We estimate the stock’s likelihood of extreme returns by measuring the extent to which the stock’s trades are correlated with market-wide and industry-wide trades during normal times, referred to as herding. We find that stocks whose trades herd most with aggregate-level trades experience most negative (positive) returns during market crashes (booms). While herding generates extreme returns in both sides, investors appear to demand compensation for the possibility of extreme low returns. This is the case even when we control for standard asset pricing variables and other tail risk proxies.

Performance share plans are an increasingly important component of executive compensation. They are equity-based, long-term incentive plans where the number of shares to be awarded is a quasi-linear function of a performance result over a fixed time period. We derive closed-form formulas for the value of a performance share plan when the performance measure is: (1) a non-traded measure following an Arithmetic Brownian Motion (e.g., earnings per share), (2) a non-traded measure following a Geometric Brownian Motion (e.g., revenue), or (3) a rank-order tournament of traded asset returns that are following Arithmetic Brownian Motions (e.g., percentile of ranked stock returns). Then we empirically test our valuation formulas. We find that our valuation formulas are more accurate for performance share plans based on earnings per share when forecasting using analyst consensus prior to the grant date. We also find that the efficiency of our valuation model greatly depends on the method used to forecast future firm performance. The policy implication is that FASB should consider requiring that grant date fair value be estimated using valuation formulas such as ours.