What is one basis point worth, in money?
Percentages do not hedge positions; money does. Ask a rates desk how much rate risk it is carrying and nobody says "4.33". They say a number in euros per basis point.
DV01, defined
DV01 — the dollar value of an 01 — is the change in a position's value for a one basis point (0.01%) change in yield. You will also see it called BPV (basis point value) or PV01. Same idea.
DV01 = Modified duration × Price × 0.0001
Our house bond: 4.3294 × €1,000 × 0.0001 = €0.4329 per €1,000 of face value.
Verify it the hard way: reprice the bond at 5.01% instead of 5.00% and you get €999.57 — a fall of €0.43. The formula and the repricing agree, as they must.
Scale it to a position
A €10,000,000 face holding is 10,000 bonds:
10,000 × €0.4329 = €4,329 per basis point
Now a 25bp move is not an abstraction — it is roughly €108,000 of profit or loss. That is the sentence a risk report needs, and "duration 4.33" is not.
Why practitioners prefer it
- It is additive in money. Add the DV01s of a bond, a future and a swap and you have the book's rate risk, even though their prices, coupons and conventions have nothing in common. Duration only averages cleanly when you weight by value first; DV01 is already weighted.
- It converts risk into P&L. Multiply DV01 by a move in basis points and you have euros.
- It sizes hedges directly.
Sizing a hedge
To offset one position's rate risk with another instrument:
Face of hedge = DV01 of position ÷ DV01 per unit of the hedging instrument
Suppose you want to offset that €10m five-year position (DV01 €4,329) using a 10-year 5% par bond with modified duration 7.72, whose DV01 is 7.72 × €1,000 × 0.0001 = €0.772 per €1,000 face:
€4,329 ÷ €0.772 ≈ 5,608 bonds → about €5.6m face of the ten-year.
Sense-check it in money duration: €10m × 4.33 = €43.3m, and €5.6m × 7.72 = €43.3m. The two legs carry the same money duration, so a 1bp parallel move nets to roughly zero.
The word "parallel" is doing a lot of work
That hedge is exact only if the five-year and ten-year yields move by the same amount. They routinely don't. When the curve twists, the hedge leaks — and the leak is not small.
Desks therefore decompose DV01 by maturity bucket: key rate durations (or partial DV01s) report sensitivity to a 1bp move at the 2-year point, the 5-year point, the 10-year point and so on, summing back to the total. A twist then shows up as a row-by-row pattern instead of hiding inside one number. Unit 4 is about the curve that does the twisting.
A related term
Money duration (or dollar duration) = Modified duration × Price. It is the same idea expressed per 1% instead of per 1bp — DV01 is simply money duration ÷ 10,000.
In the data
Rates and spreads are quoted in different units, often side by side. The table is one day of two overnight rates and the spread between them: the rates are in per cent, the spread in basis points.
3.88% minus 3.90% is −0.02 percentage points, and the table prints it as −2. The two units are a factor of 100 apart, and nothing warns you when you mix them: a 25bp move read as 25 points of yield simply produces a DV01 answer a hundred times too large.
Try it now
- Compute DV01 for a €1,000,000 position in a bond with modified duration 6 trading at 98 (per €100 of face). Per €1,000 face: 6 × €980 × 0.0001 = €0.588 → €588 per basis point on the position.
- Below is the 10-year Treasury yield on two dates a week apart. Convert the change into basis points yourself and multiply by that €588 to express the week as a profit or loss figure, with its sign. Then do it deliberately wrong, feeding the raw difference in without converting: the answer is a hundred times out, and nothing flags it.
- Say why a risk report is written in DV01 rather than duration — and name the one assumption that a single DV01 number still hides.