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Stock options and short term bonuses in executive compensation contracts

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Stock options and short term bonuses in executive compensation contracts

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Content STOCK OPTIONS AND SHORT TERM BONUSES IN EXECUTIVE COMPENSATION CONTRACTS by Yuri Marynets A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ECONOMICS) August 2007 Copyright 2007 Yuri Marynets ii Table of Contents List of Tables iii List of Figures iv Abstract v Introduction 1 Chapter 1: The Single Period Executive Stock Option Model 9 1.1 Settings 9 1.2 Existence Theorem and Properties of a Solution 13 Chapter 2: Short Term Incentives 18 Chapter 3: One Period Model with Two-dimensional Effort and Stock-based and Accounting-based Compensation 21 3.1 No “Ex Ante” Risk 25 3.2 Asymmetry of Information Flow 28 Chapter 4: Empirical Analysis 33 4.1 Data 33 4.2 Variables 33 4.3 Methodology 35 4.4 Hypotheses about Assumptions 36 4.5 Hypotheses about Theoretical Predictions 37 4.6 Results 38 Conclusions 42 References 45 Appendices Appendix 1 50 Appendix 2 51 Appendix 3 52 Appendix 4 54 Appendix 5 69 Appendix 6 73 Appendix 7 77 Appendix 8 80 Appendix 9 83 iii List of Tables Table 1: Equity Based Compensation 52 Table 2: Median Overhang Created by Employee Equity Plan 69 Table 3: Robust Regression of Stock Options Granted as a Percentage of Total Compensation 83 Table 4: Robust Regression of Bonus Paid as a Percentage of Total Compensation 84 Table 5: Robust Regression of Stock Option Granted 85 Table 6: Robust Regression of Bonus Paid 86 Table 7: Multivariate Regression of Stock Option Granted and Bonus Paid as a Percentage of Total Compensation, Option Part 87 Table 8: Multivariate Regression of Stock Option Granted and Bonus Paid as a Percentage of Total Compensation, Bonus Part 88 Table 9: Correlation Coefficients of Dependent Variables 89 iv List of Figures Figure 1: Form of a Typical Annual Incentive Plan 19 Figure 2: Geometrical Representation of Multi-dimensional Action 22 Figure 3: Agent’s Action in No “Ex Ante” Risk Settings 25 Figure 4: Bonus in No “Ex Ante” Risk Settings 26 Figure 5: Optimal Bonus in Asymmetric Information Settings 29 v Abstract In the dissertation we consider the Executive Compensation problem with the compensation plan restricted to the fixed cash salary, short- term bonuses (based on the accounting performance data) and long- term incentives (executive stock option (ESO) contract). We model executive effort and performance measure as multi-dimensional. We propose a model of asymmetric information flow, when the uncertainty about relationship between two performance measures is revealed to the agent after the contracting but before an action is taken. We provide empirical evidence that not only overall risk of companies has opposite effect on bonuses and ESO’s, but also different types of risk are primary determinants of different parts of executive compensation. 1 Introduction Executive compensation, and especially executive stock options, has skyrocketed in the last decade or so. Not surprisingly, as Murphy (1998) relates, “CEO pay research has grown even faster than CEO paycheck”. Most economic models examine the CEO incentive problem in a single-period Principal-Agent setting (see Mas-Colell (1995) for a collection of the main results, as well as the pioneering works by Mirrlees (1974, 1976), Holmstrom (1979), and Grossman and Hart (1983)). Here we re-examine the problem in a single-period setting, but use the Principal-Agent model only as a starting point, from which we develop a multi- tasking Agent (CEO) model. Our CEO model incorporates multiple performance measures that are available to a Principal (Board of Directors). In addition, it includes asymmetry of information flow as a means of accommodating different types of risk. Traditionally, CEO pay research has focused on the relation between a company’s overall risk and the pay-performance sensitivity of its CEO’s total compensation contract. One of the puzzling predictions of the Principal-Agent model is the negative relation between risk and pay-performance sensitivity - a relation that is not supported empirically. Typical executive compensation contracts consist of non-linear instruments, based not only on stock price, but also on accounting measures of performance. Principal-Agent literature deals primarily with linear contracts. Non-stock based compensation elements enter only in the signal-to-noise ratio of the biased performance measure. Option-based forms of 2 long-term compensation have garnered considerable attention as the result of recent corporate accounting scandals, but the short-term bonus part of CEO contracts has not gotten the attention it deserves. We hypothesize that the different types of risk a company faces determine the different parts of the executive compensation it offers and their non-linear forms. By introducing different types of risk, we build a model that resolves the puzzles of the Principal-Agent model and explains the non-linear functional form of the different parts of a compensation contract. The remainder of this section summarizes the handful of recent theoretical and empirical works relevant to our analysis in chronological order, starting with the most recent theoretical works. Aseff and Santos (2005) built a one period model that uses a non-linear compensation plan (salary and stock options only). Unlike previous theoretical works, which used either linear compensation plans or plans of general form, Aseff and Santos used a part of real world executive compensation practices, namely stock options, but they did not consider accounting-based short-term bonuses. Rather than test their predictions empirically, they calibrated their model using numerical simulations. However, they found the number of shares offered in the stock option contract unacceptably higher than observed in practice. Baker (2002) proposed to model multidimensional effort with a multidimensional performance measure in which the marginal product of managerial action is known to both principal and agent prior to contracting. He used a linear compensation contract. Here, we use similar relationship between 3 different performance measures, but also impose information flow asymmetry, as uncertainty about the optimal managerial action is revealed to manager after contracting but before any action has been taken. Zabojnik (1996) presented a linear payment model with one-dimensional effort and output measure, distinguishing between the uncertainty revealed to the agent after the contracting but before the action is taken (“ex ante” uncertainty) and the uncertainty revealed after the action is completed (“ex post” uncertainty), with pay-performance sensitivity (PPS) increasing with ex-ante risk. Baker (1992) proposed a model with similar asymmetry of information flow. He assumed that all information is revealed to the agent before any action is taken (no “ex post” uncertainty), and used a one-dimensional measure of performance, which could not be based on stock price, a linear contract, one- dimensional effort and risk neutral agent and principal. Baker’s (2002) results can be tested empirically. According to his model, firms with highly distorted accounting measures would grant stock options as a higher percentage of total compensation, while firms with low distortion of accounting measures rely relatively more on accounting based bonuses in their compensation packages. Based on these results, and assuming that “new economy” firms have highly distorted accounting numbers and “old economy” firms have less distorted accounting numbers, one would expect to find higher reliance of “new economy” firms on stock options, and “old economy” firms on annual bonuses. 4 Likewise, the results of Zabojnik (1996) can be tested by comparing “new economy” and “old economy” companies. “New economy” companies can be expected to pay a greater percentage of total compensation in form of stock options than “old economy” companies. Below we summarize the recent empirical studies of Dittmann and Maug (2007), Kadan and Swinkels (2006), Hull and Murphy (2003, 2002), Murphy (2003), Core and Guay (2003, 1999) Jin (2002), and Aggarwal and Samwick (1999), all of which used the CompuStat ExecuComp database, and of Ittner, Lambert and Larker (2003), which used iQuantic database. Dittmann and Maug (2007) used data from 1992-2000 and ordinary least square (OLS) regression. They found that the proportion of options as a percentage of stock-based compensation (consisting of restricted stocks and stock options) is positively associated with a firm’s stock volatility. Their theory considers contracts consisting of salary, restricted stocks and stock options with fixed strike price, which could be relevant to “pre FASB123 (R)” conditions. They argue that the observed practices are not economically optimal, suggesting higher restricted stocks and lower salary and option parts of the contract. Their econometric analysis ignores heterogeneity of firms and firm’s risks, which leads in practice to different optimal contracts. They also ignore the bonus part of total compensation, which is known to be the second most important part of total compensation in “pre FASB123(R)” times, overshadowing restricted stock and playing a critical role in the compensation contracts of traditional firms. The observations they describe as 5 suboptimal can be clearly explained in terms of the preferential treatment of at-the- money stock options, which confer no accounting charge on earnings. Accounting earnings are important for companies both directly and indirectly. Directly, they keep the cost of borrowing low. Indirectly, thru stock market specialists’ predictions, they support stock prices. The “post FASB123(R)” world will most likely show