# Internal Liquidity Adequacy Assessment Process and Modified duration: Difference between pages

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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 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. | |||

<span style="color:#4B0082">'''Example: Modified duration calculations'''</span> | |||

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. | |||

== See also == | == See also == | ||

* [[ | * [[Convexity]] | ||

* [[ | * [[Duration]] | ||

* [[ | * [[Effective annual rate]] | ||

* [[ | * [[Macaulay duration]] | ||

* [[ | * [[Matching]] | ||

* [[ | * [[Modified convexity]] | ||

* [[Price value of a basis point]] | |||

* [[Semi-annual rate]] | |||

* [[Volatility]] |

## Revision as of 14:05, 16 November 2016

(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.