Stock Options and Chief Executive Officer Compensation† Christopher S. Armstrong Armstrong [email protected] David F. Larcker Larcker [email protected] Stanford University Graduate School of Business 518 Memorial Way Stanford, CA 94305-5015 Che-Lin Su [email protected] CMS-EMS Kellogg School of Management Northwestern University 580 Leverone Hall 2001 Sheridan Road Evanston, IL 60208-2014 Draft: May 15, 2007 Keywords: Stock Options, Incentives, Agency Model JEL Classification: C61, D82, D86, J33, J41 †We would like to thank the workshop participants at Colorado State University, Columbia University, University of Chicago, and Northwestern University for their helpful comments. Discussions with Ronald Dye, Kenneth Judd and Madhav Rajan were especially helpful. Che-Lin Su is grateful for financial support from the NSF (award no. SES-0631622) Stock Options and Chief Executive Officer Compensation Abstract Although stock options are commonly observed in chief executive officer (CEO) com- pensation contracts, there is theoretical controversy about whether stock options are part of the optimal contract. Using a sample of Fortune 500 companies, we solve an agency model calibrated to the company-specific data and we find that stock options are almost always part of the optimal contract. This result is robust to alternative assumptions about the level of CEO risk-aversion and the disutility associated with their effort. In a supplementary analysis, we solve for the optimal contract when there are no restrictions on the contract space. We find that the optimal contract (which is characterized as a state-contingent payoff to the CEO) typically has option-like features over the most probable range of outcomes. i Stock Options and Chief Executive Officer Compensation Over the past decade there has been an explosion in the use of equity-based compensation (especially stock options) for top executives (e.g., Murphy (1999) and Ittner, Lambert, and Larcker (2003)). Despite the growing popularity of stock options, there is considerable academic and professional debate regarding the relative costs and benefits of equity-based compensation. Some observers view these plans as providing high-powered incentives that align the interests of employees with those of shareholders. They also contend that stock optionshelpattractandretainscarcemanagerialandtechnicaltalent. However, criticsclaim that options give away too much value by diluting the interests of shareholders. Perhaps based on this claim, some companies are dropping their stock option in favor of restricted stock (e.g., Carter, Lynch, and Tuna (2007) and Frederic W. Cook & Co. (2006)). One especially pointed academic critique is that stock options are an inefficient mech- anism for compensating executives relative to restricted stock (e.g., Meulbroek (2001) and Hall and Murphy (2002)). Similarly, Dittmann and Maug (2007) conclude that stock op- tions should almost never be part of the compensation contract for chief executive officers (CEOs). In contrast, Kadan and Swinkels (2006) develop and test an agency model where stockoptionsdominaterestrictedstockwhennon-viability(orbankruptcy)riskiszero. Aseff and Santos (2005) also suggest that option grants are a powerful instrument for providing incentives to the agent. Thus, there is considerable debate in the prior literature about the optimality of stock option compensation for senior-level executives. The purpose of this paper is to further investigate the use of stock options in compen- sation contracts for CEOs. We first develop an agency model that mimics the real world contracting problem between the board (acting on behalf of shareholders) and the CEO. 1 Some of the important features of our model are that the CEO’s compensation contract is limited to fixed salary, at-the-money stock options, and restricted stock, the fixed salary is assumed to be nonnegative (i.e., there is limited liability for the agent), the agent is assumed to have power utility where wealth plays an important role, outside wealth consists of a fixed component and a portfolio of pre-existing stock and stock options with a stochastic payoff, and the CEO exerts effort that affects all the moments of the lognormal distribution of stock price. We then employ numerical methods to solve this bi-level optimization problem for the optimal CEO compensation contract for a subsample of firms from the Fortune 500 during the 2000 to 2004 time period. Our analysis produces three important results. First, in marked contrast to the conclu- sions by Meulbroek (2001), Hall and Murphy (2002) and Dittmann and Maug (2007) that do not solve the complete bi-level optimization problem between the principal and agent, we find that stock options are