Calculator Form
Example Data Table
| Face Value | Coupon Rate % | Maturity Years | Frequency | YTM % | Market Price | Macaulay Duration | Modified Duration | DV01 |
|---|---|---|---|---|---|---|---|---|
| 1,000.00 | 5.25 | 7.00 | 2 | 4.60 | 1,032.40 | 5.9709 | 5.8367 | 0.6062 |
Formula Used
Bond price: Price = Σ [ Cash Flow at period t ÷ (1 + y / m)t ]
Macaulay duration: Duration = Σ [ Time in years × Present Value of cash flow ] ÷ Bond price
Modified duration: Modified Duration = Macaulay Duration ÷ (1 + y / m)
DV01: DV01 = Modified Duration × Bond Price × 0.0001
Convexity: Convexity improves price-change estimates when yields move more than a tiny amount.
Approximate price change: ΔP / P ≈ -Modified Duration × Δy + 0.5 × Convexity × (Δy)2
Here, y is annual yield and m is coupon frequency. The schedule table shows every cash flow, discount factor, present value, and time-weighted present value used by the calculator.
How to Use This Calculator
- Enter the bond face value.
- Enter the annual coupon rate in percent.
- Enter years to maturity.
- Select the coupon payment frequency.
- Enter yield to maturity in percent.
- Optionally enter the current market price.
- Enter a rate shock in basis points.
- Press calculate to view results above the form.
- Review the schedule table and graph.
- Use the CSV or PDF button to export output.
What This Calculator Helps You Measure
This tool estimates how sensitive a fixed-income security is to interest-rate changes. Macaulay duration measures the weighted average time needed to recover the bond price from discounted cash flows. Modified duration converts that timing concept into an immediate price-sensitivity estimate. DV01 then translates that estimate into a money amount for a one-basis-point move.
Convexity adds a second layer of insight because price changes are not perfectly linear when yields shift. That matters when rate shocks are larger, such as 25, 50, or 100 basis points. The model price uses the entered yield, while any optional market price is shown for comparison, current-yield review, and market-based DV01 scaling.
The detailed cash-flow table is useful for analysts, students, and treasury teams who want to verify every step. Each row shows the coupon or redemption cash flow, the discount factor, present value, and time-weighted present value. The Plotly chart makes the timing of value concentration easier to inspect, especially for lower-coupon or longer-maturity bonds.
FAQs
1) What does Macaulay duration mean?
Macaulay duration is the weighted average time needed to receive the bond’s discounted cash flows. It is measured in years and helps explain timing risk.
2) What does modified duration measure?
Modified duration estimates the percentage price change for a small change in yield. Higher modified duration means the bond is more rate sensitive.
3) What is DV01?
DV01 shows the approximate currency change in bond price for a one basis point yield move. It is widely used in fixed-income risk reports.
4) Why is convexity included?
Convexity improves price estimates when interest-rate moves are larger. Duration alone is linear, but real bond prices curve as yields change.
5) Why can market price differ from model price?
Model price comes from the entered yield and cash-flow assumptions. Market price may reflect liquidity, spreads, embedded options, or stale pricing.
6) Can this calculator handle zero-coupon bonds?
Yes. Enter a coupon rate of zero. The tool will value the single maturity payment and calculate duration metrics from that structure.
7) Why do periods sometimes look rounded?
The script rounds maturity into the nearest coupon period using the selected payment frequency. That keeps discounting and schedule construction consistent.
8) Is this suitable for callable or floating-rate bonds?
No. This version is for plain fixed-coupon structures. Callable, putable, floating-rate, and amortizing bonds need additional pricing assumptions and option treatment.