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.
