# possibly a stupid duration question

I am having trouble distinguishing between modified and effective duration. Can someone explain? From my pov, mod duration is just effective duration for 100 bps?

hi there, led me shed a little bit of light on the topic. there a basically 3 versions of the duration measure: 1. MacAuley duration 2. modified duration 3. effective duration 1. macauley duration. this is the earliest concept of duration devised by a guy called macAuley it measures the weighted average time until maturity, and gives rougly an estimate on when CFs are reveived. its calculated in the following way: compute the PVs of any cashflow occuring during the lifetime of your fixed income security, divide each PV by the NPV and multiply the result with the time until maturity, add all those values up. note however, that duration in this form is not so well understood/interpreted. 2. modified duration this is the most important interpretation of duration. it measures the sensitivity of the FI security with respect to changes in interest rates. this is a most important concept. macauley duration and modified duration are interrelated. the following relation holds: modDUR=macDUR/(1+ytm/n) where ytm is the yield and n the number of compounding periods. when you use continous compounding modDUR is the same as macDUR, although in practice your most likely to encounter continous compounding only in derivative pricing in my opinion, so you can safely disregard this for now. note: up until now i have just given you same background info… this didnt show up in this way in the curriculum. modDUR is also equivalent to the slope of the tangent at the price-yield relationship for a given yield level. because the slope of a tangent is linear, duration is only a first-order approximation for changes in value when yields change. the quality of this approximation decreases the higher the change in yields; in this case you should incorporate “higher-order” terms (such as convexity) to improve your approximation. conceptually this is: % change in price / % change in yield 3. effective duration for vanilla bonds (option-free) it’s the same as modDUR. effDUR takes the impact of embedded options into account. for example take the typical callable bond; its price yield-relationship, at lower yield levels, will converge to the call price and will not go beyond it. algebraically you can calculate it as effDUR=(V- ./. V+)/(2*V0*deltaY), where V-= the value of the bond for a small decrease in yield (typically 1bps, i.e. -0.0001, or +0.01%) V+= the value of the bond for a small increase in yield (typically 1bps, i.e. +0.0001, or +0.01%) V0=the value of the bond before the yield change deltaY=the change in yield (in decimal form) this is the familiar form as we are given in the curriculum. in my opinion here is a point worth noting… we are calculating V- and V+ (using an EXACT valuation model) to input it into a duration equation which we use to give ESTIMATES about price changes… why not stick with the exact valuation model in the first case so we’re not depending on estimates? my 2cents. another point worth mentioning is that, throughout the curriculum, we have been using the effDUR formula for calculating the modDUR. this of course, we only calculated duration for vanilla bonds, so we know the valuation model (or at least or TI/HP does). we havent calculated any effDUR for embdedded options bonds, i.e. the case we really need to it). the reason of course is that many of us are lacking the background in option pricing theory which is necessary for this. my 2cents again. —bottom line— effective duration = modified duration IF vanilla bond effective duration <> modified duration IF bond with embedded options (valuation model needed) effDUR explicitly considers the embedded option within it. it is not just modDUR for 100 bps yield change. EDIT: found a nice overview at investopedia, have a look at it. http://www.investopedia.com/university/advancedbond/advancedbond5.asp

Chefe_: EXCELLENT!

good review!