Modified Duration

"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 yieldOften - 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. 71With respect to the Semiannual yield: MD = 5. 00/1. 03 = 4. 85This 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.
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