what modified duration can tell you
modified duration measures the average cash weighted term to maturity of a bond it is a very important number for portfolio managers financial advisors and clients to consider when selecting investments because all other risk factors equal bonds with higher durations have greater price volatility than bonds with lower durations there are many types of duration and all components of a bond such as its price coupon maturity date and interest rates are used to calculate duration here are some principles of duration to keep in mind first as maturity increases duration increases and the bond becomes more volatile second as a bond s coupon increases its duration decreases and the bond becomes less volatile third as interest rates increase duration decreases and the bond s sensitivity to further interest rate increases goes down example of how to use modified durationassume a 1 000 bond has a three year maturity pays a 10 coupon and that interest rates are 5 this bond following the basic bond pricing formula would have a market price of market price 100 1 05 100 1 0 5 2 1 100 1 0 5 3 market price 95 24 90 70 950 22 market price 1 136 16 begin aligned text market price frac 100 1 05 frac 100 1 05 2 frac 1 100 1 05 3 phantom text market price 95 24 90 70 950 22 phantom text market price 1 136 16 end aligned market price 1 05 100 1 052 100 1 053 1 100 market price 95 24 90 70 950 22market price 1 136 16 next using the macaulay duration formula the duration is calculated as macaulay duration 95 24 1 1 136 16 90 70 2 1 136 16 950 22 3 1 136 16 2 753 begin aligned text macaulay duration bigg 95 24 times frac 1 1 136 16 bigg quad bigg 90 70 times frac 2 1 136 16 bigg quad bigg 950 22 times frac 3 1 136 16 bigg 2 753 end aligned macaulay duration 95 24 1 136 161 90 70 1 136 162 950 22 1 136 163 2 753 this result shows that it takes 2 753 years to recoup the true cost of the bond with this number it is now possible to calculate the modified duration to find the modified duration all an investor needs to do is take the macaulay duration and divide it by 1 yield to maturity number of coupon periods per year in this example that calculation would be 2 753 1 05 1 or 2 62 this means that for every 1 movement in interest rates the bond in this example would inversely move in price by 2 62 