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Effective Duration Calculator

Estimate a bond's effective duration by repricing fixed coupon cash flows after equal up and down yield shocks to measure interest-rate sensitivity.

Published

Effective duration
Effective duration
7.277 years
Current bond price
$798.70
Price if yield falls
$859.53
Price if yield rises
$743.29
Coupon per period
$50.00
Approximate price move for shock
7.28%

A 1% yield shock changes this bond by roughly 7.28% in price, before convexity effects.

Par value paid back at maturity.
$
%
yr
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The rate shock used for the up-yield and down-yield prices.
%

Results update as you type.

Effective Duration Calculator

Effective duration estimates how much a bond’s price changes when yields move. It is one of the central measures of interest-rate risk. A longer effective duration means the bond is more sensitive to rate changes; a shorter effective duration means the price is less sensitive, all else equal. This calculator measures that sensitivity by pricing a fixed cash-flow bond at the current yield, at a lower yield, and at a higher yield.

The result is expressed in years, but it is best read as a price-sensitivity number. A duration of 7 means an approximate 7% price move for a 1 percentage point yield change before convexity adjustments. Because the calculator also shows the up-yield and down-yield prices, you can see both the slope estimate and the actual prices behind it.

Use this page with the bond convexity calculator for second-order curvature, the bond YTM calculator to solve the starting yield from price, and the bond price calculator to model price directly from a yield. The yield to call calculator is the better sibling when early redemption is the main risk.

Inputs and compute behavior

Enter face value, annual coupon rate, coupon frequency, years to maturity, yield to maturity, and yield differential. The calculation converts coupon rate, yield to maturity, and yield differential from percentages to decimals, then discounts each coupon and the final face value by the yield per coupon period.

Total periods are rounded from years times coupon frequency. The coupon per period is face value times annual coupon rate divided by coupon frequency. The calculator rejects inputs that would make the lower-yield scenario less than or equal to negative 100%, because discounting would stop making sense.

The lower-yield price is labeled “Price if yield falls” and the higher-yield price is labeled “Price if yield rises.” The formula uses the difference between those two values, divided by twice the current price and the decimal yield shock.

Formula

Coupon per period is:

coupon per period=face value×annual coupon ratecoupon frequency\text{coupon per period} = \frac{\text{face value} \times \text{annual coupon rate}}{\text{coupon frequency}}

Bond price is:

price=∑k=1ncoupon(1+r)k+face value(1+r)n\text{price} = \sum_{k=1}^{n}\frac{\text{coupon}}{(1 + r)^k} + \frac{\text{face value}}{(1 + r)^n}

Effective duration is:

effective duration=Pyield down−Pyield up2×P0×Δy\text{effective duration} = \frac{P_{\text{yield down}} - P_{\text{yield up}}}{2 \times P_0 \times \Delta y}

Here P0 is the current modeled price and the yield differential (delta y) is expressed as a decimal. A 1 percent shock is entered as 1 in the form and used as 0.01 in the formula.

Worked example

Use the defaults: face value $1,000, annual coupon rate 5%, annual coupon frequency 1, years to maturity 10, yield to maturity 8%, and yield differential 1%. The annual coupon and coupon per period are both $50.00.

At the starting 8% yield, the modeled price is $798.70. When the yield falls to 7%, the price rises to $859.53. When the yield rises to 9%, the price falls to $743.29. The numerator is $859.53 minus $743.29, or $116.23. The denominator is 2 times $798.70 times 0.01, or about $15.97. The effective duration is therefore 7.277 years, which is the displayed result.

The approximate price move for the selected shock is duration times the decimal shock, displayed as a percent. In this example, 7.2765 times 0.01 equals 7.277%. That estimate is useful, but the actual price gains and losses are not exactly symmetric because convexity bends the price-yield curve.

How effective duration is used

Duration helps investors compare rate exposure across bonds and funds. A short bond fund may have a duration near two years, while a long Treasury portfolio may have a much higher duration. If yields rise quickly, the longer-duration portfolio generally has the larger price decline. If yields fall, it generally has the larger price gain.

The measure is also used in asset-liability matching. Pension plans, insurers, and income-focused investors often compare asset duration with future spending or liability timing. If asset duration is far shorter than liability duration, reinvestment risk may dominate. If it is far longer, market value may swing too much when rates change.

Tips and limitations

  • Use consistent yield shocks when comparing multiple bonds.
  • Pair duration with bond convexity for larger rate moves.
  • Do not assume the same duration for callable and noncallable bonds with similar maturities.
  • Remember that credit spreads can move independently of Treasury yields.
  • Use coupon payment first if you need to verify the cash-flow schedule.

Effective duration is a sensitivity estimate, not a guaranteed return. It assumes a parallel yield move and fixed cash flows. Real market returns can differ because of convexity, credit changes, liquidity, taxes, reinvestment rates, and embedded options.

Sources

Research correction boundary: Describe this as a fixed-cash-flow, rounded-period, flat-yield discounting scenario. Remove callable-bond/option-adjusted applicability, portfolio comparisons, asset-liability recommendations, and claims of an authoritative effective-duration convention until an exact standard or peer-reviewed formula passage is source-challenged.

Frequently asked questions

What does effective duration measure?
Effective duration estimates the percentage price sensitivity of a bond to a change in yield. It uses the difference between a lower-yield price and a higher-yield price, so the result is expressed in years but interpreted as rate-risk exposure.
How is effective duration different from Macaulay duration?
Macaulay duration is a weighted average timing measure for fixed cash flows. Effective duration is based on repricing when yields move. That repricing approach is often used for scenario analysis and can be extended to bonds whose cash flows may change.
What does a duration of 7.277 years mean?
It means a 1 percentage point yield move is estimated to change price by about 7.277 percent before considering convexity. If yields rise, price usually falls by roughly that amount; if yields fall, price usually rises by roughly that amount.
What yield differential should I use?
The yield differential is a user-selected symmetric scenario input. Results depend on that input; this page does not recommend a shock size.
Does effective duration include convexity?
No. Effective duration is a first-order sensitivity estimate based on the slope between two shocked prices. Convexity describes the curvature around that slope. For larger rate changes, use duration and bond convexity together rather than relying on duration alone.
Can I use this for callable bonds?
Use caution. The calculator reprices fixed coupon and principal cash flows and does not change the call decision when rates move. Callable bonds often need option-adjusted duration because the issuer's ability to redeem the bond can alter cash flows.

Related calculators

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