Modified duration: Difference between revisions
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Modified duration is an estimate of the market price sensitivity of an instrument, to small changes in yield. | Modified duration is an estimate of the market price sensitivity of an instrument, to small changes in yield. | ||
It is the | It is the related proportionate price change of a market instrument or portfolio. | ||
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Often - but not always - the relevant yield is defined as the annual effective 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: | 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 | For changes in simple nominal 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. | ||
'''Example''' | <span style="color:#4B0082">'''Example: Modified duration calculations'''</span> | ||
Duration = 5.00 years. | Duration = 5.00 years. | ||
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With respect to the EAR: | (i) With respect to the EAR: | ||
MD = 5.00 / 1.0609 | MD = 5.00 / 1.0609 | ||
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With respect to the Semiannual yield: | (ii) With respect to the Semiannual yield: | ||
MD = 5.00 / 1.03 | MD = 5.00 / 1.03 | ||
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== See also == | == See also == | ||
* [[Convexity]] | * [[Convexity]] | ||
* [[Duration]] | * [[Duration]] | ||
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* [[Semi-annual rate]] | * [[Semi-annual rate]] | ||
* [[Volatility]] | * [[Volatility]] | ||
[[Category:Financial_management]] | |||
[[Category:Corporate_finance]] | |||
Latest revision as of 12:29, 22 February 2018
(MD).
Modified duration is an estimate of the market price sensitivity of an instrument, to small changes in yield.
It is the related proportionate 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 nominal annual yields (R), modified duration is calculated as:
MD = Duration / (1 + (R / n) )
where n = number of compounding periods per year.
Example: Modified duration calculations
Duration = 5.00 years.
Semiannual yield R = 6.00% (so n = 2)
and so EAR = 6.09%.
(i) With respect to the EAR:
MD = 5.00 / 1.0609
= 4.71
(ii) 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.
