Duration, DV01 and curve trades
By SuperdayReps · Michigan Ross Undergrad | Wharton MBA · ex-Citi | ex-Greenhill · Former Head Mentor at a Leading IB Prep Service
14 min read · updated November 3, 2026
A rates trader who is long $50 million of 10-year notes does not really think of it as $50 million of bonds. They think of it as a bet of so many dollars per basis point. That number, DV01, is how risk is sized, how limits are set, how hedges are built and how one trader's book is added to another's. It is the first thing a desk head asks when you show them a position.
In the interview, this is where rates questions get technical. "What is duration?" is common, but the follow-ups are what count: "how would you hedge it?", "is there any risk left?", "walk me through a steepener". Those are answered with DV01, and a candidate who can size a hedge with real numbers sounds like someone who could sit on the desk next week.
Size every rates position by its DV01, the dollars it makes or loses per basis point, never by its face value. A hedge works when the DV01s match. A curve trade works the same way: two legs with equal and opposite DV01, so a parallel move in rates cancels and only the change in the gap between two maturities is left.
Duration: when you get paid, and how much the price moves
Start with a bond from the Treasuries lesson: it pays a fixed coupon every year and its face value at the end. Its price is the present value of those payments. Yields are quoted in basis points, hundredths of a percent, so a move from 4.00 to 4.10 percent is 10 basis points.
Macaulay duration is the weighted average time until you are paid, in years. Each payment's weight is its present value as a share of the price. Take a 3-year bond with a 5 percent annual coupon, priced at par with a 5 percent yield:
| Year | Payment per $100 | Present value | Share of price | Year × share |
|---|---|---|---|---|
| 1 | $5 | $4.76 | 4.8% | 0.05 |
| 2 | $5 | $4.54 | 4.5% | 0.09 |
| 3 | $105 | $90.70 | 90.7% | 2.72 |
| $100.00 | 2.86 years |
Most of the value arrives at the end, so the average lands close to three years.
Modified duration turns that into a sensitivity. Divide Macaulay by one plus the yield: 2.86 / 1.05 = 2.72. It means the price moves about 2.72 percent for a 1 percentage point move in yield, in the opposite direction. (With coupons paid twice a year, as on Treasuries, you divide by one plus half the yield. The examples here use annual coupons to keep the arithmetic visible.)
The duration that matters on a desk is modified duration, and three things raise it:
- Longer maturity. More of the value sits far away.
- Lower coupon. Less cash comes early, so the final payment carries more weight. A zero-coupon bond's Macaulay duration equals its maturity.
- Lower yield. Distant payments are discounted less, so they count for more.
For the rest of this lesson, use three bonds, all with 4 percent annual coupons and priced at par with a flat 4 percent yield:
| Bond | Macaulay duration | Modified duration |
|---|---|---|
| 2-year | 1.96 years | 1.89 |
| 5-year | 4.63 years | 4.45 |
| 10-year | 8.44 years | 8.11 |
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Frequently asked
- What is the difference between Macaulay and modified duration?
- Macaulay duration is the weighted average time until a bond's payments arrive, measured in years, with each payment weighted by its share of today's price. Modified duration is Macaulay divided by one plus the yield, and it turns that time into a sensitivity: the approximate percent change in price for a one percentage point change in yield.
- What is DV01?
- DV01, the dollar value of a basis point, is how many dollars a position gains or loses when yields move by 0.01 percent. It equals modified duration times market value times 0.0001. Traders use it because it adds up across bonds, futures and swaps into one number for a whole book.
- How do you hedge a bond position with another bond?
- You match DV01, not face value. Divide the position's DV01 by the hedge instrument's DV01 per unit of face to get the face amount to sell. A 10-year bond has roughly twice the DV01 of a 5-year, so hedging $10 million of 10-years takes roughly $18 million of 5-years, not $10 million.
- What is a 2s10s steepener?
- A trade that profits when the gap between the 10-year yield and the 2-year yield widens. You buy 2-year notes and sell 10-year notes, sized so both legs have the same DV01. A parallel move in rates then roughly cancels, and the profit or loss comes from the change in the spread.
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