Modified Duration Calculator

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. The yield cannot be negative and Macaulay duration must be above zero.

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.