes the yield curve moves in parallel. Non-parallel shifts (twists, butterfly moves) can produce different P&L.
• Instrument specifics: callable bonds, floating-rate notes, and instruments with embedded options have cash flows that change with rates; standard dollar duration can be misleading.
• Market conventions: DV01 is often quoted per 1 basis point; be clear which convention is being used when comparing figures.
• Use alongside convexity: include convexity adjustments for better accuracy when yield changes are material.

Bottom line

Dollar duration (DV01) is a practical, widely used measure that translates duration into dollar exposure to small yield changes. It simplifies portfolio aggregation and hedging, but because it is a linear approximation, it is most reliable for small rate moves and should be used with awareness of convexity, non-parallel yield-curve shifts, and instrument-specific features.