diminished differences between stocks and options (with any strike price). This shifts the question to constructing the optimal contract in the form of salary plus bonuses of general form plus stock options of general form (even with strike price equal to 0). Similarly Kadan and Swinkels (2006), using data for 1992-2004, have found that the proportion of restricted stocks (as a percentage of all stock-based compensation) is negatively associated with volatility of the returns. Like Dittmann and Maug (2007), Kadan and Swinkels (2006) ignore bonuses and exclude all companies not granting stocks or options from the sample. In their theoretical discussion, they argued that non-viability risk plays a crucial role in the decision of whether to grant restricted stocks or stock options. They assume that both new companies and those emerging from bankruptcy represent higher non-viability risk, and tested this assumption in the latter case. Having found the evidence supporting the assumption among near bankrupt firms, they concluded that it should hold for newly established firms as well. We would agree with their findings concerning near bankrupt firms, accepting the assumption, that restricted stocks could partially serve the same purposes as bonus. But, by contrast, the analysis presented here 6 dramatically refutes this conclusion in case of young firms, predicting a greater percentage of remuneration as stock options, especially in case of “new economy firms”. Hall and Murphy (2003) compared the percentage of outstanding shares granted in options and the average grant date value of options per employee for all employees in “old economy”, “new economy”, finance, and utilities companies over the years 1993 through 2001. They report the highest numbers for “new economy firms” and the lowest for utilities. Murphy (2003) found more firms offering stock-based pay to CEO’s and top five executives and higher grant frequencies in “new economy” firms over the period 1992-2001. In both papers (Hull and Murphy (2003) and Murphy (2003)) “new economy” firms are found to grant relatively more stock options. Core and Guay (2003) report a significant positive relationship between pay-performance sensitivity and firm risk, measured as volatility of return, in the regression of CEO’s firm specific wealth (share of stock and stock options) controlling for firm market value. They used data years 1993 through 1996. Ittner, Lambert and Larker (2003) using iQuantic proprietary data (1999- 2000) compared ESO grants in “new economy” and “old economy” firms and found significantly higher ESO grants in “new economy” firms. Hall and Murphy (2002) consider a dual problem where the Principal maximizes incentive keeping the expected cost of the stock option contract fixed. 7 They assume that the shift in distribution of future stock price is already incorporated into stock price as of the grant date. Empirically for the years 1992- 1999 they found a statistically significant relation between CEO’s total compensation and size of the company as well as industry. Jin (2002) found a negative relationship between pay-performance sensitivity, measured as dollar change in CEO’s total wealth associated with $1000 increase in firm value, and idiosyncratic risk. Effect of systematic risk was ambiguous. The sample covered years 1992-1999. Contrary to Jin (2002), Core and Guay (1999) using data for years 1992- 1997 observed a statistically significant positive relationship between pay- performance elasticity, measured as the logarithm of dollar change in CEO’s total wealth associated with a 1% increase in stock price, and idiosyncratic risk. Aggarwal and Samwick (1999) report a negative relationship between pay- performance sensitivity and risk (variance of stock price) for the sample of years 1993-1997. But as Core and Guay (2003) commented, the relationship becomes positive, if the regression is controlled for the firm size. According to Ellig (2002), the executive compensation package consists of five elements: salary, benefits, short-term incentives, long-term incentives, and perquisites. Murphy (1998) distinguishes four basic components: salary, annual bonus tied to accounting performance, stock options and long-term incentive plans. In this work, compensation is considered as having three main components: salary (including salary, benefits and perquisites in terms of Ellig or salary in terms of 8 Murphy), annual bonus (short-term incentives in terms of Ellig, or annual bonus in terms of Murphy), and stock options (long-term incentives in terms of Ellig, or stock options and long-term incentives in term of Murphy). The latter is by far the largest part of total equity compensation observed in practice. The presentation is structured as follows. Chapter 1 presents a one period model of salary and stock options granted only. It includes existence theorem, as well as some qualitative analysis of the solution. Chapter 2 briefly describes short- term incentives. Chapter 3 presents the main framework for reconciling short-term and long-term incentives, and proposes a model of two-dimensional effort using a two-dimensional performance measure, and introduces the “ex ante” risk. Chapter 4 discusses our empirical findings. We finish with conclusions and present the unsolved problems and directions for future research. Appendix 1 consists proofs of some of the results. Appendix 2 describes conditions for optimality of stock option contract in the unrestricted case. Appendix 3 discusses the diluting effect of ESO’s. Appendix 4 summarizes the most important accounting and tax issues related to executive compensation. Appendix 5 presents the basic multi-period executive stock-option model. Appendix 6 discusses retention mechanism of ESO’s. Appendix 7 describes some puzzling questions of ESO’s. Appendix 8 discusses robust regression. Appendix 9 contains empirical results. 9 Chapter 1 The Single Period Executive Stock Option Model 1.1 Settings We start from one period Principal-Agent model, where the principal is thought as an owner of the firm, and the agent as a CEO. In practice the Board of Directors would act on behalf of the shareholders. We assume that the Board has exactly the same preferences as all shareholders in total. We also assume that it is an initial contract and the CEO does not have yet any managerial power in the company. Those assumptions are applicable for the initial contracting. In this chapter we assume that the compensation scheme consists of a fixed payment and the stock option grant only, and it is the only income of the agent. We could easily add some fixed diversified preexisting wealth. Again it is a viable assumption for the initial contract. For modeling renewal contracts one would rather assume some preexisting undiversified portfolio of the agent’s wealth and changing reservation utility. We assume standard Principal-Agent problem settings. At the beginning (time t=0) the principal (in our case Board of Directors) hires the agent (CEO) for the one period project. We normalize the total number of shares at the beginning of the period to 1. Contract is designed as follows. At the end of the period (time t=T=1) the agent receives a cash compensation of w and the right to buy n shares of the stock with the pre-specified exercise price K. The agent exercises the option if S T >K. We will define the set of stock prices of S T for which the agent exercises 10 the option as E={S T : S T ≥ K}. The payoff of such option contract signed by the third party (not by the principal) is n(S T -K) + = max{0, n(S T -K)}, which is standard notation in mathematical finance. The correct payoff of the employee option contract should be written as n(S T -K) + /(1+n). Changing notation q=n/(1+n) we can work with q “undiluted” equivalent of option grant of n. The agent’s payoff could be written as q(S T -K) + . More about diluting effect of employee options in Appendix 3. We will call the couple (w,q) the compensation scheme which consists w in cash, and the stock option contract of q “undiluted” shares with the fixed exercise price of K. See Appendix 4 for the reason why K must be bounded from below by share price as of the grant date, and Appendix 5, explaining why even in case of multiple optimal strike prices principal would optimally choose the lowest possible strike price. Also, Appendix 4 provides important accounting, tax and SEC regulation issues of the ESO’s. Along with the standard agency theory assumptions, our principal is risk neutral, and the agent is risk averse. Those assumptions are made to analyze pure agency effect, excluding risk-sharing effect. The agent’s utility function from the consumption will be written as v(•), and a disutility from effort of taking action a from [0,1], as g(a). For the utility function we will assume that it is bounded, strictly concave, strictly increasing and twice continuously differentiable with coefficient of relative risk aversion not grater then 1. As example we will use logarithmic utility function. The disutility of effort is twice continuous 11 differentiable, g’(a)>0 for any a>0, g’(0)=0, and g”(a)>0. As an example we will use g(a)=a 2 /2. We will assume that fixed component of the compensation package is bounded below by some number w>0, and above by w¯ , and q, the number of options in the contract, is bounded below by 0, and above by q - ≤1. q=1 corresponds to the case of infinite number of shares granted. In practice q is much lower then 1, about 0.1 for the total employee option plans over 10 years period (see Appendix 5). For reasons why w must be bounded above see Appendix 4. Also we need some technical assumptions: 1) The set of all actions available is A=[a L ,a H ], where a L =0,a H =1. 2) The value of the firm, S T , is a continuous random variable, which takes values in the interval S=[S, S - ]. For each fixed aєA, function F(•;a) is the probability distribution function of S with continuous density f(•;a) such that f(S;a)>0 for all SєS. 3) F’ a (•;a)<0, which means that effort is productive. 