Annuity factors, duration, and convexity: Insights from a financial engineering perspective

This paper applies a unified and integrative financial engineering perspective to key derived concepts in traditional fixed income analysis, with the purpose of enhancing conceptual insights and motivating computational applications. The emphasis on annuity factors and their impact on duration and convexity differs from the focus prevailing in related discussions. By decomposing the cashflow streams of a coupon bond into different, specific, and clearly defined portfolios of component bonds with known duration and convexity measures, equivalent but appearently different expressions for the coupon bond’s duration and convexity are obtained as particular weighted averages. One such convexity formula closely corresponds to Babcock’s (1985) formula for duration. The Fabozzi (1993) shortcut duration formula does not immediately carry over to convexity, but the required modifications are derived. The interrelationships between various durations, convexities, and annuity factors or transformations thereof are also exhibited. Throughout the paper the results are illustrated numerically, for a particular coupon bond discussed elsewhere in the literature.