Effective Duration Calculator
Calculate the effective duration of a bond to measure its price sensitivity to parallel shifts in the yield curve, accounting for embedded options.
How to use this tool
- Enter current bond price (p₀), price if yield falls (p⁻), price if yield rises (p⁺) and yield change (δy) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your effective duration and the full breakdown beneath it.
⚠ This tool provides general estimates for education only and is not financial, tax or legal advice. Figures may not reflect your situation — verify with a qualified professional.
Formula
Effective Duration = (P− − P+) / (2 × P0 × Δy)
Where P⁻ is the bond price when yield decreases by Δy, P⁺ is the bond price when yield increases by Δy, P₀ is the current bond price, and Δy is the yield change in decimal form.
How it works
Effective duration measures the approximate percentage change in a bond's price for a 1% parallel shift in the yield curve. Unlike modified duration, it accounts for cash flow changes due to embedded options (e.g., callable or putable bonds) by using actual repriced values rather than assuming fixed cash flows. The result is expressed in years and represents the weighted average time to receive the bond's cash flows.
Worked example
Simple Bond with 1% Yield Shift
- Inputs: P₀ = $100, P⁻ = $102 (yield falls 1%), P⁺ = $98 (yield rises 1%), Δy = 1% = 0.01
- Apply formula: Effective Duration = (102 − 98) / (2 × 100 × 0.01)
- Numerator: 102 − 98 = 4; Denominator: 2 × 100 × 0.01 = 2
- Effective Duration = 4 / 2 = 2.0 years
Effective Duration = 2.0 years, meaning a 1% rise in yields causes approximately a 2% price decline.
Common mistakes to avoid
- Using too large a yield shift (Dy) — small parallel shifts (25-50 bps) give more accurate duration estimates; large shifts introduce convexity error that makes effective duration less meaningful.
- Forgetting to reprice the bond's embedded option (call or put) at each shifted yield level — effective duration requires full option-adjusted pricing at P- and P+, not just adjusting the yield to maturity.
- Confusing effective duration with modified duration: modified duration ignores optionality and will be identical to effective duration only for option-free bonds.
Key terms
- What is effective duration?
- Effective duration measures a bond's price sensitivity to a 1% parallel shift in the yield curve, expressed in years. It accounts for embedded options by using repriced values at different yield levels.
- How does effective duration differ from modified duration?
- Modified duration assumes cash flows are fixed, while effective duration recalculates the bond price at each yield level, making it suitable for bonds with embedded options like callable bonds.
- What does a higher effective duration mean?
- A higher effective duration means greater price sensitivity to interest rate changes. A bond with effective duration of 5 years will lose approximately 5% in price for every 1% rise in yields.
- What is Δy in the formula?
- Δy is the size of the yield change used in the calculation, typically a small value like 0.01 (1%) or 0.005 (0.5%). Smaller Δy values give more accurate estimates for bonds with embedded options.
Frequently asked questions
- When should I use effective duration instead of modified duration?
- Use effective duration for bonds with embedded options (callable bonds, putable bonds, MBS) because the option changes cash flows when rates shift; modified duration assumes cash flows are fixed.
- What does an effective duration of 5 mean?
- A duration of 5 means the bond's price will fall approximately 5% for each 1 percentage point (100 bps) increase in yields, and rise about 5% for a 1% rate decrease.
- How does the size of the yield shift affect the result?
- Larger yield shifts (e.g., 200 bps) introduce convexity effects that cause the duration estimate to diverge from the true sensitivity. Use small, symmetric shifts (typically 25-100 bps) for accuracy.