Dollar Duration Explained: Definition, Formula & Limitations
By Markets & Investing DeskUpdated Nov 10, 2026
Definition
Dollar duration estimates how many dollars a bond's or bond portfolio's value changes when interest rates move, found by multiplying duration by the price or position value.
Key takeaways
- Dollar duration, also called money duration, converts a bond's interest rate sensitivity into a dollar figure.
- DV01 expresses the dollar change for a 1 basis point move. Dollar duration is often quoted for a 100 basis point move, which is 100 times DV01.
- Dollar durations add up: a portfolio's dollar duration is the sum of each position's dollar duration.
- The measure is a linear approximation. It is reliable for small rate changes and drifts from the actual result as moves get larger.
- It assumes fixed cash flows and a parallel shift in yields, which limits its use for callable bonds, mortgage-backed securities and curve reshaping.
Dollar duration is an estimate of how many dollars a bond’s value, or a bond portfolio’s value, changes when interest rates move. It turns duration, which is a percentage sensitivity, into a dollar amount by multiplying it by the bond’s price or position value. A closely related measure, DV01 (dollar value of an 01), states that same sensitivity for a 1 basis point (0.01%) move instead of a 100 basis point (1%) move. Some sources use the two terms interchangeably. Others scale dollar duration to a full 1% shift. Whichever convention you see, check the size of the rate move it refers to before comparing figures.
The dollar duration and DV01 formulas
Dollar duration starts from modified duration, which estimates the percentage price change for a 1% change in yield.
Dollar duration (per 100 bp) = Modified duration × Price × 0.01
DV01 (per 1 bp) = Modified duration × Price × 0.0001
The price can be a single bond’s price or the market value of a whole position. In the money-duration convention, the full price including accrued interest is used.
If you only know Macaulay duration, convert it first:
Modified duration = Macaulay duration ÷ (1 + y/k)
Here y is the yield to maturity and k is the number of coupon periods per year. Combining these steps gives the version of the formula that some texts present directly:
Estimated dollar change = −DUR × Δi ÷ (1 + i) × P
Where:
- DUR = the bond’s Macaulay (straight) duration
- Δi = the change in interest rates
- i = the current interest rate per period
- P = the bond price
The minus sign reflects the inverse relationship between yields and bond prices: when yields rise, prices fall. For background on the yield input, see yield to maturity.
Worked example
Hypothetical example for illustration only.
An investor holds a corporate bond position with a market value of $1,000,000. The bond has a Macaulay duration of 6.7 years and a 3% yield, compounded annually.
- Modified duration = 6.7 ÷ 1.03 ≈ 6.50
- Dollar duration (per 100 bp) = 6.50 × $1,000,000 × 0.01 = $65,000
- DV01 = 6.50 × $1,000,000 × 0.0001 = $650
If yields rise by 25 basis points, the estimated loss is 25 × $650 = $16,250. If yields fall by 25 basis points, the estimated gain is about the same amount. Both figures assume the yield change is small and applies evenly across the bond’s cash flows.
How dollar duration is used
Measuring portfolio risk. Percentage durations have to be weighted by market value before they can be combined. Dollar durations are already in dollars, so they simply add. A portfolio holding the bond above ($650 DV01) and a second position with a $400 DV01 has a combined DV01 of $1,050. That makes dollar duration a practical way for fund managers to state total rate exposure as one number.
Hedging. Traders match dollar sensitivities, not face values. To offset the $650 DV01 position with a hedge instrument that has a DV01 of $65 per unit, the hedger would need roughly 650 ÷ 65 = 10 units sold short. The same logic underlies hedge ratios for Treasury futures and interest rate swaps.
Comparing positions of different sizes. A small long-dated bond and a large short-dated bond can carry similar dollar risk even though their durations differ widely. Dollar duration shows which one actually puts more money at stake.
Beyond bonds. Any instrument whose value changes with interest rates, including swaps, futures and bond funds or ETFs, can be described by its dollar duration or DV01.
Dollar duration vs. Macaulay and modified duration
| Measure | What it answers | Unit |
|---|---|---|
| Macaulay duration | Weighted-average time until the bond’s cash flows are received | Years |
| Modified duration | Percentage price change for a 1% change in yield | Percent |
| Dollar duration / DV01 | Dollar price change for a 1% or 1 bp change in yield | Dollars |
Macaulay and modified duration describe a bond regardless of how much you own. Dollar duration depends on position size, so doubling a holding doubles its dollar duration while leaving its modified duration unchanged.
Limitations
Convexity. The price-yield relationship is curved, not straight. For an option-free bond, the linear estimate overstates losses when yields rise and understates gains when yields fall. The larger the rate move, the bigger the error. A convexity adjustment narrows that gap.
Parallel shifts. A single dollar duration assumes every point on the yield curve moves by the same amount. When short and long rates move differently, as in a steepening or flattening, a portfolio can lose money even if its total dollar duration is hedged. Key-rate DV01s, which measure sensitivity to individual maturities, address this.
Fixed cash flows. The formula assumes coupons and principal are fixed in amount and timing. Callable bonds, mortgage-backed securities and floating-rate notes change their cash flows as rates move. For these instruments, analysts use effective duration, which is estimated by repricing the security under shifted rates.
It decays. Dollar duration changes as time passes, prices move and yields shift, so a hedge set today drifts out of balance and needs periodic rebalancing.
FAQs
Is DV01 always negative?
No. Mathematically, the price change for a rise in yields is negative for a long bond position, but DV01 is usually quoted as a positive number for long positions. A short bond position or a pay-fixed swap has the opposite exposure and is shown with the opposite sign. Conventions differ between systems, so confirm which one a report uses.
Does long DV01 mean long duration?
Generally, yes. Being "long DV01" means holding exposure that gains value when rates fall, which is the same direction of risk as being long duration. The difference is that DV01 states the size of that exposure in dollars.
The Bottom Line
Dollar duration matters most to fund managers, traders and investors who need to state rate exposure in dollars or size a hedge. Because dollar durations add across positions, they give one clear number for total risk, though you should confirm whether a figure refers to a 1 basis point or 100 basis point move. For large rate moves, curve reshaping, or callable and mortgage-backed securities, pair it with convexity, key-rate DV01s or effective duration.
