Why modified duration matters
It provides a practical, comparable measure of first-order interest-rate risk. Portfolio managers use it to set rate exposure, estimate gains and losses, compare securities, and size hedges.
How it is applied
Modified duration equals Macaulay duration divided by one plus yield per compounding period. Approximate price change is negative modified duration multiplied by the yield change in decimal form. Modified duration converts Macaulay duration into an estimate of percentage price sensitivity to a yield-to-maturity change. It is calculated using the bond’s yield and compounding frequency. Managers multiply modified duration by a small yield change to approximate price return before convexity and credit effects.
Portfolio example
A bond with modified duration of six is expected to lose about 3% if its yield rises by 0.50 percentage points, before convexity and other effects. A fall of the same size produces an approximate 3% gain. A bond with modified duration of 6.2 is expected to lose about 3.1% if its yield rises 0.50 percentage points, calculated as minus 6.2 times 0.005. Convexity may adjust the actual result, and accrued income contributes separately to total return.
How to interpret it
Higher modified duration means greater local sensitivity to yield. The minus sign expresses the usual inverse price-yield relationship. The estimate applies to the specified yield measure, not automatically to every curve point or credit spread. Higher modified duration means greater local sensitivity to a parallel change in the bond’s yield. It is most appropriate for option-free instruments with fixed cash flows. Comparing duration contributions can show which holdings drive portfolio interest-rate exposure even when their market weights are modest.
Limitations and common misconceptions
It assumes fixed cash flows and a small, generally parallel yield move. Convexity matters for larger changes, and callable or prepayable securities require effective duration. Credit, liquidity, currency, and default effects are separate. The approximation weakens for large yield moves and nonparallel curve shifts. Yield-to-maturity treats all cash flows as if one discount rate applied. Callable, puttable, and prepayable securities require effective-duration models because their expected cash flows can change when rates move.
Sources and further reading
- Fixed-Income Securities: Defining ElementsCFA Institute
- Fixed-Income Bond Valuation: Prices and YieldsCFA Institute
- BondsFINRA