Modified duration: Difference between revisions
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MD = Duration/ | MD = Duration / ( 1 + EAR ) | ||
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MD = Duration/ | MD = Duration / ( 1 + ( R / n ) ) | ||
where n = number of compounding periods per year. | where n = number of compounding periods per year. | ||
'''Example''' | |||
Duration = 5.00 years. | |||
Semiannual yield R = 6.00% (so n = 2) | Semiannual yield R = 6.00% (so n = 2) | ||
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With respect to the EAR: | With respect to the EAR: | ||
MD = 5.00/1.0609 | MD = 5.00 / 1.0609 | ||
= 4.71 | = 4.71 | ||
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With respect to the Semiannual yield: | With respect to the Semiannual yield: | ||
MD = 5.00/1.03 | MD = 5.00 / 1.03 | ||
= 4.85 | = 4.85 | ||
Revision as of 16:39, 16 March 2015
(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.
Example
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.
