How to Calculate Weighted Duration Bond

Because a bond typically makes fixed interest payments, rising market rates can put a dent in its value. The sooner you recover your initial investment in a bond, the less exposure you have to changing rates. You can measure this risk by calculating a bond’s Macaulay duration. This metric reveals the weighted average number of years it takes to make back your money through a bond’s interest and principal payments. A bond with a higher duration experiences greater price swings when interest rates fluctuate than one with a lower duration.

Multiply a bond’s coupon, or interest, rate by its par, or face, value to determine the annual interest. Add the annual interest to the par value to determine the final payment when the bond matures. For example, assume a bond with four years until maturity pays a 7 percent coupon and has a $1,000 par value. Multiply 7 percent, or 0.07, by $1,000 to get $70 in annual interest. Add $70 to $1,000 to get a final payment of $1,070 at maturity.

Look up the current interest rate, or yield to maturity, of similar bonds on any financial website that provides bond information. In this example, assume similar bonds are yielding 6 percent.

Substitute each year’s annual interest and the final payment at maturity into the formula (P x T)/[(1 + R)^T]. In the formula, P represents the amount of the payment, T represents the year the payment occurs and R represents the yield to maturity for similar bonds as a decimal. Use a different formula for each payment. In this example, you need three formulas for the annual interest payments and one for the final payment. The formulas are ($70 x 1)/[(1 + 0.06)^1], ($70 x 2)/[(1 + 0.06)^2], ($70 x 3)/[(1 + 0.06)^3] and ($1,070 x 4)/[(1 + 0.06)^4].

Solve each formula. In this example, add 1 to 0.06 and raise the result to the first power to get 1.06. Multiply $70 by 1 to get $70. Divide $70 by 1.06 to get $66.04 for the first formula. The second through third formulas equal $124.60, $176.32 and $3,390.16, respectively.

Add each result. In this example, add $66.04, $124.60, $176.32 and $3,390.16 to get $3,757.12.

Divide your result by the bond’s current market price to determine the bond’s duration. You can find out the bond’s market price from your broker or from the Financial Industry Regulatory Authority’s website. Concluding the example, assume the bond’s price is $1,034.65. Divide $3,757.12 by $1,034.65 to get a duration of 3.63 years.

Tip

  • Compare a bond’s duration with those of other bonds to determine which has a lower risk of price fluctuations. For example, a bond with a duration of 3.63 years has lower risk than one with 4.5 years.

Warning

  • A bond’s duration measures only a bond’s sensitivity to interest rates, but there are other risks to consider when buying a bond, such as the issuer’s creditworthiness.