4) f” aa (S;a) ≤ 0 at least for SєE. This assumption, particularly, implies that f(•;a) satisfies the monotone likelihood ratio property: the ratio f’ a (S;a)/f(S;a) is non-decreasing in S. The agent’s expected utility under the scheme (w,q) and action a will be expressed as V(w,q;a)= ∫ S v(q(S-K) + +w)f(S;a)dS-g(a) The principal’s expected payoff: U(w,q;a)= ∫ S Sf(S;a)dS-C(w,q;a), 12 where C(w,q;a)= ∫ S q(S-K) + f(S;a)dS+w is an expected cost of the contract under the action a. It is natural to assume that the expected cost of the contract is bounded. The principal could not compensate the agent with the payment higher than the value of the firm. Following standard agency theory results we will write individual rationality (IR) and incentive compatibility (IC) constraints for the agent, which are basically the consequence of maximization problem of the agent under the fixed scheme (w,q): (IR) V(w,q;a*) ≥ V (IC) a* = arg max{V(w,q;a): aєA} We assumed that the principal intends to implement the highest possible action a H . We note, that implementing of a L is trivial: fixed salary with no shares granted. Now we could write the set of feasible choices of compensation contracts as B={(w,q): (IR),(IC) hold, 0 ≤ q ≤ q - , and w ≤ w ≤ w - }. For the sake of technical meaning we need to assume that B is not empty. The optimal stock contract now may be defined as (P1) (w*,q*) є arg max{U(w,q;a*): (w,q) є B}. 13 1.2 Existence Theorem and Properties of a Solution Let’s start form the agent’s problem. Let’s release for a moment (IR) constraint. Proposition 1.1 For any q, such that 0 ≤ q ≤ q - , there exist unique a* - solution of (IC). Proof: Existence of a* comes from maximization of continuous function over the compact set. Uniqueness is a consequence of Assumption 4. Note: If q=0, we must have a*=0. Without loss of generality we can assume w=1 in the contract for the logarithmic utility function. Therefore a*, solution of (IC), could be written as a*(q). Now we will prove that a*(q) is an increasing function of q, if the relative risk aversion is less than 1. It means that the agent with the relative risk aversion of 1 or less always could be provided with incentive by increasing of number of the stock on the option contract. da*/dq=-V” aq (1,q;a)/V” aa (1,q;a). Due to Assumption 4, V” aa (1,q;a)<0. Therefore it is enough to prove the following proposition: Proposition 1.2 Let w > 0 and the relative risk aversion of the agent is not higher than 1 for any positive consumption. Than V” aq (w, q;a) > 0. Proof: Differentiating by part we will obtain V” aq (w, q;a) =- ∫ E F’ a (S;a) (q(S-K)v''((S-K)+w)+v'((S-K)+w))dS. 14 It is positive as long as (q(S-K)v''((S-K)+w)+v'((S-K)+w)) is positive, because - F’ a (S;a) is positive by Assumption 3. By the assumption about the risk aversion, 1 ≥ |[q(S-K) +w] v''((S-K)+w)/v'((S-K)+w)|. For w > 0 it follows that |[q(S-K) +w] v''((S-K)+w)/v'((S-K)+w)| > |[q(S-K)v''((S-K)+w)/v'((S-K)+w)|. Therefore, q(S-K)v''((S-K)+w)+v'((S-K)+w)= [q(S-K)v''((S-K)+w)/v'((S-K)+w)+1]v'((S-K)+w)>0, which ends the proof. The previous proposition, along with the fact that a*(q) is a continuous function by construction, assures that a*(q) is invertible, so, for any a, such that 0 ≤ a ≤ a*(q¯), we could define continuous function q(a)=a* -1 (q). If q(a H )>q¯, the highest possible option grant could not assure the highest possible effort. If q(a H )<q¯, the highest possible effort could be enforced with the lower than maximal number of option granted. Let a¯=min{a H , a*(q¯)}. Therefore for any a*, such that 0 ≤ a* ≤ a¯, contract {1, q(a*)}, assures that the agent optimally chooses action a*, i.e. (IC) condition is satisfied. Note, that for logarithmic utility function, if contract {1, q(a*)} satisfies (IC), the contract {w, wq(a*)} for w>0 satisfies (IC) too. Similar results could be obtained for power utility. Therefore, scaling wage and number of options, we can satisfy both (IC) and (IR) with equality. Here we used the fact that q(a*) is a continuous function. Now, the optimal a* could be found as a solution of principal’s maximization problem. For any a*, such that 0 ≤ a* ≤ a¯, the couple {w*, w*q*} is 15 a contract, satisfying both (IR) and (IC), and q*=q(a*), and it solves (P1). Therefore the principal maximization problem is reduced to the optimization over a*, and uniqueness of a* leads to uniqueness of the solution of (P1). This result could be formulated as Theorem 1.1: There exists unique solution of (P1). Now, let’s assume that principal’s utility is at maximum if a*=a¯, and, therefore, {w*,w*q*} is the contract enforcing a¯. Let’s look at some properties of the solution. Increase in reservation utility (right hand side of (IR)) leads to increase in w* and, therefore, increase in both parts of compensation contract {w*,w*q*}. That fact could be formulated as Lemma 1.1. Let (w 0 ,q 0 ) satisfies (IR) and (IC) for the fixed level of reservation utility v 0 . If the reservation utility increases to v 1 >v 0 , the option grant and fixed payment must increase: q 1 >q 0 and w 1 >w 0 . Another result following from the specific form of the compensation contract {w*,w*q*} could be formulated as follows: Lemma 1.2. (i) Assume that (w 0 ,q 0 ) strictly satisfies (IR) and (IC). Than if (w 1 ,q 1 ) satisfies (IR) and (IC), but (IC) is not binding, than q 1 >q 0 and w 1 <w 0 , so the Principal could decrease the cost of the compensation increasing fixed payment and decreasing stock option granted. 16 (ii) Assume that (w 0 ,q 0 ) strictly satisfies (IR) and (IC). Than if (w 1 ,q 1 ) satisfies (IR) but not (IC), than q 1 <q 0 and w 1 >w 0 , so the Principal could achieve needed incentive decreasing fixed payment and increasing stock option granted. Up to the moment we ignored the fact, that w and q are bounded. Let’s consider situations, when that fact distorts the optimal contract. Let w*q(a*)>q¯. Therefore contract {w*, w*q(a*)}is not admissible. The best what the principal can do, is to schedule a contract {w**, q¯}, such that (IR) is satisfied. That contract enforces a**, such that q(a**)= q¯/w**. Note, that a**<a*, and w**>w*. Therefore, a cap on the number of stocks granted could result in inefficient effort choice. Also, increased reservation utility can lead to the corner solution {w**, q¯}, also enforcing lower than optimal effort. Let now w*<w, meaning that the optimal {w*, w*q(a*)} is not admissible, because the optimal w* is too low. Contract {w, wq(a*)} would enforce the correct a*, but would satisfy (IR) with inequality. The optimal contract in that case is {w, wq(a**)}, which satisfies (IR) with equality, and enforce lower than optimal effort level: a**<a. Let’s look at the case, when w*>w¯, meaning, that the optimal contract includes inadmissibly high wage level. Then the contract {w¯, w¯q(a**)}, which satisfies (IR) with equality, would over provide incentives: q(a**)> q(a*), meaning that {w¯, w¯q(a**)} is an inefficient contract comparing to {w*, w*q(a*)}. Now, if in addition to that, w¯q(a**)>q¯, the best, what the principal can do, is {w¯, q¯}, and it makes (IR) unsatisfied, meaning the agent would not accept the contract. 17 Now we provide some qualitative characteristics of a solution of the problem. Lemma 1.3. The derivatives of U and V must satisfy the following properties |U w (w,q;a*)/ V w (w,q;a*)| < |U q (w,q;a*)/ V q (w,q;a*)|. Proof: See Appendix 1. This lemma presents an important result. The inequality could be interpreted as the fact that the agent, being risk avers, prefers increase in fixed payment to the increase in the number of shares in the contract. In other words, if the principal intends to increase the total expected compensation by $1, higher increase in the agent’s expected utility would be achieved by the direct transfer of $1 in cash to the agent, and lower one would be done by the increase of number of shares granted. The increase in fixed payment does provide the agent with higher increase in the expected utility, but does not provide any incentive for taking high effort. 18 Chapter 2 Short-Term Incentives Most companies use some form of short-term incentives to adequately reward performance for short-term results (i.e., a year or less). The accounting, tax, and SEC implications for the short-term incentives are basically simple and straightforward. The cost is an expense and is taken as a charge to earnings in the income statement. Unlike the long-term incentives, the payment is 100-percent taxable as income to the executive and 100-percent tax deductible to the company. While there is no federal law requiring shareholder approval of the incentive plan, some states have requirements for companies incorporated under their laws. Similarly, the stock exchange on which the company stock is listed may have such a requirement. 19 Figure 1 Form of a Typical Annual Incentive Plan Annual The “Incentive Zone” Bonus Maximum award Target award Threshold award Performance measure Threshold Target Maximum The form of the annual bonus as a function of the “underlying” accounting measure is much richer than the form of long term incentives, which are basically, as we describe in Appendix 4, the number of shares granted. Following Murphy (1998), Murphy (2000) and Ellig (2002), the Figure 1 presents a “typical” annual incentive plan. The “Incentive Zone” could be linear, convex or concave (the total number of parameters describing the general “typical” short term bonus is 6). The specific form of “Incentive Zone” will be explained in the next chapter. If the “Incentive Zone” shrinks to 0 (i.e. “Performance Threshold” = “Performance Maximum”), the annual plan could be described as a “Digital Option”. The 20 threshold of the award could be 0, as well as there could be no bonus “Cap” (no maximum for the award). In that case the short-term bonus looks like a standard call option on the underlying performance measure. The performance measures, which are used for the annual bonuses, are almost always some accounting-based measures: earnings, ROA, cash flow measures, sales, and others. 