# How to Calculate Weighted Effective Duration

by C. Taylor

Duration is typically calculated for bonds as a way to access the overall risk involved in the investment. Bonds pay a fixed amount each payment period, with the last payment including the face value of the bond. Duration takes each of these periodic payments into account and weighs them against the payment time. The final duration figure offers the amount of effective time before recovering your original investment.

1. Divide the bond's coupon rate and yield by the number of periods in a year. This gives you the periodic coupon and yield rates. As an example, a bond that pays a 6 percent coupon rate twice per year with an annual yield of 8 percent would have a 3 percent periodic coupon rate and a 4 percent periodic yield.

2. Multiply the periodic coupon rate times the bond's face value to calculate the periodic payments. If the example bond had a \$1,000 face value, it would offer \$30 coupon payments twice per year. The final payment would be \$1,030, because the face value of the bond is also included.

3. Add 1 to the periodic yield rate, then raise this figure to the power of the payment number. Divide the result into that period's payment to calculate its present value. Repeat this calculation for each payment. Continuing with the example, raising 1.04 to the power of 3, and then dividing it into \$30 calculates the present value of the third payments, which results in 26.67. For a 2-year bond, the values would be \$28.85, \$27.74, \$26.67 and \$880.45 for each of the four payments.

4. Add each of these present values to get the bond's present value. In the example, the bond's present value is \$963.71.

5. Multiply each of payments' present values by its payment number, then divide by the bond's present value. In the example, this results in values of 0.0299, 0.0576, 0.0830 and 3.654, respectively.

6. Add each of these values to calculate the weighted effective duration. In the example, this means the bond would effectively take 3.825 years before you recouped the original investment.