In the notes, Macaulay duration = (1+i ) volatility. Modified duration = Macaulay duration/(1+i) = (1+i) v(i)/(1+i) Mod duration = volatility,v(i). Question is when are the two measures modified duration and volatility different ?
To start off with I'll say that modified duration has never been examined in either CM1 or its predecessor CT1. So don't let this trouble you too much. The practical use of volatility and modified duration is to help us to estimate the change in price that will occur when the underlying yield changes from its current value. vol = Macaulay duration / (1+i). This relates to the case where the underlying yield is quoted as an annual effective interest rate. It can be used to estimate the change in the price that will occur when the yield expressed as an annual effective interest rate changes by a given amount. Modified duration = Macaulay duration / (1 + i(p)/p). This relates to the case where the underlying yield is quoted as a nominal rate of interest convertible p times per year. It can be used to estimate the change in price that will occur when the yield expressed as a nominal rate of interest convertible p times per year changes by a given amount. When p = 1, the nominal rate is convertible annually, so it is an annual effective rate. In this case vol = modified duration. Otherwise they are different.