21 Chapter 3 One Period Model with Two-dimensional Effort and Stock-based and Accounting-based Compensation Let’s assume that the principal has three instruments in the compensation package: cash w, stock option grant q, and bonus x(Y) based on accounting measure Y (for example, Y is book value of company’s stock). As before, let function F S (•;a) be the probability distribution function of S with continuous density f S (•;a) such that f S (S;a)>0 for all SєS. We will introduce one more source of randomness - θ, and function F(•) is the probability distribution function of θ with continuous density f(•) such that f(θ)>0 for all θєΘ Θ Θ Θ=[θ min , θ max ] which could be interpret as a slope of the vector of the “optimal” direction of effort in the following sense. Assume that book value Y is deterministic function of action a, and for simplicity let Y(a) = ||a||cos(θ), where a=(||a||cosθ,||a||sinθ). We assume that the action is a two-dimensional vector, so the agent can take the action in any direction on a two-dimensional plane. We assume as before that the effort is continuous in the range ||a|| є [0,1]. Without any changes in the analysis we could assume, that our dimension of effort is more than 2, but both parties know the true direction of the “accounting” effort, and the true direction of “stock” effort may point anywhere as long as the slope among them is θ. 22 Figure 2 Geometrical Representation of Multi-dimensional Action Optimal Direction for the Market Value Increase θθ Optimal Direction for the Book Value Increase Assume that the principal and the agent have perfect understanding which direction must be taken for the effort to be most effective for the increase of book value. If principal’s objective function is value of the firm, and the agent takes an action in the direction most effective for the increase of the value of the firm, the only randomness is ex post uncertainty of form F S (•;a). The latest approach is close to one analyzed by Baker (1992). Now assume that the direction for the optimal action to increase book value, which is common knowledge prior contracting, is x-axis. On the other hand, we assume that optimal direction for firm’s value increase is not known for both parties before contracting. We shell spend a little time here, because that point is very important. Unlike the standard Principal-Agent model, where all uncertainties are symmetric, and the agent does not possess any additional information comparing to the principal, we assume that even though the principal and the agent θ 23 have symmetric information at the time of contracting, the agent can observe realization of at least part of the uncertainty (or has a superior costless ability to obtain information about the optimal direction for stock increase in our settings) before she takes the action. This assumption seems to be relevant, because the principal delegates the governance of the firm to a person who is not only the hard working individual, but also believed to have “superior” ability to determine the optimal direction in the firm’s future development (who has a “vision”). In our case this “superiority” is ability to observe the true slope θ* before an action taken. In terms of Zabojnik (1996) it is “ex ante” uncertainty. In the terminology of Arrow (1995) and Holmstrom and Milgrom (1987) this is a hidden information model. The proposed solution for the hidden information problem is to make contract contingent on “self-reported” θ, and use the “revelation principle” for the optimal contract. Unlike that approach, we will follow Zabojnik’s setting, and assume that the contract cannot be made contingent on θ (because θ is never observed by the owner or else it is not verifiable). In our two dimensional settings, the principal maximizes the expected value of the firm less the expected cost of contract: U(w,q,x(·);a)= ∫ S Sf(S;a)dS-C(w,q, x(·);a), where C(w,q,x(·);a)= ∫ S [q(S-K) + ]f(S;a)dS+w+x(Y(a)) is an expected cost of the contract under the action a. Recall that we assumed that Y(a) = ||a||cos(θ). Therefore for the highest level of effort ||a||=1: C(w,q,x(·);a)= ∫ S [q(S-K) + ]f(S;a)dS+w+x(cosθ) 24 The agent maximizes the expected utility under action a. Here we need an additional assumption, that the agent cannot leave the company after the contract is signed and before the terminal time of the contract T=1. Also we will make some convenient change in modeling of disutility of effort: assume that g 1 (||a||) is monetary equivalent of disutility of effort. It will allow us to bring the g 1 (||a||) term inside v(·) function: V(w,q,x(·);a)= ∫ S v(q(S-K) + + w + x(||a||cosθ) - g 1 (||a||))f(S;a)dS. As before agent’s optimization leads to two sets of condition: (IR) and (IC). Unlike before, (IC) condition has to assure not only the optimal choice of action effort: ||a*|| (assume the principal tries to implement effort level equal to a H =1), but also the optimal choice of slope θ*, which is known by the agent after contracting, but not known revealed to the principal. It could be useful explicitly split original (IC) condition into two parts. The first part of (IC) condition is an optimal choice of ||a||. We will call this as before: (IC). The condition for the optimal θ* will be called “Self Selection” condition (SS): (IR) V(w,q,x(·);a H *) ≥ V (IC) V(w,q,x(·);a H *) ≥ V(w,q,x(·);a*) for any ||a*||<||a H *|| and ||a|| є [a L , a H ]) (SS) V(w,q,x(·);a H *) ≥ V(w,q,x(·);a H ) for any a H ≠ a H * If the principal uses the stock option contract only, we are in the settings of the Chapter 1. The question is: can the principal increase her expected payoff (for example, decrease the cost of contract) using the accounting measures (i.e. “annual 25 bonus”) for the compensation in addition to cash and stock option grant? The answer is “yes”. 3.1 No “Ex-ante” Risk First, let’s consider the case when θ* is known by both parties, 0<θ*<π/2, and ||a|| є [0,1]. In that case observing partial information about action undertaken by the agent through accounting measure Y, the principal is able to enforce an action a, such that ||a||cosθ=cosθ*: Figure 3 Agent’s Action in “No Ex Aante Risk” Settings θ∗ 1 1 θ cosθ∗ The bonus x(Y) in that case should be in the form of step function: 26 Figure 4 Bonus in “No Ex Aante Risk” Settings c o s θ ∗ $ Y g 1 ( c o s θ ∗ ) Now, the stock based compensation part of the contract should enforce action a*=(cosθ*,sinθ*) over any other action a=(cosθ*,sinθ), for any positive θ<θ*. Therefore principal’s problem reduces to the one-dimensional problem: Maximize U(w,q;a) choosing w and q with (IR) V(w,q,x(·);a*) ≥ V (IC) V(w,q,x(·);a*) ≥ V(w,q,x(·);a) where x(·) is the step function described above. Assuming the disutility function is g 1 (||a||)=||a|| 2 /2, we could rewrite the (IC) as follows: (IC) ∫ S v( q(S-K) + + w + (cos 2 θ*)/2–1/2 ) f(S;1) dS ≥ ∫ S v( q(S-K) + + w + (cos 2 θ*)/2 - (cos 2 θ*+sin 2 θ)/2)f(S;cos(θ*-θ))dS for any positive θ<θ*, or (IC) ∫ S v(q(S-K) + + w - (sin 2 θ*)/2)f(S;1)dS ≥ 27 ∫ S v(q(S-K) + + w - (sin 2 θ)/2)f(S;cos(θ*-θ))dS Without loss of generality, it is enough to show that (IC) is satisfied for θ=0: (IC) ∫ S v(q(S-K) + + w - (sin 2 θ*)/2)f(S;1)dS ≥ ∫ S v(q(S-K) + + w)f(S;cosθ*)dS The last inequality is similar to (IC) constrain in original one-dimensional problem with lower disutility: (sin 2 θ*)/2 instead of ½ in the case of the highest effort (left-hand side); and “better” density function f(S;cos θ*) instead of f(S;0) (right-hand side). Therefore the two-dimensional problem is reduced to the one-dimensional problem of optimal stock option contract. Now, this new one-dimensional stock option problem is similar to one described in the Chapter 1, with lower agency losses, and the results similar to the results of Chapter 1 are applicable here. Interestingly, that this agency cost decrease (comparing to the one dimensional problem when principal is prohibited from use of accounting measures) leads to the lower “additional” effort (sinθ*) needed in the direction of stock increase. Also, it allows the principal to decrease the incentive part of the stock option contract (the higher cosθ, the lower “additional” incentive needed). The decrease of the incentive part of the stock option grant could be accomplished by decreasing q. It leads to the following conclusion. If a firm is able to influence the direction of accounting measures (reference point), in other words, to choose the accounting system, which more precisely reflects the true economic results of the firm, it is optimal from the agency point of view to do that (assuming that “ex post” risk of the accounting 28 measure is the same, and that the optimal direction for stock increase expresses the true economic position of the firm and could not be manipulated). We shall note here, that the bonus paid effectively is seen by the agent as a part of the fixed compensation, while provides the compensation for the “partial” effort in the direction of the stock increase. Note, that if the correct θ* is known in advance by both parties, our problem is similar to the problems discussed first by Lambert and Larcker (1987), who compared relative efficiency of accounting-based and stock-based measures, and stated that in some specific settings, relative weights of the accounting-based and stock-based instruments in the linear compensation scheme are proportional to the “signal-to-noise” ratios of the measures. Recently Baker (2002) analyzed the case of known θ* in liner payment scheme. 