almost always an important part of the optimal CEO compensa- tion contract. Second, consistent with Aseff and Santos (2005), restricting the compensation contract to fixed salary, at-the-money stock options, and restricted stock produces roughly the same expected payoff to owners as the optimal unrestricted second-best compensation contract. This result suggests that simple observed compensation contracts are robust to restrictions on the contract space. Finally, similar to the observations made by Core, Guay, and Verrecchia (2003), the incentive effects of fixed salary, at-the-money stock options, and restricted stock for some CEOs are dominated by the level and composition of the execu- tive’s pre-existing wealth. For these CEOs, the principal’s choice of compensation contract is essentially the amount of fixed salary that is necessary to satisfy the outside reservation wage (i.e., the individual rationality constraint). The remainder of the paper consists of six sections. The relevant prior research on ob- 2 served executive compensation contracts is reviewed in Section I. We specify our agency model and develop our numerical optimization approach in Section II. Section III discusses our sample and measurement choices. The contracting results for our sample are presented in Section IV. Section V provides sensitivity and validation analyses. Conclusions and limi- tations are discussed in Section VI. I. Prior Research The analysis of compensation contract choice, especially the use of stock options and re- stricted stock, has been a popular topic for analytical and numerical research. For example, Meulbroek (2001) argues that risk averse and undiversified executives do not place enough value on the risky payout they will receive from an option to justify the cost given up by shareholders (and implicitly the incentives provided by the options). However, Meulbroek (2001) does not model the incentive effects of the stock options and this makes it problematic for her to assess the net benefit to shareholders from using stock options. Similarly, using the certainty equivalent approach of Lambert, Larcker, and Verrecchia (1991), Hall and Murphy (2002) conclude that restricted stock (which is essentially an option with an exercise price of zero) dominates options with a non-zero exercise price. However, their numerical results are also based on a “partial equilibrium” analysis that does not formally incorporate the cost of the option, the value to the employee, or the incentives provided by the options into an optimization program. Since the incentives provided by stock options are a key reason for their use in compensation contracts, it is impossible to make substantive conclusions about the relative desirability (and optimality) of stock options or restricted stock unless incentives are actually modeled in the analysis. IncontrasttoMeulbroek(2001)andHallandMurphy(2002),KadanandSwinkels(2006) 3 analyze and provide some empirical tests of a fully specified optimization model where the agent’s compensation contract consists of salary and either stock options or restricted stock (i.e., a stock option with an exercise price of zero), but not both.1 Their formulation departs fromthetraditionalagencymodelbyincorporatingaminimumpaymentconstraintorlimited liability (e.g., Innes (1990)) and a positive probability that stock price is equal to zero, which they term “non-viability risk”. Using the first order approach (FOA) to represent the agent’s optimizationproblem,KadanandSwinkels(2006)findthatstockoptionsdominaterestricted stock when non-viability risk is zero.2 Using a sample of firms from ExecuComp, they also find that the probability of bankruptcy (as a measure of non-viability) risk is positively related to the use of restricted stock. Since the probability of non-viability risk is likely to be low for most firms, the results in Kadan and Swinkels (2006) imply that stock options should be part of the optimal CEO compensation contract.3 Aseff and Santos (2005) examine a standard agency model where the agent takes either a high or low action which results in a continuous stock price outcome. They also assume that the FOA can be used to represent the agent’s problem. The agent’s salary is bounded from below (but can be negative), the compensation contract consists of only fixed salary 1Feltham and Wu (2001) also develop a fully specified optimization model that includes either stock options or restricted stock. They find that restricted stock dominates (does not necessarily dominate) option-based contracts that when the agent affects only the mean (both the mean and the variance) of the outcome, However, their model structure and solution technique exhibit several problematic features such as a mean-variance approximation to the agent’s expected utility which is unlikely to be accurate when the agent’s payoff is skewed with stock option contracts, reliance on the first-order approach which is inappropriate for this setting, and unconstrained salary for the agent. 