Modified duration
What is Modified duration?
Modified duration estimates the percentage change in a bond's price for a small one-percentage-point change in yield, holding other factors constant.
How modified duration works
Modified duration adjusts Macaulay duration for the bond's yield and compounding frequency. For a small yield change, approximate price change equals negative modified duration multiplied by the change in yield. The negative sign reflects the usual inverse relationship between fixed-rate bond prices and yields. It is a sensitivity, not a forecast.
Example
A bond with modified duration of five is expected to lose about 5% if its yield rises by one percentage point and gain about 5% if yield falls by one point, before convexity. For a 0.25-point rise, the first-order estimate is a 1.25% decline. Actual price change depends on curvature and changing cash flows.
Modified versus other duration
Macaulay duration is expressed as a weighted time, modified duration as price sensitivity, and effective duration estimates sensitivity by repricing under curve shocks when cash flows may change. Key-rate durations allocate sensitivity to maturity points. The unqualified label duration can refer to different measures across systems, creating avoidable reporting and hedging errors.
How to interpret it
Confirm whether yield means the bond's own yield, a government curve, or another spread-inclusive rate. A portfolio's modified duration may approximate a parallel shift but hide curve exposures. Separate rate and credit-spread duration when analyzing corporate bonds. Compare with limits and with the duration of liabilities or the selected benchmark.
Limitations
The linear approximation is less accurate for large yield changes and instruments with strong convexity or embedded options. It assumes other variables remain constant and usually does not capture default, liquidity, currency, or volatility. A one-number measure cannot describe steepening, flattening, or twists across several yield curves.
Practical checklist
Record the formula, compounding frequency, curve, and bump convention used by each data source. Reprice sample securities to verify sensitivities. Combine modified duration with convexity, key-rate duration, spread sensitivity, and scenarios. For hedging, compare dollar duration rather than percentages alone, and monitor how duration changes as yields, time, and option exercise probabilities change. Reconcile results after every material trade.