3.2 Asymmetry of Information Flow Now let’s turn to the case when θ* is not known in advance. Now (IR) and (IC) must be satisfied in expectations over unknown θ*. Results similar to the case of known θ* can be obtained here about known in advance expected value of θ*: E(θ*). As before the lower distortion of the accounting measure, the higher is the bonus payment and the lower is stock-based payment. More interesting question not yet studied is how the uncertainty about θ* prior contracting influence both bonus and stock based parts of the contract. Assume as before that the possible levels of effort are from the interval [0,1], and that 0<θ<π/2 and cosθ is distributed 29 on [cosθ max , cosθ min ], and effort disutility function is of the quadratic form: g 1 (a)=||a|| 2 /2. The payoff x(Y) be of the form: Figure 5 Optimal Bonus in Asymmetric Information Settings x(Y) Y cosθ max cosθ min (where the “incentive zone” is a portion of the disutility function g 1 (Y)=Y 2 /2) will guaranty that any action of the form a=(cosθ, sinθ’), where cosθє[cosθ max , cosθ min ] and sinθ’ is fixed, will be rewarded with the same bonus payment. It is least “distorting” way to use the distorted (accounting) measure. Taking expectation over θ* in (IR) could be thought as increase of reservation utility: the agent faces risk associated with θ* unknown prior to contracting. The risk neutral principal must insure that risk. The higher uncertainty about θ*, the higher the expected payment to the agent should be. If θ* were revealed to the agent after the action is taken, that would be part of “ex-post” risk, studied extensively at the agency literature. If, as in our settings, the true θ* is revealed to the agent before an action is taken, the agent 30 can adjust the action. The higher the “ex ante” risk (the higher the uncertainty about θ* keeping E(θ*) fixed), the higher must be the insurance provided by the principal. That insurance must come in the form of scaling both parts of the contract: cash payment (total of wage and bonus), and ESOs. As we showed in Chapter 1, in case of plain vanilla stock option that could be accomplished by the higher number of shares granted and higher cash payment. But this scaling does not change the ratio of ESO to cash payment. Now let’s look how taking the expectation over (IC) constraint changes the optimal contract. Here it is useful to look at two parts of the original (IC): (IC) which assures the highest possible effort level, which we called actually (IC) – incentive compatibility constraint, and (SS) – “self selection”, which assures that agent does not deviate form the optimal direction of effort. Taking expectation over θ* in (IC) does not change the optimal choice of effort level. Taking expectation over θ* in (SS) leads to the solution, which enforce θ**>E(θ*), and therefore the higher q – number of options granted, compared to the case of enforcing E(θ*). It makes the ratio of ESO to cash payments to increase. Effectively, increase of overall payment and rearranging payment to increase of ESO part make the agent risk-loving in the sense of “ex ante” θ* risk. As we mentioned above, the principal should schedule the bonus scheme precisely as agent’s disutility of effort function g 1 (a). It is impossible in practice to accomplish that even in the case if the principal knows the function. However, we would argue, that six parameters, which determine the shape of the actual bonus 31 plan could lead to a fairly good approximation of the optimal bonus plan and the diversity of observed annual bonus schemes could be thought as an attempt to construct the closest approximation. In case if disutility of effort is modeled in additive form as we did in Chapter 1, g(a), the optimal bonus part will depend not only on g(a), but also on the utility function v(c). Using “first order” results we are able to predict the higher overall weight of the stock option in the total compensation for firms with E(cosθ*) close to 0. It explains the difference between firms in early market stages (threshold and growth) and in later market stages (maturity and decline). Smith and Watts (1992) hypothesize and find a positive relationship between firms’ growth opportunities and the degree to which firms use equity incentives to tie a manager’s wealth to firm value. Gaver and Gaver (1993), Mehran (1995), Himmelberg, Hubbard, and Palia (1999), and Palia (2001) provide additional support for this hypothesis by documenting a positive association between proxies for growth opportunities and CEOs’ equity incentives. The “second order” results can explain the observed differences for different “new” firms. That could be one of the reasons to observe much higher stock option grants (as a percentage of total compensation package) for the executive of “new economy” firms comparing to the “old economy” firms. If we compare two growing companies: one is a small retail company with growth opportunities related to opening new store, second is a small R&D biotech company. Even both are risky in terms of high “first order ex ante risk” E(θ*), it is 32 more understandable what kind of accounting results investors are expecting from the first company, namely growth of capital expenditure. We could interpret this as narrow [θ min , θ max ] interval. In contrast it is little understood what kind of accounting results we should expect from successful company of the second type. 33 Chapter 4 Empirical Analysis 4.1 Data In our empirical part we are using ExecuComp database. The database contains over 2500 companies, both active and inactive. The universe of firms cover the S&P 1500 plus companies that were once part of the 1500 plus companies removed from the index that are still trading, and some client requests. Data collection on the S&P 1500 began in 1994. However, there is data back to 1992 but it is not the entire S&P 1500. It is mostly for the S&P 500. The last year in the database is 2005 fiscal year (fiscal year ending before or on May 31, 2006). Executive Compensation data is collected from each company's annual proxy, which must be filed 120 days after each company's fiscal year end. ExecuComp collects up to 9 executives for a given year, though most companies do only report five. We look at CEOs only. 4.2 Variables There are 3 sets of variables in ExecuComp dataset: 1) company information: industry group, SIC code, sales, income, etc. 2) executive information: ID number, Name, etc. 34 3) compensation data: salary, bonus, options granted, options exercised, etc. In addition, following Ittner, Lambert and Larcker (2003), and Hall and Murphy (2003) we created indicators for New Economy firms, defined as companies with primary SIC codes 3570, 3571, 3572, 3576, 3577, 3661, 3674, 4812, 4813, 5045, 5961, 7370, 7371, 7372, and 7373, and Old Economy firms, with SIC codes less than 4000 not otherwise categorized as new economy. Total we have 3 categories: “New economy”, “Old economy” and all other companies as a base category. In our analysis we use a set of dependent variables. We go further then the previous studies analyzing different parts of executive compensation. We use BLK_VALU (Black-Scholes value of Options Granted measured in thousands of dollars) and BONUS (measured in thousands of dollars), and we create two more variables OptionGrantedPart and BonusPart representing options granted and bonus as a fraction of total compensation. Our explanatory variables include measure of overall risk of companies VOLAT measured as standard deviation of stock return calculated over 60 month. We use SALECHG (sale change), EPSCHG (EPS change), ASSETCHG (asset change), ROA (return on assets), TOBINS_Q (measured as a reciprocal of book-to- market of equity) as proxies to different types of risk. In addition we use DummyNewSIC and DummyOldSIC as indicators for “new economy” and “old economy” firms. 35 We control for the size of a company using MKTVAL (market value) or LOG_MKTVAL (natural logarithm of market value). Also we control for a year using dummies for 1993-2005, and year 1992 as a base year. 4.3 Methodology Empirically our primary goal is to explore the role different types of risk play in observed compensation practices. By its nature ESO’s payoff depend on realized stock price. On the other hand, determinants of annual bonus could vary. One of our goals is to test a set of performance measures, as possible explanation of bonus payoff. In our regression analysis, after running OLS regression, we found that assumptions of OLS are violated, especially in case of levels of bonus and option as dependant variables. One of the possible solutions, adopted in particular by Core and Guay (1999, 2003), is to use Median Regression. We used Robust Regression in our analysis. Appendix 8 contains basic discussion of Robust Regression. In addition, in case of bonus part and option part as dependent variable we present results of Multivariate Regression, which takes care of explicit correlation between option and bonus parts of compensation package. In this case results are qualitatively almost identical to the results of Robust Regression. In our Multivariate Regression of option and bonus parts we used 17,246 observations. Final versions of Robust Regression use 17,235 observations for option part, and 17,212 observations for bonus part. In case of the levels of option 36 and bonus, final versions of Robust Regressions use 15,518 and 16,468 observations respectively. 4.4 Hypotheses about Assumptions As we mentioned in Chapter 2, performance measure used in determining bonus part are mostly various accounting data. We will test following hypotheses: H1A: Ceteris paribus, a positive association will exist between Sales growth and the percentage of bonus in total CEO compensation. H1B: Ceteris paribus, a positive association will exist between Sales growth and the bonus in total CEO compensation. H2A: Ceteris paribus, a positive association will exist between EPS growth and the percentage of bonus in total CEO compensation. H2B: Ceteris paribus, a positive association will exist between EPS growth and the bonus in total CEO compensation. H3A: Ceteris paribus, a positive association will exist between Asset growth and the percentage of bonus in total CEO compensation. H3B: Ceteris paribus, a positive association will exist between Asset growth and the bonus in total CEO compensation. H4A: Ceteris paribus, a positive association will exist between Return On Assets (ROA) and the percentage of bonus in total CEO compensation. H4B: Ceteris paribus, a positive association will exist between Return On Assets (ROA) and the bonus in total CEO compensation. 