2In order to justify the FOA, Kadan and Swinkels (2006) assume that the distribution of F(x|e), or the cumulative distribution of stock price given the agent’s choice of effort, satisfies the convexity of the distributionfunction(CDFC).Itisinterestingtothinkaboutwhattypedistributionsatisfiesthisassumption. In their numerical examples, F(x|e) is set to either (1−e+ex) or (x+(1−2x)(1−2e)/2. It is difficult to imagehowthesedistributionstranslateintotherealworlddistributionsorhowtheyareusefulformotivating empiricaltestsofhypothesesgeneratedbyamodelmakingthesedistributionalassumptions. InSectionII.C, we show that it is generally problematic to use the FOA for analyzing compensation contracts that involve stock options. 3This hypothesis is somewhat at odds with the general observation that young technology firms (with a high probability of bankruptcy) aggressively use stock options, as opposed to restricted stock, in the executive compensation programs (e.g., Ittner, Lambert, and Larcker, 2003). 4 and stock options, agent wealth is explicitly considered in the model, and the power function is used to represent the agent’s utility function. The primitive model inputs are developed by selecting parameters to mimic observed compensation payments and stock prices for a typical firm. Their numerical results suggest that the cost of moral hazard (where the agent selects the low action) to the principal is large, but that the use of a simple stock option contract can motivate the agent to select the high action with a very small additional cost. Thus, Aseff and Santos (2005) show that stock options are an important component of the observed executive compensation contracts. Finally, Dittmann and Maug (2007) consider an agency model with a number of realistic features and use the FOA to assess whether observed CEO compensation contracts are opti- mal. In particular, their analysis assumes that observed compensation contracts implement the optimal action and asks whether the principal can write a contract that induces the same action with less cost. Thus, their analysis abstracts from the typical agency model by focusing only on the contract design (which is only one level (i.e., the “upper-level” or the principal’s) of the bi-level optimization). They find the very surprising result that stock options should almost never be part of the optimal compensation contract for CEOs. Although this is a provocative conclusion, there are two questionable aspects in their analysis. First, they appear to assume that the beginning stock price anticipates the optimal effort that will be selected by the agent for a given compensation contract. If stock options are issued at-the-money and the strike price already reflects the expected optimal level of effort, then stock options have little incentive effect because the payoff to the agent (i.e., the intrinsic value) will be very small in expectation. Thus, it is not surprising that stock options do not enter the “optimal” contract in the analysis by Dittmann and Maug (2007). Second, their analysis relies on the ability of the FOA to construct a measure for the incentives 5 imposed on the agent. As we demonstrate below, the combination of lognormal stock price and power utility for the agent renders the FOA invalid, and consequently, their use of the utility-adjusted pay for performance sensitivity is problematic. This brief literature review illustrates that there is controversy regarding the use of stock options in executive compensation plans. In order to provide some insight into the optimal use of stock options, we develop an agency model that mimics many of the features of the “real world” contracting problem between shareholders and the CEO. We also incorporate a number of the structural features from Aseff and Santos (2005), Kadan and Swinkels (2006), and Dittmann and Maug (2007) into our model. II. Model A. Basic Model Structure We assume that the traditional moral hazard model is an appropriate representation of the contracting problem involving shareholders and the CEO.4 Our model is based on a tradi- tional single period agency setting with a risk neutral principal and a risk and effort averse agent.5 Rather than selecting a set of assumptions to produce mathematical tractability, we develop the structure of our model based on features of the contracting environment that are observed in the real world. The cost associated with this choice is that the resulting model will be mathematically intractable and numerical methods are necessary to generate 4We could have also used the adverse selection (or hidden information) rather than the moral hazard (or hidden action) framework for modeling executive compensation. Although there is some debate about whichmodelbestapproximatescontractingwithaCEO,Milgrom(1987)andHagertyandSegal(1988)show that the adverse selection and moral hazard models are fundamentally similar and this modeling choice is largely arbitrary. Although this is essentially true in our modeling, the use of limited liability complicates the transformation from a moral hazard to an adverse selection model. 