DV01 (dollar value of a basis point, also called "dollar duration" or "PV01") measures the dollar change in a bond's price for a 1 basis point (0.01%) change in yield. It is the standard unit of interest rate risk in fixed-income trading.
The formula is:
DV01 = modified duration x price / 10,000
For a par bond (priced at 100) with a modified duration of 8.2 years (roughly a 10-year Treasury at current yields), the DV01 is approximately 0.082 per 100 face value. For a 1 million position, that is 820 per basis point.
DV01 is used to:
DV01 varies across the curve. Short-term bills have very low DV01. Long-dated bonds have high DV01. This difference is why curve trades are constructed on a DV01-neutral basis: matching the dollar risk of the long and short legs so the trade profits only from changes in the curve shape, not from parallel shifts.
DV01 sits at the end of a short chain, and each link answers a different question.
The last step is the one that makes the measure usable on a trading desk. A percentage change tells you nothing until you know the size of the position. A dollar amount can be added across positions, netted against a hedge, and compared to a risk limit.
Take a 10 Yr note priced at 100 with a modified duration of 8.2 years. Its DV01 is 8.2 multiplied by 100 multiplied by 0.0001, or 0.082 per 100 of face value. A position of 10 million face therefore has a DV01 of 8,200. Every basis point of yield change moves the position by 8,200 dollars.
DV01 turns hedging into division.
Suppose the same 10 million 10 Yr position needs to be hedged with 2 Yr notes. A 2 Yr note priced at 100 with a modified duration of 1.95 years has a DV01 of 0.0195 per 100 face, or 195 per million.
The position risk is 8,200 per basis point. The hedge instrument delivers 195 per million. Divide 8,200 by 195 and the answer is about 42. The hedge needs roughly 42 million face of 2 Yr notes.
The size is the point worth pausing on. Hedging a 10 million position takes 42 million of the shorter instrument. Matching notional instead of risk would leave the position almost entirely unhedged, because the 2 Yr leg would carry less than a quarter of the risk it needed to offset. This mistake is common enough that duration-neutral construction is treated as the default on every rates desk.
DV01 is a first order measure. It describes the slope of the price and yield relationship at one point. Two things make that description incomplete.
Large yield moves. The relationship between price and yield is curved, not straight. DV01 draws the straight line that touches the curve at today's yield. Over a few basis points the line and the curve are close to identical. Over 100 bps they separate, and DV01 overstates the loss from a yield rise and understates the gain from a yield fall. Convexity measures that gap and corrects for it.
Non-parallel curve moves. DV01 assumes every yield on the curve moves by the same one basis point. Real curves twist. A position built to have zero net DV01 across a 2 Yr leg and a 10 Yr leg is protected against a parallel shift and fully exposed to a change in the slope between them. That exposure is usually the intent of the trade, but it means a zero DV01 position is not a riskless one.
Desks handle the second problem by reporting DV01 by bucket rather than as a single number. Risk is measured separately at the 2 Yr, 5 Yr, 10 Yr, and 30 Yr points, which shows where on the curve the exposure actually sits.
In most desk usage, yes. Both describe the price change for a one basis point move in yield. Some systems draw a fine distinction, using PV01 for a shift applied to the underlying curve and DV01 for a shift applied to the bond's own yield. The two agree closely for a Treasury and can differ for instruments valued off a curve, such as a swap.
Yes. DV01 is calculated at the current yield and price, and both of those move. A bond's DV01 generally rises as yields fall, because the price rises and the cash flows are discounted less heavily. This drift is why hedges are rebalanced rather than set once.
Because a bond returns its principal at maturity, and a payment due soon is barely affected by a change in the discount rate. A 3 Mo bill repays in a quarter of a year, so one basis point of yield changes its value by about 25 dollars per million. A 30 Yr bond discounts its principal over thirty years, so the same basis point moves it by a few thousand.