Modified duration
(MD).
Modified duration is an estimate of the market price sensitivity of an instrument, to small changes in yield.
It is the 'proportional 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 annual yields 'R', modified duration is calculated as:
MD = Duration/[1+(R/n)]
where n = number of compounding periods per year.
For example,
say Duration = 5.00 years,
Semiannual yield R = 6.00% (so n = 2)
and so EAR = 6.09%.
With respect to the EAR:
MD = 5.00/1.0609
= 4.71
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.
