Modified duration

(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

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.

See also

• CertFMM
• Convexity
• Duration
• Effective annual rate
• Macaulay duration
• Matching
• Modified convexity
• Price value of a basis point
• Semi-annual rate
• Volatility