Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 14. Effective Duration and Convexity

GERALD W. BUETOW Jr., PhD, CFA

President and Founder, BFRC Services, LLC

ROBERT R. JOHNSON, PhD, CFA

Deputy CEO and Managing Director, CFA Institute

Abstract: Modified duration and effective duration are two ways to measure the price sensitivity of a fixed income security. Both measure the percentage price change of a security from an absolute change in yields. Effective duration is a more complete measure of price sensitivity since it incorporates embedded optionality while modified duration does not. Combining effective duration with effective convexity is a superior risk management and measurement approach than using modified duration and convexity. In general, for fixed income securities with embedded options numerical approaches (effective) to risk measurement are superior to analytic (modified) approaches.

Keywords: duration, convexity, effective duration, standard convexity, Black-Derman-Toy model, straight bond, callable bond, putable bond, option-free bond, price compression, truncated price, negative convexity

Modified, duration ignores any effect on cash flows that might take place as a result of changes in interest rates. Effective duration does not ignore the potential for such changes in cash flows. For example, bonds with embedded options will have very different cash flow properties as interest rates (or yields) change. Modified duration ignores these effects completely. In order to apply effective duration, an available interest ...