DV01 and the shape of rate risk

Equity desks talk in delta. Rates desks talk in DV01 — the dollar value of a basis point. It is the change in a position's value when the relevant yield moves by one hundredth of a percent.

That is all it is. A bond with a DV01 of £850 gains roughly £850 if yields fall one basis point, and loses roughly £850 if they rise one. You will also see it as PV01 or BPV; for most purposes the distinction is not worth arguing about.

Why a basis point

Because it makes unlike things comparable. A ten-year gilt, an interest-rate swap, a futures contract and a portfolio of all three have no common unit until you express each as sensitivity to the same small move. Once you do, you can add them up, and the sum is the position.

This is the practical reason DV01 wins over duration on a trading desk. Duration is a percentage, so it needs a notional and a price before it means anything. DV01 is already in money.

The relationship to duration

They are the same idea in different clothing:

DV01 ≈ modified duration × price × 0.0001

A £10m position with modified duration 8 and a price of par has a DV01 of roughly £8,000. Duration tells you the percentage sensitivity; DV01 tells you the cash. Risk systems report the cash, because that is what a limit is denominated in.

Convexity, and the direction of the error

DV01 is a first derivative — a straight-line approximation to a curved relationship. For a plain bond, the price/yield curve bends favourably: convexity is positive, so prices rise more than DV01 predicts when yields fall, and fall less than it predicts when they rise.

For a one-basis-point move that error is negligible, which is why the unit is one basis point. For a fifty-basis-point move it is not, and a DV01-only view understates your position in a rally and overstates the damage in a sell-off.

Not everything is positively convex. Mortgage-backed securities and callable bonds can exhibit negative convexity — as yields fall, borrowers refinance and the expected life shortens, so the position stops rallying. Here DV01 is not merely imprecise; it points the wrong way about what happens next. Anything with an embedded option needs the second-order term.

One number is not enough

DV01 as usually quoted assumes a parallel shift — every point on the curve moves by the same basis point. Curves do not oblige. They steepen, flatten and twist, and a portfolio can be flat on parallel DV01 while carrying a large bet on the shape.

Consider a book that is long two-year and short ten-year in DV01-neutral size. Total DV01: zero. A parallel move does nothing. A steepening move can cost a great deal.

The fix is key-rate, or partial, DV01: bucket the curve by tenor and shift each bucket separately, holding the rest fixed. You get a vector rather than a scalar — sensitivity at 2y, 5y, 10y, 30y — which is what a rates risk report actually shows. The scalar is the sum, and the sum is the least informative row.

Hedging with it

DV01 is how hedge ratios are set. To hedge a position with an instrument, you match the DV01s:

hedge notional = position DV01 ÷ hedge instrument DV01 per unit

If a corporate bond position has a DV01 of £42,000 and a futures contract has a DV01 of £70 per contract, you need about 600 contracts. In practice this is adjusted for the basis between the two instruments and rebalanced as DV01 itself drifts with yields — the hedge ratio is not constant, which is convexity appearing again.

Where it sits in a risk stack

DV01 is a sensitivity, not a loss estimate. It tells you how exposed you are per unit of move; it does not tell you how large a move to expect. That is the job of VAR and Expected Shortfall, which combine sensitivities with a view on distribution.

Both matter, and they fail differently. Sensitivities are precise and local: correct for small moves, silent about large ones. Distributional measures cover the large moves and depend entirely on the history or model you feed them. A desk watches both, and trusts neither alone.

From the build side

My first serious risk work was extending Deutsche Bank's FX desk risk calculator to Fixed Income — taking a system that priced one asset class and teaching it another, then migrating the workflow off spreadsheets onto a live platform. Later, at Revolut, DV01 was one line in a greenfield engine that also carried mark-to-market, collateral and variation margin, VAR/ES and Greeks.

The recurring difficulty was never the derivative. It was agreeing what a position was: the same trade represented differently in three systems, settlement conventions that shifted a cash flow by a day, and day-count conventions that quietly changed the answer. Anyone who has built one of these will tell you the same thing — the risk number is a thin layer of arithmetic over a deep pile of reference data, and the pile is where the bugs live.