DV01 and PV01

Duration tells you a bond's sensitivity to yield as a percentage — useful for comparing bonds, useless for answering the question a trading desk actually asks a hundred times a day: "if rates move one basis point against me, how many dollars do I lose?" DV01 (dollar value of a basis point, also called PV01, price value of a basis point) answers that directly, in dollars, for a specific position size.

From duration to dollars

$$DV01 = \text{Duration} \times \text{Price} \times 0.0001$$

In words: take the bond's (modified) duration, multiply by its current dollar price, and scale by one basis point (0.0001 in decimal). The result is how many dollars the position's value changes for that tiny yield move — small enough that duration's linear approximation is accurate, unlike for a full 100bp move, where convexity effects start to matter.

Worked example

A $10 million face-value bond position, priced at 98 (i.e., $980,000 per $1 million face, so $9.8 million market value), has a modified duration of 7.5.

• DV01: $7.5 \times 9{,}800{,}000 \times 0.0001 = 7{,}350$, i.e. about $7,350 per basis point.

That means if yields rise by 10 basis points, this position loses roughly $7{,}350 \times 10 = 73{,}500$, i.e. about $73,500 — a number a risk manager can act on immediately, unlike "duration 7.5," which says nothing about position size.

Hedging with DV01

DV01 is additive across a portfolio (approximately, ignoring convexity and curve-shape effects), which makes it the natural unit for hedging. To hedge a bond position's rate risk with a hedging instrument (say, a futures contract or another bond), match DV01s:

$$N_{hedge} = -\frac{DV01_{position}}{DV01_{hedge, per\ unit}}$$

In words: the number of hedge units needed is the position's total DV01 divided by how much DV01 one unit of the hedge carries, with a negative sign because you want the hedge to move opposite to the position.

Suppose the $7,350/bp position above needs hedging with a 10-year Treasury future carrying a DV01 of $95 per contract: $N_{hedge} = -7{,}350 / 95 \approx -77$ contracts — sell roughly 77 futures contracts to neutralize the rate exposure.

What this means in practice

DV01 is quoted on everything from a single bond to an entire swap book, and portfolio-level DV01 (summing every position's contribution) is a standard daily risk report. It's also strictly a local, linear measure — accurate for the small moves it's named for, but it says nothing about how the position behaves under a large rate shock (that's convexity) or under a non-parallel curve move (that's where key-rate durations, which split DV01 by maturity bucket, take over).