Modified duration

(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.

See also

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