37 4.5 Hypotheses about our Theoretical Predictions Our theoretical results predict difference in bonus and option parts of the optimal contract as a result of differences in “ex ante” and “ex post” risks of companies. Overall risk of company measured as percentage volatility of firm’s stock price combines both of those risks, and therefore could have ambiguous effect on bonus and option parts of optimal contracts. We propose the following proxies for “ex ante” risk. “New economy” companies are examples of high “ex ante” risk firms. Growth in sales (used by Lambert and Larcker (1987)) and high Tobin’s Q (measured as reciprocal of equity book-to-market ratio, and used by Ittner, Labbert and Larcker (2003)) are traditionally thought as indicators of growth opportunities, and therefore we use them as proxies for “ex ante” risk. Higher “ex ante” risk would mean higher option part and lower bonus part, as well as higher option level. The effect of higher “ex- ante” risk on level of bonus could be ambiguous. Level of bonus is primarily determined by θ. But we can speculate, that higher growth opportunity could be associated not only with higher “ex ante” risk, but also with age of company or industry, meaning high θ. Growth in Sales is not only proxy for growth opportunities. As we mentioned in section 4.3, it may be a determinant of bonus. Therefore we do not use it in this section in case of bonuses and bonus levels. Thus we will test following hypotheses: H5A: Ceteris paribus, “New Economy” firms are granting higher stock options as a percentage of total compensation 38 H5B: Ceteris paribus, “New Economy” firms are granting higher stock options H5C: Ceteris paribus, “New Economy” firms are granting lower bonus as a percentage of total compensation H5D: Ceteris paribus, “New Economy” firms are granting lower bonus H6A: Ceteris paribus, a positive association will exist between Tobin’s Q and the percentage of stock option in total CEO compensation. H6B: Ceteris paribus, a positive association will exist between Tobin’s Q and the stock option in total CEO compensation. H6C: Ceteris paribus, a negative association will exist between Tobin’s Q and the percentage of bonus in total CEO compensation. H6D: Ceteris paribus, a negative association will exist between Tobin’s Q and bonus in total CEO compensation. H7A: Ceteris paribus, a positive association will exist between Sales Growth and the percentage of stock option in total CEO compensation. H7B: Ceteris paribus, a positive association will exist between Sales Growth and the stock option in total CEO compensation. 4.6 Results In our empirical analysis we control for the size of a company, using Market Value (MKTVAL) or natural logarithm of Market Value (LOG_MKTVAL). Also we use dummies for years 1993-2005 to control for year 39 effect. We perform Robust Regression for both level and percentage of option and bonus (Appendix 9, Tables 3-6) and for comparison reason we present results of Multivariate Regression for level of option and bonus (Appendix 9, Tables 7 and 8) along with correlations in dependent variables (Appendix 9, Table 9). It was necessary to use Robust Regression especially in case of level of option and bonus, because assumptions of OLS regression are not satisfied. We found significant differences in effects of “ex ante” risk on fraction and level of option and bonus in the compensation contract. The coefficient of “New economy” indicator (DummyNewSIC) is positive and significant in regressions of level and fraction of stock option. The opposite is true for bonuses. Therefore we found evidence in favor of hypotheses H5A-D. “Old economy” indicator (DummyOldSIC) does not have such profound effect, suggesting that difference between traditional manufacturing firms (“Old economy”) and base class, containing all other industries not included in the “New” or “Old” categories, is not that deep as in case of “New economy” firms. Similarly, coefficient of Tobin’s Q (TOBINS_Q) is positive and significant in regressions of option, and negative and significant in regressions of bonus, which provides evidence in favor of hypotheses H6A-D. We found evidence in favor of hypothesis H7B in our Multivariate Regression only, and we did not found evidence in favor of hypothesis H7A, as the coefficient of Sales Growth (SALECHG) has been found statistically insignificant in the regression of option level. Interestingly, Asset Growth (ASSETCHG) has been found to be a useful 40 predictor of option part and option level, with positive coefficient, and a useful predictor of bonus part in the bonus part median regression, with negative coefficient. This suggests that Asset Growth could be considered as a better proxy for growth opportunities, comparing to Sales Growth (SALECHG). Among determinants of bonus in the compensation contract, coefficients for Sale Growth (SALECHG), EPS growth (EPSCHG) and ROA (ROA) are positive and significant providing evidence in favor of hypotheses H1A-B, H2A-B, and H4A-B. Coefficient for Asset Growth (ASSETCHG) is not significant in Robust Regression of bonus level and Multivariate Regression of bonus part in the total compensation. Robust Regression of bonus part in the total compensation shows negative and significant coefficient for Asset Growth (ASSETCHG). Therefore we do not have evidence in favor of H3B, and we have some evidence in favor of the opposite to H3A. On the other hand as we mentioned above, Asset Growth (ASSETCHG) appears to be positive and significant in regressions of option and option part. Therefore we suggest that Asset Growth (ASSETCHG) could be thought as proxy for growth opportunities. In the Robust Regression including Net Income (NI) Growth as an additional explanatory variable, which we do not present here, NI Growth appears to be not useful in predicting level or percentage of both option and bonus. It could be interpreted as NI Growth been a poor performance measure. In all models size of company (MKTVAL or LOG_MKVAL) is significantly positively associated with dependent variable. Percentage volatility of stock price (VOLAT), as proxy for overall risk of a company, is useful in 41 prediction of all dependant variables, but it has opposite effect on options versus bonuses. The coefficient for volatility is positive and significant in regressions with options, and negative and significant in regressions of bonuses. It suggests that overall risk has opposite effects on different performance based parts of compensation contract. 42 Conclusions We proposed a new framework for the modeling of the executive compensation including fixed component, long-term incentives of the form of “at- the-money” stock option, and short-term incentive of the general form function of an accounting measure. This framework allows us to capture some important characteristics of the executive compensation, to name: rich universe of short-term bonuses; that the option is of little importance as motivation mechanism if the firms are well established and it’s value is closely related to the accounting measures; that stock options are important as a motivation mechanism for new firms; the difference in use of stock options between different “new” firms. In our empirical part of the paper we provide evidence that not only overall risk of companies has opposite effect on bonuses and ESO’s, but also that different types of risk are primary determinants of different parts of executive compensation. This framework which we developed in the theoretical part of the paper could be successfully used if we assume heterogeneous agents on the labor market, in sense of different prior F(θ) distributions. That will lead us to the theory of signaling and monopolistic screening if we have one firm and several agents. In case of heterogeneous agents as well as heterogeneous firms (in the sense of different true θ) we could develop the theory of matching, there the stock option grants are the mechanism of attraction of the right agent rather than motivation mechanism. Oyer and Schaefer (2005) provide evidence consistent with the hypothesis that firms use option programs to attract employees who have optimistic 43 beliefs about the firm’s prospects (we would say the Agents who have the clearest “vision” of firm’s prospects). It is important to mention the problems with executive options, which are not captured by our model. First, we used an exogenous constraint K = S 0 as imposed by the accounting standards and tax treatments; it should be explained by the economic reason. Here we would agree with observations of Murphy (2003) that firms use options rather because of low ”perceived” costs. Dechow, Hutton, and Sloan (1996) and Core and Guaya (1999 and 2001) provide some evidence that option grants are larger when it is more costly for firm to have low earnings (because of dividend constraints or debt covenants)). The evidences presented by Murphy (and Ittner at al. (2002)) rather explain the wide use of options by all firms, not just by “new economy” firms. Our model could explain the difference as an incentive instrument used wider by “new economy” firms, and if extend to the “matching” model, as an instrument of attraction right agents. Also new firm could be more concerned about managerial turnover, so the wider use of the option grants could be due to higher retention needs. The other economic reason for the constraint is the following: many companies have outstanding loans agreement, which include debt covenants. Under a typical debt covenant, the interest rate of loan increases if the borrower’s financial position worsens (for example when the net income, earnings before income tax (EBIT), or some other measure of earnings drops below a certain threshold). By using non-recognized options as compensation, the company can avoid breaching the debt covenants. Empirical 44 evidence for that was presented by Matsunaga (1995). High concern of executives about accounting results, even if the results have no impact on the economic value of the firm, is explained mostly as the need to meet the forecasts of analysts. It moves the problem of executive stock option to the different direction, namely “market efficiency”. In the case if semi-strong form of market efficiency holds, there should not be any difference between accounting expensing and not- expensing executive option. 