To control risk-related incentive problems, equity holders are expected to manage both the convexity and slope of the relation between firm performance and managers' wealth. I find stock options, but not common stockholdings, significantly increase the sensitivity of CEOs' wealth to equity risk. Cross-sectionally, this sensitivity is positively related to firms' investment opportunities. This result is consistent with managers receiving incentives to invest in risky projects when the potential loss from underinvestment in valuable risk-increasing projects is greatest. Firms' stock-return volatility is positively related to the convexity provided to managers, suggesting convex incentive schemes influence investing and financing decisions. (C) 1999 Elsevier Science S.A. All rights reserved.