β±οΈ Effective Duration Calculator
Bond price sensitivity to rate moves.
Effective duration
Estimates for planning only, not financial advice.
Effective duration measures a bond's price sensitivity to interest rate moves using actual repriced values. With prices of $96.40 if yields rise 50 basis points and $103.85 if they fall, around a $100 current price, effective duration is (103.85 - 96.40) / (2 x 100 x 0.005) = 7.45 years. Roughly, a 1 percent rate rise cuts the price about 7.45 percent. It is the risk number bond managers actually trade on.
How to Use This Calculator
Enter the bond's repriced values for equal yield shifts up and down, the current price, and the shift size in basis points. The calculator returns effective duration plus the estimated price impact of a full 1 percent rate move.
Price the bond at the current yield plus the shift, and at the current yield minus the shift, using any bond pricer.
Enter both prices, the current price, and the shift in basis points.
Read the duration and translate it: duration 7.45 means about 7.45 percent price swing per 1 percent rate move.
The Formula
Unlike Macaulay or modified duration, which assume fixed cash flows, effective duration reprices the bond and therefore handles embedded options like calls and puts correctly. For an option-free bond it matches modified duration closely; for callable bonds it is the only honest measure, since the cash flows themselves change with rates.
Worked Example
Current price $100. At +50bps the bond reprices to $96.40; at -50bps to $103.85. Effective duration = (103.85 - 96.40) / (2 x 100 x 0.005) = 7.45 / 1.0 = 7.45 years. A 1 percent rate increase should cut the price roughly 7.45 percent, to about $92.55. Note the asymmetry: the down-yield gain ($3.85) exceeds the up-yield loss ($3.60), the convexity that duration alone misses and that benefits bondholders.
Duration in Practice
| Duration | Typical bond | 1% move impact |
|---|---|---|
| 1 to 3 years | Short-term notes | 1-3% price swing |
| 4 to 7 years | Intermediate bonds | 4-7% price swing |
| 8+ years | Long bonds | 8%+ price swing |
Managing Duration Risk
Portfolio managers set duration targets to express rate views: longer than the benchmark when rates are expected to fall, shorter when they are expected to rise. A barbell of short and long bonds can match a bullet portfolio's duration with different convexity, profiting from volatility itself. And liability-driven investors match asset duration to liability duration, immunizing the surplus against rate moves entirely.
Duration drifts as time passes and yields move, so it needs rebalancing. A bond bought at 7.45 years of duration will not stay there; falling yields extend it, the passage of time shortens it. Professional desks monitor it continuously, which is why the measure exists in the first place: it turns an abstract risk into a single tradable number.
Common Mistakes
Using modified duration on callable bonds understates the real risk; effective duration is built for exactly this. Forgetting convexity means the estimate worsens for large rate moves; duration is a linear approximation of a curved relationship. And comparing durations across currencies or credit qualities mixes different risks. Price the bond itself with our bond calculator, convert yields with our equivalent rate calculator, and check the income with our interest rate calculator.
Duration Matching for Retirement Income
Retirees face the purest duration problem in finance: liabilities, living expenses, arrive on a schedule, and the portfolio must fund them regardless of rate moves. Duration matching aligns the bond portfolio's duration with the spending horizon's duration, so a rate rise that cuts bond prices simultaneously reduces the present value of future spending needs. The surplus is immunized; the retiree can ignore the headlines.
The classic implementation is a bond ladder: equal rungs maturing each year for ten years, rolled forward annually. The ladder's duration naturally approximates the spending horizon, it generates predictable cash, and it avoids the single-duration bet of a bond fund. When a rung matures, spending needs decide whether it is consumed or reinvested, which keeps the strategy tethered to reality rather than to forecasts.
The enemy is reaching for yield by extending duration beyond the horizon. A retiree spending over 15 years who buys 25-year bonds for their higher coupons takes rate risk the spending plan never asked for; a rate spike then cuts the portfolio without cutting the liabilities. Match the duration to the need, take the market yield for that duration, and let the immunization do the worrying.
Duration and Reinvestment Risk
Duration measures price risk, but short-duration investors face the mirror risk: reinvestment. A portfolio of 2-year bonds has little price volatility, yet when the bonds mature in a fallen-rate environment, the proceeds reinvest at much lower yields. The income stream suffers exactly when the price stability looked comforting. Duration chose price safety; reinvestment risk collected the bill.
The two risks trade off across the duration spectrum, and the right point depends on the horizon. Match duration to when the money is actually needed: money needed soon wants short duration and accepts reinvestment risk it will never face; money needed in twenty years wants long duration and the price volatility is irrelevant. Horizon, not temperament, should set the duration.
Estimates for planning only, not financial advice.
Frequently Asked Questions
What is effective duration?
A bond risk measure computed from actual repriced values at higher and lower yields. It estimates the percentage price change per 1 percent rate move and handles bonds with embedded options.
How do you calculate effective duration?
Subtract the up-yield price from the down-yield price, divide by twice the current price times the yield shift as a decimal. With $103.85, $96.40, $100, and 50bps, duration is 7.45 years.
What is the difference between effective and modified duration?
Modified duration assumes fixed cash flows; effective duration reprices the bond, so it works for callable and putable bonds whose cash flows change with rates. For option-free bonds they nearly match.
What does a duration of 7.45 mean?
Roughly a 7.45 percent price fall for each 1 percent rise in yields, and a similar gain for each 1 percent fall. Higher duration means higher interest rate risk.
What is convexity?
The curvature in the price-yield relationship that duration, a linear measure, misses. Positive convexity means gains when rates fall exceed losses when rates rise, which benefits holders.
How do investors use duration?
To express rate views and manage risk: lengthen duration to bet on falling rates, shorten to bet on rising rates, or match liability duration to immunize a portfolio.
Does duration change over time?
Yes. Time passage shortens it, falling yields extend it, and coupon payments matter. Portfolios need periodic rebalancing to hold a duration target.
Why do callable bonds need effective duration?
Because the issuer may call the bond when rates fall, changing the cash flows. Measures assuming fixed cash flows misstate the risk; repricing captures it.
What is dollar duration?
Duration times price: the dollar price change per 1 percent rate move. It translates the percentage risk into money terms for position sizing.
Can duration be negative?
For most bonds no, but some instruments like interest-only strips or certain derivatives gain when rates rise, giving negative duration. They are hedges, not investments.