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Zabojnik, J., 1996, Pay-performance Sensitivity and Production Uncertainty, Economic Letters 53, 291-296 50 Appendix 1 Proof of the Lemma 1.3: The inequality may be rewritten as ∫ E v'(q(S-K)+w)h(S;a*)dS<∫ S v'(q(S-K) + +w)f(S;a*)dS, where h(S;a*) = [(S-K)f(S;a*)]/[∫ E (S-K)f(S;a*)dS]. Lets prove it in two steps: ∫ E v'(q(S-K)+w)h(S;a*)dS<∫ E v'(q(S-K)+w)s(S;a*)dS, and ∫ E v'(q(S-K)+w)s(S;a*)dS≤ ∫ S v'(q(S-K) + +w)f(S;a*)dS, where s(S;a*) = f(S;a*)/(1-F(K;a*)). Let’s start from the second step. By construction, s(S;a*) is a density in E with s(S;a*) ≥ f(S;a*) for all SєE. By concavity of v(·) the expected marginal utility over S must be at least as large as the expected marginal utility over E. The first inequality may be rewritten as ∫ E v'(q(S-K)+w)h(S;a*)dS ≤ ∫ E v'(q(S-K)+w)s(S;a*)dS. That inequality comes from the fact that both s(S;a*) and h(S;a*) are densities in E, and h(S;a*) stochastically dominates s(S;a*). Since v(•) is concave, we get the needed result. 51 Appendix 2 Now we will find for which conditions the solution of unrestricted Principal-Agent problem (see Mas-Colell (1995)) coincides with the solution of the problem form Chapter 1. In other words, when the unrestricted solution w(S) has a form of a pair (w,q). It is an important question, because the solution of the restricted problem is not necessarily the solution of the unrestricted problem, and in practice, if we use richer set of option contracts, we could construct a contract, which is “closer” to the solution of the unrestricted problem. The following Proposition gives the answer for the question in the case of logarithmic utility function. Proposition A.2.1. Let v(c)=log(c). The sufficient and necessary condition for the optimal contract w(S) to be of the form of stock option contract (w,q) is that the term f’ a (S;a)/f(S;a) has the form (S-K) + -K 0 for some constant K 0 >0. Proof: The solution of the unrestricted Principal-Agent problem is a function w(S) of a stock price S: w(S)=(v') -1 ([λ+μf’ a (S;a)/f(S;a)]] -1 ), there λ and μ are the Lagrange multipliers for the (IR) and (IC) constraints of the unrestricted problem respectively. Substituting v(•)=log(•) the expression simplifies and we could find the constants K 0 from the equation w=λ-μK 0 . 52 Appendix 3 Diluting effect of ESO To avoid common mistakes in the analysis, we will explain some terms, which are widely used in economic literature. There are four possible methods of providing equity compensation to employees of a corporation. The variables include the decision to grant real equity versus equity equivalents, as well as the decision to grant a whole share value versus the value of appreciation only. The effect of these decisions is portrayed in the following chart: Table 1 Equity Based Compensation Equity Equity Equivalent Whole Share Value: Restricted Stocks Phantom stock Appreciation Only: Stock Options Stock Appreciation Rights (SAR) Real equity grant increases the total number of shares, and that dilution effect must be taken into account in the analysis. Some economic papers do not distinguish between equity and equity equivalents, practically analyzing phantom stocks and SARs, but referring to them as stocks and stock options, while the accounting and tax consideration of them differs. Diluting effect of the employee option traditionally is recognized for the purpose of corporate finance and financial statement analysis 53 (see White et al. (1997)). Black and Scholes in their famous article “The pricing of Option and Corporate Liabilities” (1973), the article where they presented the “Black&Scholes formula” for standard options, noted how the formula should be changed for proper calculation of potentially diluting instrument such as warrants. Huson, Scott, and Weir (2001) found that investors do in fact understand the dilution costs associated with ESOs and other diluting instruments. The payoff of a call option contract granting n stocks at time T with a strike price K signed by the third party (not by the principal) is n(S T -K) + , which is standard notation in mathematical finance. Sometimes this payoff is mechanically assumed for the executive options. This assumption contradicts real practice, where the execution of the option grant leads to the issue of new shares and therefore dilution of the existing shares. This observation, which is commonly known in corporate finance and accounting literature, could be of little importance in case if n is small, but it makes a big difference if a model predicts significant number of executive stock options. To model it correctly we need to normalize the Agent’s payoff not by 1 (the assumed initial number of shares outstanding) but by 1+n. Therefore the correct payoff of the employee option contract should be written as n(S T -K) + /(1+n). We shall note here, that for the analysis without dilution effect we could use the same S T for both stock price and value of the firm. If we take into consideration the dilution effect, the total value of the firm remains the same and will be called S T , while the price per share after options exercised is S T - n(S T - K) + /(1+n). 54 Appendix 4 Accounting and Tax Issues of Stock Option Compensation A4.1 Accounting Issues Accounting recognition of employee stock options has been a hot topic in the accounting literature. For some of the problems see Subramanyam (1996). The accounting of the employee options has been reported according to two main documents: APB25, and FAS123. Recently FASB revised FAS123. As a result, starting from the financial year beginning June 15, 2005 or later large publicly traded companies (and December 15, 2005, privately held or smaller public companies), FASB requires to report according to the FAS123(R). We will briefly explain those documents and their results for the purpose of economic modeling The rules governing accounting for stock-based compensation are complex and detailed, and a full description is beyond the scope of this dissertation. We will explain the existing rules for the moment when the dissertation is written, mentioning that the accounting principles have been under active debate and are far from the perfection right now from point of view of economists, accountants and politicians. There are two principal standards accounting for employee stock compensation: 1. Accounting Principles Board Opinion No. 25 (APB 25), “Accounting for Stock Issued to Employee”, published by FASB’s (The Financial Accounting Standards Board) predecessor in 1972. 55 2. Statement of Financial Accounting Standards No. 123 (FAS 123), “Accounting for Stock-Based Compensation”, published by FASB in 1995. (Revisited version of FAS 123(R) has been published by FASB December 2004, and going to replace FAS 123). A4.1.1. APB 25 APB 25 requires that the cost of stock-based compensation be measured using the “intrinsic value” method. The intrinsic value of an equity award is equal to the spread between the market value of the stock less the amount, if any, that the employee is required to pay. For the standard “at-the-money” and “out-of the-money” employee stock options, the intrinsic value at the date of grant is zero, resulting in no compensation cost. This is one of the reasons such stock options have been so popular as incentive. FASB has provided additional guidance for the APB 25 in the form of the following: FASB Interpretations (FIN) (a) FIN 28: “Accounting for Stock Appreciation Rights and Other Variable Stock Options or Awards Plan, an interpretation of APB Options No. 15 and 25”, December 1978. (b) FIN 44:”Accounting for Certain Transaction involving Stock Compensation, an interpretation of APB Option No. 25”, March 2000. EITF (Emerging Issues Task Force) issues 56 The most noteworthy issue is Issue 00-23, a lengthy series of questions intended to illuminate the accounting treatment of specific situations not clearly addressed in FIN 44 or APB 25. The EITF began deliberation on Issue 00-23 in 2000. Now we will explain basics of APB 25, which are relevant for the economic modeling. (a) The Three Fundamental Questions Under APB 25, the accounting treatment of a stock-based compensation plan depends on the answer on the three questions: (i) Is the plan compensatory or non-compensatory? (ii) If the plan is compensatory, are awards under the plan fixed or variable? (iii) How is compensation cost measured and recognized? (i) Is the plan compensatory or non-compensatory? A plan that is non- compensatory does not result in any charges to earnings; however, four criteria have to be met for a plan to fall into this category: 1. All employees may participate 2. Stock is offered uniformly. 3. Reasonable time for exercise. 