Equity duration and convexity when firms can fail or stagnate

Previous analysis of equity duration and convexity has either ignored the risk that firms can fail or stop growing, or else has incorporated the risk of failure in an ad hoc way. This paper derives equity duration and convexity rigorously corrected for the risk of failure or stagnation. We show that the correction is large enough to be important in standard applications. Further, equity duration is unaffected by any liquidation payout at the time of failure.