How to Calculate Modified Duration

In many ways, bonds are more complex than stocks. Investors use a host of different metrics to evaluate bond investments, and one involves a concept known as duration, which helps an investor understand how sensitive a bond's value is to interest rate changes. There are several different types of duration calculations, but one involves what's known as modified duration and produces the percentage change in price for a given change in interest rates.

A two-step process to calculate modified durationThe easiest way to come up with the modified duration for a bond is to start by calculating another type of duration called Macauley duration. This type of duration produces the weighted average time in which the investor will receive cash flows from the bond.

To calculate Macauley duration, you have to figure out the timing of all cash flows from the bond. Most bonds make relatively small interest payments and then make a big principal repayment at maturity.

Once you know how much and when all payments will be made, you have to time-weight their discounted values. To do so, take the present value of each bond payment, discounted by the current yield to maturity. Keeping each present value separate, multiply the present value by the period in which the payment is made. For instance, with a two-year bond paying annual interest payments, you'll multiply the present value of the first payment by 1 and the second payment by 2. Then add those numbers together and divide by the present value of all the bond's payments.

For example, say you have a two-year bond paying annual interest at 5% and with a yield to maturity of 5%. Its current price is $1,000. The present value of the first payment would be (1000 x 5%) / (1 + 5%), or $47.62. The present value of the second payment, including the maturity amount, would be ((1000 + (1000 * 5%) / (1 + 5%)^2), or $952.38. So the Macauley duration would be (($47.62 x 1) + ($952.38 x 2)) / ($47.62 + $952.38), which works out to 1.952.

To calculate modified duration, you take the answer above and divide it by the sum of 1 and the bond's yield to maturity. So 1.952 / (1 + 5%) = 1.859.

What modified duration meansThe modified duration tells you how much the price of a bond will change for a given change in its yield. So in the example above, investors can expect to see a 1.859% move in price when the bond's yield to maturity changes by one percentage point.

In general, the longer the maturity of a bond, the higher its modified duration. Higher-interest bonds tend to have smaller modified durations because more of their cash flow comes from interest payments that come sooner in the bond's lifespan.

Bonds that have high modified durations are especially subject to interest rate risk. When rates are looking to head higher, looking at modified duration is important to understand exactly what could happen in a rising-rate environment.

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