Bond price, yield and duration calculator
Price a bond from its yield or find the yield from its price, with duration, convexity and how much the price moves when yields change.
Example figures
Your figures
Result
Price
A$98.0045
- Coupon each period
- A$2.125 × 20 payments
- Current yield (annual coupon ÷ price)
- 4.337%
- Macaulay duration
- 8.23 years
- Modified duration
- 8.05
- Convexity
- 77.09
- DV01 (price change per 0.01 point)
- A$0.0789
| Yield change | New price | Actual change | Duration estimate | With convexity |
|---|---|---|---|---|
| −2.0 pt | A$115.3994 | Up +17.75% | +16.09% | +17.64% |
| −1.0 pt | A$106.2823 | Up +8.45% | +8.05% | +8.43% |
| −0.5 pt | A$102.0439 | Up +4.12% | +4.02% | +4.12% |
| +0.5 pt | A$94.1541 | Down −3.93% | −4.02% | −3.93% |
| +1.0 pt | A$90.483 | Down −7.67% | −8.05% | −7.66% |
| +2.0 pt | A$83.6432 | Down −14.65% | −16.09% | −14.55% |
| Payment | In (years) | Amount | Present value |
|---|---|---|---|
| 1 | 0.5 | A$2.125 | A$2.0782 |
| 2 | 1 | A$2.125 | A$2.0325 |
| 3 | 1.5 | A$2.125 | A$1.9878 |
| 4 | 2 | A$2.125 | A$1.944 |
| 5 | 2.5 | A$2.125 | A$1.9013 |
| 6 | 3 | A$2.125 | A$1.8594 |
| … 11 more payments … | |||
| 18 | 9 | A$2.125 | A$1.4237 |
| 19 | 9.5 | A$2.125 | A$1.3924 |
| 20 | 10 | A$102.125 | A$65.4434 |
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How this is calculated
The bond is valued on a coupon date, so there is no accrued interest and the price is the clean price. With n coupon periods, a coupon c each period, face value F and yield y per period (the annual yield divided by the coupons a year):
price = c ÷ (1 + y) + c ÷ (1 + y)² + … + (c + F) ÷ (1 + y)ⁿ
Finding the yield from a price reverses that sum; the calculator searches for the yield that reproduces the price to within a tiny fraction of a cent.
Macaulay duration is the average time to the bond's cash flows, each weighted by its present value. Modified duration (Macaulay ÷ (1 + y)) is the approximate percentage fall in price for a one-percentage-point rise in yield. Because the price–yield curve is curved, duration alone overstates falls and understates rises for large moves; adding convexity (½ × convexity × Δy²) corrects most of that. DV01 is the price change for a 0.01 percentage point move in yield.
Real bonds settle between coupon dates, may be callable or inflation-linked, and trade on yields quoted with market-specific conventions, so a broker's or the issuer's figures can differ slightly.