We consider a model in which shareholders provide a risk-averse CEO with risk-taking incentives in addition to effort incentives. We show that the optimal contract protects the CEO from losses for bad outcomes and is convex for medium outcomes and concave for good outcomes. We calibrate the model to data on 1,707 CEOs and show that it explains observed contracts much better than the standard model without risk-taking incentives. When we apply the model to contracts that consist of base salary, stock, and options, the results suggest that options should be issued in the money. Our model also helps us rationalize the universal use of at-the-money options when the tax code is taken into account. Moreover, we propose a new way of measuring risk-taking incentives in which the expected value added to the firm is traded off against the additional risk a CEO has to bear.
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