Modified duration: Difference between revisions
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For changes in EAR, modified duration is calculated from Macaulay’s duration as: | 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: | 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%. | For example, say Duration = 5.00 years, Semiannual yield R = 6.00% (so n = 2) and so EAR = 6.09%. | ||
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* [[Semi-annual rate]] | * [[Semi-annual rate]] | ||
* [[Volatility]] | * [[Volatility]] | ||
Revision as of 14:36, 28 May 2013
(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.
