A modified duration is a process that identifies the amount of change in value that a particular security experiences when interest rates change. The idea behind this type of measurement is that bond prices and interest rates tend to move is different directions. This means that if the interest rate associated with the bond issue increases, the price of the bond decreases.
In understanding the concept of modified duration, it is important to note that the bond price and the value of the bond issue are not necessarily the same. The bond price is simply the amount that the issuing entity is asking for the bond. In contrast, the bond value is based on more criteria than simply the asking price. Differentiating between the two makes it easier to understand how a modified duration works, since the bond price does not respond to changes in the interest rate in the same manner that a bond value responds.
One factor that does impact the bond value is the degree of risk associated with the issue. While somewhat subjective, this factor can indicate that even if the relationship between the interest rate and the bond price are constant, questions about the stability of the entity issuing the bond may mean that more risk is present. Additional risk can have a negative effect on the value of the bond, in terms of the number of investors who are willing to buy into the bond issue, without necessarily exerting any influence on the bond price.
The basic formula for calculating a modified duration involves comparing the current price and the interest rate attached to the bond issue. In most situations, these two factors will tend to move in opposite directions. That means if interest rates go up, the bond price may go down and the bond gains in value to investors who find the issue more desirable, owing to the chance to earn a higher return while making a smaller investment. Should the interest rate drop, the bond becomes less attractive to investors and the value to investors is likely to decrease accordingly. Once the comparison is made, it is possible to determine what a shift in interest rate would do to the bond value between the time the change occurs and the maturity date of the bond.
In actual practice, this means that the modified duration uses a formula with a one plus the yield to maturity to determine the impact of the interest rate change on the bond value. While this may appear to be somewhat convoluted, this process is not unlike the formulas used to predict the change that occurs with a mortgage carrying a floating or variable rate. By identifying the change in the interest rate, the investor can determine what type of return can be reasonably expected over the life of the bond if that change should actually occur.
