The Basics of Modified Duration for Bond Calculations

Bond duration is a measure of a bond's value using a comparison between price and interest rate of the bond. Basically, these two factors tend to move together to offset potential changes in a bond's value. If the interest rate a bond promises to deliver goes up, making it more desirable, the bond will become more expensive. If the interest rate drops, making it less desirable, the bond will become cheaper. Modified duration takes the basic comparison of bond duration and uses it to determine how much the price of a bond will change if its interest rate changes one percent.

Bond Price

The price of a bond is not equivalent to its value. Some people get confused and think the price ultimately determines the value, but there are more factors at play. The price is simply the amount of money the issuing organization is asking for in order to issue the debt note. 

Bond Interest Rate

Interest rate is the second factor that comes into play when attempting to determine the value of a bond. The interest rate is how much the bond will pay out in coupons per year every year until maturity. Bonds with higher prices tend to have higher interest rates. This means, to get a part of the most profitable bond issuance, an investor must pay more.

Bond Risk

The value of a bond partly depends on the riskiness of the bond, which is slightly harder to measure. If one bond has a very high interest rate and low price but presents a high risk of losing all its value in the coming year when an issuing organization defaults, then its value is actually very low. These three factors all come into play, making it hard to determine the actual value of a bond at any given time. In order to assist with this estimation, advisers developed the bond duration formula. 

Bond Duration

Duration is a measure of a bond's price over its interest rate across a given period of time. The more stable a bond's duration is over time, the less risky a bond will be, and the more valuable it will be as a result. Duration pulls the three elements together, expressing price relative to the potential profit of a bond. If duration is consistent, the investor knows that the value of a bond will remain stable, giving her the ability to sell the bond for profit or capitalize on promised returns over the life of the bond.

Bond Modified Duration

Modified duration takes the duration formula one step further. It places duration over a formula of one plus the yield to maturity (YTM) over the number of coupon periods. This sounds complicated, but it is similar to the formulas used to determine the value of a car loan, home loan or other financial instrument with a consistent interest rate and number of payment periods. When you know the modified duration of the bond, you know how much you can expect the bond's value to change when the interest rate changes, which gives you insight into its worth over time. 

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