Modified duration is a tool bond investors use to measure the sensitivity of a bond’s price to a change in its yield. It is a measure of how much a bond's price may be expected to move up or down as market interest rates rise or fall. It is expressed as a percentage of the current price of the bond and is calculated by looking at how a 1% change in yield will affect the price and cash flow of the bond.

To understand how modified duration works and why it is so important, consider a 10-year semi-annual coupon bond with a 6% coupon. If the yield on comparable bonds were to rise from 6% to 6.1%, the bond price would drop by approximately 6.3%. This means that if the yield rises by 1%, the bond's price will drop by 6.3%. The modified duration of the bond is 6.3%; this is the percentage change in the price of the bond relative to the percentage change in the yield.

Conversely, if the yield on this bond were to fall from 6% to 5.9%, its price would increase by 6.3%, indicating that if the yield falls by 1%, the bond's price will increase by 6.3%, which is the same as its modified duration. This calculation also applies to a bond portfolio, as well as to a single bond.

In summary, modified duration is a way for bond investors to measure the sensitivity of a bond's price to a change in its yield. It expresses how much a bond's price may be expected to move up or down as market interest rates rise or fall. While it is impossible to predict exactly how the bond will react, the modified duration gives a good indication of how the bond's price will likely change in response to a given change in the yield. This is why modified duration is an important concept for bond investors to understand.