Modified duration

Before you rely on it

What to check

For a large yield move, add a convexity adjustment.

The common error

Where people go wrong with modified duration

Extrapolating it across a big rate shock. The estimate is a straight line drawn against a curve, and it lies further the harder you push.

Worked through

Modified duration in plain numbers

A bond has a Macaulay duration of 8 years and a yield of 5%, compounded annually. Modified duration is 8 ÷ 1.05, or 7.62. If yields rise by one percentage point, the price is estimated to fall about 7.6%. If yields fall by one point, it rises about the same. With semiannual compounding, the divisor is 1 plus half the yield, so 8 ÷ 1.025, or 7.80. On a $10,000 holding, a 0.5 point rise costs roughly $381. Modified duration makes duration usable: it converts a timing measure in years into a price sensitivity.

Easily confused

Modified duration and its neighbours

Modified duration is not Macaulay duration, but a scaled version of it. Macaulay is the weighted average time to receive cash flows, in years. Modified divides by one plus the periodic yield to give the percent price change per unit change in yield. Effective duration measures the same sensitivity for bonds with options by repricing. DV01 is dollar sensitivity to one basis point. When someone says duration in the market, they usually mean modified or effective duration.

In real decisions

Where modified duration turns up

Bond managers use it to gauge and control interest-rate risk; a fund with a modified duration of 6 is expected to lose about 6% for a one-point rise in yields; investors compare funds with it. Analysts use it in hedging and immunization. It also helps convert a forecast of rate moves into an estimate of gains or losses across a portfolio.

Know the edges

Where modified duration stops being reliable

It is a linear approximation and works for small yield changes. For larger moves, convexity matters. It assumes cash flows do not change with rates, which fails for callable and prepayable bonds; it assumes a parallel shift in yields; it says nothing about credit risk. Use it as a guide to sensitivity rather than a precise prediction.

Quick answers

What people ask about modified duration

What yield do I use? The bond's yield to maturity, expressed per period. Divide Macaulay duration by one plus that yield, using the compounding frequency of the bond.

Why does the estimate get worse for large moves? Because price responds to yield in a curve, not a straight line. Convexity adds the correction for the bend.

Can modified duration be greater than maturity? For a standard bond, no. It is at most the maturity, and it equals it only for a zero-coupon bond, before the yield adjustment.

What is the difference between modified and effective duration? Modified duration assumes cash flows do not change when yields move. Effective duration reprices the bond and works for bonds with options.

Can duration be used for a stock? Some analysts estimate an equity duration, but it is less reliable. The concept fits fixed cash flows best.