How Important are Risk-Taking Incentives in Executive Compensation

Ingolf Dittmann is Professor in Finance at Erasmus University Rotterdam. This post is based on a recent article by Professor Dittman; Ko-Chia Yu, Assistant Professor at National Chiayi University; and Dan Zhang, Associate Professor at BI Norwegian Business School. Related research from the Program on Corporate Governance includes Paying for Long-Term Performance by Lucian Bebchuk and Jesse Fried (discussed on the Forum here); and Regulating Bankers’ Pay by Lucian Bebchuk and Holger Spamann (discussed on the Forum here).

There is an extensive theoretical discussion whether risk-taking incentives play a role in executive pay. In our article How Important are Risk-Taking Incentives in Executive Compensation? forthcoming in the Review of Finance), we analyse the problem with a calibration of a principal-agent model to observed contracts. We show that including risk-taking incentives does help to explain observed compensation practice. We also show that the provision of risk-taking incentives is consistent with efficient contracting. Besides, our model rationalizes the universal use of at-the-money options, which is often seen as evidence for managerial rent-extraction. In addition, we propose a new measure of risk-taking incentives (available online) that better describes the trade-off between the expected firm value and the additional risk a CEO has to take.

Risk-taking incentives are important in CEO compensation contracts, because CEOs are often heavily exposed to firm-specific risk through their large stock and option holdings and bear the employment risk. Risk-averse CEOs will want to reduce the firm risk, even if this destroys value. Therefore, we need risk-taking incentives to induce the CEO to take risks that benefit well-diversified shareholders (Smith and Stulz (1985) and Haugen and Senbet (1981)). Indeed, empirical evidence suggests that risk-taking incentives matter for CEOs’ actual risk-taking (see, for example, Low (2009), Knopf et al. (2002), Coles et al. (2006), and Acharya et al. (2011)).

In our model, the CEO not only exert costly effort but also determines the firm’s strategy. We capture these dimensions by assuming that the CEO affects both the mean and the volatility of future firm value. If the contract does not provide sufficient risk-taking incentives, the risk-averse CEO chooses a strategy that avoids risk and depresses the firm value. The best way for shareholders to mitigate this inefficiency is to provide both effort and risk-taking incentives by rewarding good outcomes and not punishing bad outcomes. While high stock prices are a clear indicator of good performance, low stock prices are ambiguous: they can be indicative of low effort (which is undesirable) or of extensive risk-taking (which is good, if the CEO leans towards inefficiently low risk). Our model predicts similar patterns to those in the observed compensation contracts that emphasize “carrots” over “sticks”: Firms pay a flat wage for large stock price decreases and provide incentives only for medium and high stock price ranges.

The optimal contract in our model differs markedly from the one in the standard model without risk-taking incentives. As shown in Dittmann and Maug (2007), the standard model predicts a concave optimal contract that emphasizes “sticks” rather than “carrots” and that includes large penalties for stock price decreases and small gains for stock price increases. By comparison, our model predicts similar patterns as in the observed compensation contracts that emphasize “carrots”: Firms pay a flat wage for poor performance, a convex wage for medium performance, i.e., increasing wealth for higher stock prices, and a concave wage for high performance. For the calibration analysis, we compare optimal contracts to observed contracts and find that our model can explain observed contracts much better than the standard model without risk-taking incentives. In a sample of 1,707 CEOs, the average distance, i.e., the expected absolute value between the observed contract and the optimal contract, is 5.4% for our model as compared to 16.1% for the model without risk-taking incentives.

We also apply our model to contracts that consist of base salary, stock, and options, and we establish that in-the-money options are preferable to the portfolio of stock and at-the-money options that we observe in practice. In our sample, the median strike price should be 55.4% of the firm’s stock price when issued. Compared to the observed portfolio contract, this in-the-money option contract provides higher incentives at the center of the distribution and lower incentives in the tails of the distribution. If we take into account the tax penalties that apply to in-the-money options in the U.S., we achieve optimality of the observed portfolio contract for a majority of the CEOs in our sample. Therefore, the universal use of at-the-money options, which is often seen as evidence for managerial rent-extraction (see Bebchuk and Fried (2009)), is consistent with efficient contracting if the tax code is taken into consideration. Specifically, Hall and Murphy (2000) already make this theoretical point; we add calibrated evidence for this.

We also propose a new way of measuring risk-taking incentives that better describes the trade-off between the expected firm value and the additional risk a CEO has to take. Empirical studies usually measure risk-taking incentives as “vega”, i.e., the change in the manager’s wealth with respect to the change in the firm’s stock return volatility. However, the effect of “vega” can be mitigated by high “delta”, i.e., the change in the manager’s wealth with respect to the change in the firm’s stock price. Our measure, called risk avoidance, essentially combines both the utility-adjusted vega and the utility-adjusted delta. We demonstrate that the vega alone is not the best measure of risk-taking incentives, but that it should be scaled by the delta. To understand why this scaling is necessary, first consider the case where vega is negative, and so the manager wishes to avoid risky, positive net present value (NPV) projects. However, this effect is mitigated if the CEO has a high delta as this means that he gains from taking positive NPV actions. Second, consider the case where vega is positive, and thus the manager has an incentive to take risky projects, even if they have negative NPV. Once more, this effect is mitigated if the CEO has a high delta as it means that he will be hurt by taking negative NPV actions. Regardless of the sign of vega, the incentives to take too little or too much risk are offset by a high delta, so the measure of risk-taking incentives depends on the ratio of vega to delta.

This risk avoidance measure is available at https://personal.eur.nl/dittmann/data.htm. The full article is available for download here.

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