Modified duration estimates bond price changes. Investors can use modified duration to assess the price volatility of individual bonds or an overall portfolio. Frederic Macaulay developed the Macaulay duration in 1938 to measure the number of years required to recover the true value of a bond. Modified duration expands upon the Macaulay duration to measure the percentage change in a bond’s price for a 100 basis point change in interest rates.
Determine the bond’s coupon rate and coupon dollars. The coupon rate is the stated rate of interest on the bond. This rate divided by 2, multiplied by $1,000, equals the coupon dollars.
Determine the present value factor using the yield per period, calculated as 1 / (1+i)^t. Divide the market yield by 2 to find the yield per period and substitute for “i” in the equation; “t” is the payment number.
Multiply the present value factor by the coupon dollars to determine the present value of the coupon payment.
Repeat the above steps for each payment bond payment. Add the present values of all future coupon payments; this sum is the market value of the bond.
Divide the present value of each coupon payment by the calculated market value of the bond. For each result, multiply the result by the number of years that have elapsed; multiply that result by -1. The result is the bond duration for that year.
Sum all durations to arrive at the Macaulay duration – the total weighted average time for recovery of payment and principal in relation to the current market price of the bond. Solve the formula 1/(1+i) to calculate the modified duration factor; “i” represents the market yield divided by 2.
Multiply the Macaulay duration by the modified duration factor. The result is the modified duration, which represents the approximate change in bond value for a 100 basis point change in interest rates.
You can use the modified duration to calculate the percent change in bond value. Multiply the change in yield by the modified duration to calculate the percentage change. This percent multiplied by the current market value of the bond estimates the new price of the bond.
Calculating the Macaulay duration and modified duration is an intensive calculative process. Spreadsheets and on-line applications can help automate these calculations.
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