Duration and convexity of zero-coupon convertible bonds

Duration and convexity are important measures in fixed-income portfolio management. We have derived closed-form expressions for duration and convexity of zero-coupon convertibles, incorporating the impact of default risk, conversion option, and subordination. The overall effect is to shorten duration, while the effect on convexity is ambiguous. Both measures were found to be very different from those of straight bonds, in magnitude and in their response to parameter changes; e.g., a subordinated convertible duration can even be negative. Thus, it would be inappropriate to use traditional duration/convexity measures for evaluating or hedging interest rate risk in convertibles.