Modified Duration of Bonds

There is an inverse relationship between price and yield. What should be the change in price with a change in yield? It can be answered with the help of duration concept and especially with modified duration. Modified duration is a modified version of the Macaulay model that accounts for changing interest rates. Modified formula shows how much the duration changes for each percentage change in yield. There is an inverse relationship between modified duration and an approximate 1% change in yield. The calculation of the same is as follows:

Where ‘f’ is frequency of payment of coupon

Illustration:

Consider a bond with a YTM of 12% and duration is 5 years. If the interest rate increases by 50 basis points , change in the price of the bond will be..

Modified duration of the bond is 5/1.12 = 4.46 years

Change is price can be calculated as follows:

%ΔPrice = -Dmod ×%Δyield

                  = -4.46 ×0.5 = -2.23%

Hence price will decline by 2.23% for a given change in yield.

As duration is an easy approach to calculate the price change but it also suffers from its own limitations. As we have already understood that for the same change is yield either side, price change is not same but duration assumes that there is a linear movement between price and yield. Hence duration is useful for smaller changes in interest rates but should not be used in isolation when larger changes are predicted. The error caused by duration can be eliminated using the concept of ‘convexity’. Learning convexity is out the scope for the CFP aspirants. So will discuss the same on other time.

I hope you have enjoyed learning bonds.

Thank You.

Prashant V Shah

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