Modified duration

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(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.


See also