# Modified Duration of a Bond

Modified duration indicates the percentage change in the price of a bond for a given change in yield. It is a more adjusted measure of Macaulay duration that produces a more accurate estimate of bond price sensitivity.

$Modified Duration (MD) = \frac{D}{\left (1+ \frac{y}{m} \right )}$

m is the # of compounding period per year.

The relationship between percentage changes in bond prices and changes in bond yields is approximately:

$\frac{\triangle P}{P}=\triangle \% P\approx -MD \times \triangle y$

Example

Assume a 5-year bond, providing a coupon of 5%, with a current yield of 7%.

The Duration of the bond is 4.52.

The modified duration will be:

MD = 4.52/(1.07) = 4.23

Interpretation

The modified duration of the bond is 4.23. This means that the price of the bond will increase to 4.23 with a 1% or 100 basis point increase in interest rates.

Modified duration provides a good indication of a bond’s sensitivity to a change in interest rates. The more your duration changes with a 1% increase in interest rates, the more volatility your bond will exhibit.

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### One Response to “Modified Duration of a Bond”

1. Vince April 16, 2013 at 9:55 am #

Shouldnt this be a price decrease and not increase?

The modified duration of the bond is 4.23. This means that the price of the bond will increase to 4.23 with a 1% or 100 basis point increase in interest rates.