A rates desk needs one number that answers: "if yields move one basis point, how many dollars does this position gain or lose?" That number is DV01 — dollar value of an 01 (basis point) — and it is the universal language for hedging fixed-income risk. DV01 is more general than duration: it applies equally to a plain vanilla bond, an interest rate swap, a mortgage prepayment model, or an embedded-option callable, because it only requires computing (or observing) two nearby prices, not any analytical formula.
This note defines DV01 precisely, shows how to estimate it numerically, derives the hedge ratio for a two-security position, and connects DV01 to dollar duration. It then introduces convexity — the rate of change of DV01 — which becomes the second-order risk factor when rate moves are large.
Learning objectives. By the end of this note you should be able to:
- define DV01 and compute it from two prices at rates one basis point apart;
- derive the DV01 hedge ratio and explain the two-rule sign convention;
- define dollar duration and state its relation to DV01 and duration;
- define convexity and explain why it is positive for plain-vanilla bonds;
- describe a hedging example where DV01 tracking fails over a large rate move because of convexity.
In this lesson
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- The price-rate function and one-factor assumptions
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- DV01 defined
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- The DV01 hedge ratio
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- Dollar duration and portfolio aggregation
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- Convexity: the second-order term
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- The hedging example revisited: convexity drift
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
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