This paper documents that riskier firms with higher idiosyncratic volatility grant more stock options to nonexecutive employees. Standard models in the literature cannot easily explain this pattern; a model in which a risk-neutral firm and an employee with prospect theory preferences bargain over the employee's pay package can. The key feature which makes stock options attractive is probability weighting. The model fits the data on option grants well when calibrated using standard parameters from the experimental literature. The results are the first evidence that risky firms can profitably use stock options to cater to an employee demand for long-shot bets.

[We analyze the efficiency of indexing executive pay by calibrating the standard compensation model to a large sample of U.S. CEOs. The benefits from indexing the strike price of options are small, and fully indexing all options would increase compensation costs by 50% for most firms. Indexing has several effects with overall ambiguous outcome; the quantitatively most important effect is to reduce incentives, because indexed options pay off when CEOs' marginal utility is low. The results also hold if CEOs can extract rents and extend to the case of indexing shares. Our findings may justify the common practice of "pay-for-luck."]

We examine whether the trading activities of retail and institutional investors cause comovements in stock returns. Around stock splits, retail trading correlations (RTCs) decrease with stocks in the presplit price range and increase with stocks in the post-split price range. These shifts in RTCs induce changes in return comovements. In the cross section, return comovements among low-priced stocks are amplified when retail trades are more correlated and when aggregate uncertainty amplifies behavioral biases. We find similar patterns among local stocks and when firms change their corporate headquarters. In contrast to retail trading, institutional trading attenuates return comovements.