5Ourmodelonlyfocusesonincentiveissues. Wedonotconsiderotherpotentiallyimportantdeterminants ofcontractchoicesuchastaxes,executiveselection,anddifferentialaccountingtreatments(e.g.,salaryversus stock options). This is a limitation of our analysis, as well as the prior research reviewed in Section I. 6 solutions. However, we believe that the insights produced by such a model outweigh the absence of a closed form solution for the contract. In our model, the risk and effort averse agent has an additively separable utility function defined over terminal wealth (which consists of pre-existing wealth and the current period’s compensation) and effort. The agent’s disutility of effort is a convex and increasing function of effort. The agent selects an effort level to maximize the expected utility of flow compen- sation provided by the principal and existing wealth less the disutility of effort. We assume that the agent’s effort choice is made to satisfy the incentive compatibility (IC) constraints. Finally, we assume that the effort choice affects both the mean and variance of the stock price distribution.6 The risk neutral principal selects a compensation contract to maximize the expected value of the firm net of the expected compensation payment to the agent. In our primary analysis, the contract space is constrained to include fixed salary, stock options that are granted at-the-money (similar to most actual option grants), and restricted stock. Thus, the principal selects the level of salary, number of stock options, and number of restricted shares in the flow pay for the agent. Although this is a simplified characterization of actual executivecompensationcontracts, basesalary, stockoptions, andrestrictedstockcapturethe majority of the value of compensation paid to executives. Similar to observed compensation arrangements, we also require the salary to be non-negative (i.e., the agent has limited liability). The principal also observes the dollar level and individual components of the agent’s wealth at the beginning of the period. This is a reasonable assumption for the stock options 6As discussed below, the agent’s action affects one of the parameters of the lognormal stock price distri- bution, which effects all of the moments of the price distribution, including the mean and variance. 7 and shares owned by the agent since these amounts are disclosed in proxy statements, but it is perhaps more questionable for the other cash component of agent wealth. We assume that the compensation payment satisfies the traditional (ex ante) individual rationality (IR) constraint that the expected utility of compensation less the cost of effort is greater than or equal to the utility of the outside reservation wage that the agent can earn in the labor market. This reservation wage is assumed to be constant and known to both the agent and the principal. The structure of our basic agency model (exclusive of the agent’s pre-existing holdings and fixed wealth) is given by the following program (#1): maximize IE[NP −(α+β P +β max{P −K,0})|a] 1 2 (α,β1,β2,a) subject to a ∈ argmax{IE[U(α+β P +β max{P −K,0})|a˜]−D(a˜)} (IC) 1 2 a˜ IE[U(α+β P +β max{P −K,0})|a]−D(a) ≥ U (IR) 1 2 α ≥ 0 (LL) β , β ≥ 0 (SS) 1 2 β +β ≤ N (TS) 1 2 where N is the number of shares outstanding,7 P is the terminal per share price of the firm’s stock, α is the fixed salary payment, β is the number of shares of restricted stock granted to 1 the agent, β is the number of options granted to the agent with a strike price of K, D(a) is 2 the agent’s disutility of effort, and U is the agent’s reservation utility. (IC) and (IR) denote the agent’s incentive compatibility and individual rationality constraints, respectively, (LL) 7Note that number of shares granted to the agent (i.e., β ) is a reduction to the principal’s ownership of 1 the firm, N. However, rather than modeling the options granted to the agent (i.e., β ) as a reduction of the 2 principal’s equity in only certain states (i.e., when P >K), we model stock options as if a cash payment is made to satisfy this claim upon the realization of the stock price. 8