Bond Duration & Rate-Shock Calculator
Duration is the first-order effect; convexity adjusts for curvature. The approximation weakens for large moves or securities with embedded options.
What it calculates
Bond prices generally fall when yields rise, but the sensitivity depends on duration and curvature. This calculator uses modified duration and convexity to estimate the price change, new price, and approximate one-year total return after adding the starting yield.
How this bond duration & rate-shock calculator works
The model multiplies modified duration by the yield change for the linear effect and adds half of convexity times the squared yield change. It then adds the starting yield as a rough one-year income buffer.
Formula
Price change ≈ −duration × Δyield + ½ × convexity × Δyield²
Callable bonds, mortgage-backed securities, credit-spread changes, defaults, and nonparallel curve moves can produce materially different results.
Primary specifications
Before you use the result
Assumptions
- • The yield curve shifts in parallel.
- • Duration and convexity remain stable through the move.
- • Starting yield approximates one year of income before defaults, fees, and reinvestment.
Quick start
- 1. Take duration, convexity, and yield from a consistent bond or fund source.
- 2. Enter the yield move in basis points.
- 3. Test both rising- and falling-rate scenarios and review option exposure.
Inputs and units
| Input | Unit | Default |
|---|---|---|
| Current bond price | US dollars | $100 |
| Modified duration | years | 7 years |
| Convexity | number | 60 |
| Yield change | basis points (100 bps = 1 percentage point) | 100 basis points |
| Starting annual yield | percent | 4% |
Worked example (hypothetical)
Bond Duration & Rate-Shock Calculator: worked example
Hypothetical example using the calculator's default inputs. The numbers are illustrative, not a forecast or a quote.
| Current bond price | $100 |
|---|---|
| Modified duration | 7 years |
| Convexity | 60 |
| Yield change | 100 basis points |
| Starting annual yield | 4% |
| Estimated price change | -6.70% |
|---|---|
| Estimated new price | $93.30 |
| Approx. 1-year return | -2.70% |
With these inputs, the estimated price change is -6.70%.
Frequently asked questions
What does duration measure?
Modified duration approximates the percentage price change for a one-percentage-point change in yield.
Why include convexity?
The price-yield relationship is curved, so convexity improves the linear duration estimate, especially for larger moves.
Does a bond fund have maturity?
A fund continually replaces holdings and does not mature like one bond, but its reported duration still summarizes current rate sensitivity.
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