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Modified Duration Calculator

Enter Macaulay duration, yield to maturity, and coupon frequency.

How it is calculated

Modified duration rescales Macaulay duration by the yield: ModDur = Macaulay / (1 + YTM / (100 × f)). Macaulay duration is in years, YTM is the yield to maturity as a percentage (5 for 5 percent) and f is the number of coupon payments per year (2 for semi-annual, 1 for annual). If the frequency is left empty the tool assumes 2. The estimated price change for a one percentage point rise in yield is −ModDur × 1, shown as a percentage with a minus sign. This is a linear approximation: it ignores convexity, so it is accurate for small yield moves and less so for large ones. A negative yield is accepted as long as the divisor stays above zero, and Macaulay duration must be above zero.

Worked example

A bond has a Macaulay duration of 6.5 years, a yield to maturity of 5 percent and pays coupons twice a year. The yield per period is 5 / (100 × 2) = 0.025. Modified duration: 6.5 / 1.025 = 6.341, shown as 6.341. So if yields rise by one percentage point, the bond's price is expected to fall by about 6.34 percent, which the tool displays as −6.34%. If the same bond paid annually, the divisor would be 1.05 and the result 6.190.

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Common mistakes

  • Entering the yield as a decimal (0.05) instead of a percentage (5). The tool then divides by almost nothing and the modified duration comes out almost equal to the Macaulay duration.
  • Using the wrong coupon frequency. Semi-annual bonds need 2, annual bonds 1; with the wrong value the answer shifts, as 6.341 versus 6.190 in the example above.
  • Mixing up Macaulay and modified duration. The first is a time in years; the second is a sensitivity. Enter the Macaulay figure here, not a modified duration you already have.
  • Applying the price change to a large yield move. The estimate is for one percentage point and ignores convexity, so for a 3 point rise it understates the price after the move.
  • Reading the minus sign as a loss that always happens. It shows the direction for a yield rise; if yields fall by one point the price rises by about the same amount.

Sources

About this calculator

Macaulay duration measures the weighted-average time (in years) until a bond's cash flows are received. Modified duration converts that into a direct measure of price sensitivity: it's Macaulay duration divided by (1 + yield/coupon frequency), and it approximates the percentage change in a bond's price for a 1 percentage-point change in yield.

This calculator converts your bond's Macaulay duration into modified duration using its yield to maturity and coupon payment frequency, then estimates the price impact of a 1% yield move. Fixed-income investors and portfolio managers use modified duration to gauge how exposed a bond or bond portfolio is to interest rate risk — a bond with a modified duration of 7 will drop roughly 7% in price if yields rise 1%.

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Comments (1)

  • Editorial team

    This tool needs the Macaulay duration as an input; it does not derive it from cash flows. For a zero-coupon bond the Macaulay duration equals the time to maturity, so a 5-year zero at 4 percent with semi-annual compounding gives 5 divided by 1.02, about 4.902. For coupon bonds, take the figure from a factsheet or your own cash-flow sheet. Where do you usually find duration numbers?

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