Modified duration: Difference between revisions
imported>Kmacharla No edit summary |
imported>Doug Williamson m (Spacing 22/8/13) |
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(MD). | (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. | |||
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: | 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'). | Often - but not always - the relevant yield is defined as the annual effective yield ('EAR'). | ||
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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] | |||
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)] | MD = Duration/[1+(R/n)] | ||
where n = number of compounding periods per year. | 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%. | ||
With respect to the EAR: | With respect to the EAR: | ||
MD = 5.00/1.0609 = 4.71 | MD = 5.00/1.0609 = 4.71 | ||
With respect to the Semiannual yield: | With respect to the Semiannual yield: | ||
MD = 5.00/1.03 = 4.85 | 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. | 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 == | == See also == | ||
Revision as of 08:51, 22 August 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.
