# Modified duration

(MD).

Modified duration is an estimate of the market price sensitivity of an instrument, to small changes in yield.

It is the related proportionate price change of a market instrument or portfolio.

The estimate of change in market price is given by:

**Modified duration x Starting Market price x Change in yield**

Often - but not always - the relevant yield is defined as the annual effective yield (EAR).

For changes in EAR, modified duration is calculated from Macaulay’s duration as:

MD = Duration / (1 + EAR)

For changes in simple nominal annual yields (R), modified duration is calculated as:

MD = Duration / (1 + (R / n) )

where n = number of compounding periods per year.

**Example: Modified duration calculations**

Duration = 5.00 years.

Semiannual yield R = 6.00% (so n = 2)

and so EAR = 6.09%.

(i) With respect to the EAR:

MD = 5.00 / 1.0609

= 4.71

(ii) With respect to the Semiannual yield:

MD = 5.00 / 1.03

= 4.85

This shows that there would be a greater proportionate change in price for a 1% change in the Semiannual yield, than for a 1% change in the EAR.