## Duration as a Weighted Average of Two Factors

**Abstract**

echnical two equations is easily shown. Duration as a Weighted Average First, the interest present value factor of a one of Two Factors dollar annuity can be written: by Guilford C. Babcock, Associate Professor of Finance, = PVIFA (1/y) [1 - (1 + y)-M]. (3) University Graduate School of Business Administration, Thus the in the first first term Equation (2) equals of Southern California term in Equation (1). Second, the price of any bond can be written: In a recent article in this journal, Jess Chua pre- the dura- sented a closed-form formula for calculating B C(1/y) [1 - (1 + y)m] + F(1 + y)m tion of a bond.* In effect, he eliminated the summa- = C/y - (C/y) (1 + y)m + F(1 + m. (4) y) tion signs from Macaulay's definition to show that: Dividing both B and one we sides by moving term, D = (C/By2) [1 - (1 + + y) y)-M)](l have: - (C/By)M(1 + y)-M + (F/B)M(1 + (1) y)m 1 C/By = -(C/By) (1 + y)-M + (F/B) (1 + y)M. where Thus the second term in Equation (2) equals the C the coupon payment per period, remaining terms in Equation