Free tool
Bond Calculator
Give it a coupon, a maturity, how often it pays, a face value and either a yield or a price, and it works out the rest: price, current yield, Macaulay and modified duration, DV01 and convexity, live as you type. Nothing you enter is stored or sent anywhere, it all runs in your browser.
Priced on a coupon date, so clean price and dirty price are the same number here: there is no partial coupon period, so nothing to add accrued interest for. Price, yield and duration below are always quoted per 100 of face value, the way a bond is actually quoted; face only scales the position value and position DV01 rows at the bottom.
| Metric | Value |
|---|---|
| Price (per 100 face) | 100.0000 |
| Yield to maturity | 5.0000% |
| Current yield | 5.0000% |
| Macaulay duration (years) | 7.9894 |
| Modified duration | 7.7946 |
| DV01, per 100 face | 0.077946 |
| DV01, per $1,000,000 face | $779.46 |
| Convexity (years squared) | 73.6287 |
| Position value (face 100.00) | 100.00 |
| Position DV01 (face 100.00) | 0.0779 |
- Yield to maturity is the single rate that makes the cash flows equal this price. It is only your realized return if you hold to maturity and reinvest every coupon at that same rate, which is the trap in “buy at a discount, what is your return” questions.
- Current yield is just the coupon over the price. It ignores the pull to par and reinvestment, so it is not a substitute for yield to maturity even though the two get mixed up constantly.
- Macaulay duration is a time, the cash-flow-weighted average number of years to get your money back, not a price sensitivity.
- Modified duration is the percentage price change for a 1 percentage point move in yield, a slope, not a time. Higher yields mean lower prices, so the sign is implicit.
- DV01 is the dollar price change for a one basis point move in yield: price units, not a percentage, which is the usual mix-up with modified duration.
- Convexity is the second-order correction to the duration estimate. It only works added to the duration term, never used alone, and the size of the correction grows with the size of the yield move.
A parallel move in yield
Duration alone treats price and yield as a straight line. Adding convexity curves that line back toward the truth. The gap between “duration plus convexity” and “exact” is what is left over, and it grows fast as the move gets bigger.
| Yield shock | Duration only | Duration + convexity | Exact reprice |
|---|---|---|---|
| +100bp | -7.7946% | -7.4264% | -7.4387% |
| -100bp | +7.7946% | +8.1627% | +8.1757% |
Where this comes up
The interview questions this checks
The technical round tests exactly this arithmetic, usually with no calculator allowed. Bond math interview questions works through the price-yield relationship, the duration and convexity trade-off, and the forward-rate and discount-bond questions candidates actually get asked, so you can check your own hand math against this calculator. For how bond math questions fit into the wider technical and behavioral round, see fixed income interview questions.
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