4. Discount from market no greater than in offering of stock to stockholders. APB 25 specifies that a Section 423 employee stock purchase plan is an example of a non-compensatory plan. As a practical matter, a plan that meets the criteria to 57 qualify under section 423 is the only common type of stock compensation arrangement that can qualify as non-compensatory. (ii) If the plan is compensatory, are awards under the plan fixed or variable? Any plan that does not qualify as non-compensatory is compensatory. Compensation cost in a compensatory plan must be measured. The measurement date may be fixed or variable. The measurement date for a fixed award is the date of grant. An award is fixed if the following two features are known at the date of the grant: 1. Number of shares 2. The exercise or other purchase price For example, a classic stock option award, under which the number of shares that can be purchased and the exercise price are set as of the date of grant, is a fixed award. The measurement date is the grant date, and compensation cost (if any) is measured as of that date. For a variable award, “mark-to-market” accounting is required during the period beginning on the grant date and ending on the measurement date – that is, value must be estimated at each reporting date, with any increase since the last reporting date as cost. Typically, a variable award will result in greater accounting cost than a fixed award, as well as greater administrative burden. Most companies find that plan with variable accounting treatment are unacceptable because of their impact on earnings: the amount of expense is both uncontrollable and unpredictable. For 58 this reasons, performance-contingent award – those where the number of shares or exercise price are contingent upon specific performance criteria – are used infrequently. Not going into the details, we will mention a compromise performance- contingent award, which do not trigger the variable accounting. “Performance- accelerated” awards vest at some time in the future based solely on continued service of the employee; however, the award may vest earlier, that is, vesting is accelerated if certain performance goals are achieved. Thus, these award meet the two requirements for fixed accounting: The number of shares that may be issued is fixed and known at the grant date, as is the exercise price. The only variable is the timing of the vesting. (iii) How is compensatory cost measured and recognized? APB 25 measures compensation cost using the “intrinsic value” method: Compensation cost is equal to the quoted market price of the stock at the measurement date minus the amount, if any, the individual is required to pay for the stock. The intrinsic value method produces a favorable result for “at-the-money” and “out-of-the-money” options. The intrinsic value of such options is zero. The “in-the-money” options will generate an expense equal to the amount of the discount (i.e., the intrinsic value). Most of stock compensation awards, other than stock options, result in compensation cost. 59 Compensation cost is recognized over the service period to which the award relates – typically, the vesting period. (b) Those Awards Are Covered Under APB 25? FIN 44 specifies that APB25 is applicable only to “common law” employees, which is generally the same as the definition of “employee” for the payroll tax purposes, and elected members of the Board of Directors. In general, stock-based grants to any non-employees are accounted for under FAS123, discussed in the section A1.1.2. (c) What Happens If the Terms of an Outstanding Award Are Changed? The accounting rules governing modifications to stock-based awards are detailed and cumbersome. The most important thing to know about modifications is that any change to an existing award, no matter how minor it may appear, can trigger potentially unfavorable accounting treatment. Practically, the only way is to cancel it, and grant the new one not sooner than in six months. This “six-month” rule has resulted in many companies canceling out-of-the-money option with a promise to grant new ones in six month and a day (”six and one” grants). A4.1.2. FAS 123. In the early 1990s, FASB attempted to replace APB 25 with a different standard for stock-based compensation that would measure the value of stock options using economic “fair value” models. For employee stock options, this 60 means using an option-pricing model such as the Black-Scholes or binomial model “that takes into account as of the grant date the exercise price and expected life of the option, the current price of the underlying stock and its expected volatility, expected dividends on the stock…, and the risk-free interest rate for the expected term of the option”. FAS 123 provides specific guidance regarding selection of appropriate assumptions for each of these variables. FASB’s attempt to require companies to book an expense for stock options, in contrast to APB 25’s far more favorable treatment, was thwarted by vociferous protests from companies and some members of Congress. As a result, FASB issued a new standard in 1995 in the form of FAS 123, which permits companies to adopt the fair value method of valuing employee stock options, but requires only pro forma (footnote) disclosure of the fair value cost. For most companies, FAS 123 has been relevant only because of its mandated footnote disclosure. Since the issuance of FIN 44, however, companies have been clearly required to use FAS 123 to value stock-based grants to non- employees. FIN 44 clearly specifies the scope of APB 25: It may be used only to account for stock-based grants to common-law employees and outside directors elected to the company’s Board. Stock-based awards to all non-employees (except outside directors) must be accounted for under FAS 123. Additional guidance regarding the implementation of FAS 123 has been issued since 1995. This includes: 61 · EITF 96-18, “Accounting for Equity Instruments That Are Issued to Other Than Employees for Acquiring, or in Conjunction with Selling, Goods or Services.” · FASB Technical Bulletin No. 97-1, “Accounting under Statement 123 for Certain Employee Stock Purchase Plans with a Look-Back Option.” A4.1.3. The Impact of the Accounting Issues. The accounting rules presented above makes unfavorable use of any option except standard “at-the-money” or “out-of-the-money” options. Now we will mention some other strategic consideration of the stock option grants. The procedure of executive stock option grant normally requires the shareholders’ approval of the share grant plan (usually, 10 years plan), which clearly states the total number of shares available for the grant, and typically is equally divided into 10 regular annual grants. The company intended to grant the contract with the high out of the money exercise price (and therefore high number of shares, to keep total expected utility of the agent unchanged) could find itself in the position that too few shares remain available for their regular annual grant. It is one of the possible explanations why the “out-of-the-money” grants are used much less frequently than “at-the-money” grants. Another issue comes from the way an employee exercises the option. To purchase the stock at the strike price the employee needs to invest sometimes considerable amount of money. Occasionally corporations provide some 62 mechanism of lending for the purpose, but still it is costly for the employee. Those costs are higher for the grants with higher exercise price even if the total value of the grant remains unchanged (i.e. if the increase in the strike price is compensated by increase in the shares granted). For the purpose of Individual Rationality (IR) constrain, such execution costs of the employee effectively are transferred to the employer. A4.2 Selected Tax Aspects of Executive Compensation A4.2.1. Description Mostly due to different tax treatment, two types of option exist. Incentive Stock Options (ISOs) ISOs satisfy the requirement of various provisions of the IRS and therefore receive preferential tax treatment: allowing the employee to postpone the recognition of taxable income until the underlying shares are sold, and taxing the resulting gain at long-term capital gain rates (although the alternative minimum tax may apply to certain taxpayers on exercise of the option). Nonqualified Stock Options (NQSOs) NQSOs do not receive preferential tax treatment but do not require satisfying the requirements needed for the ISOs. Incentive Stock Options. An option qualifies as an ISO only if it meets the following requirements: • The option is issued pursuant to a written plan (approved by shareholders within 12 month before or after the date of adoption by the Board of 63 Directors) stating the maximum number of shares that may be subject to option grants under the plan, and the employees or class of employees eligible to receive option grants. • The option is granted within 10 years from the time the plan is adopted by the board or approved by the shareholders whichever is earlier. • The option is not exercisable more than 10 years from the date of grant (5 years for holders of more than 10% of the company’s stock). • The exercise price is not less than 100% of the fair market value of the underlying stock at the time of grant (110% for the more-than-10% shareholders). • The option is not transferable except by will or the laws of descent and distribution. • The value of the employee’s options that first become exercisable in any given calendar year may not exceed $100,000. In calculating this amount, the value of the stock is determined at the date of grant. Any purported ISOs that exceed the $100,000 limit are treated as nonqualified stock options on pro-rata basis. A4.2.2 Tax Treatment Incentive Stock Options: Employee: In the case of ISOs, taxation of the employee is deferred until the shares acquired on exercise are sold (although the “spread” at exercise may well be 64 subject to alternative tax at that time), and any appreciation above the exercise price receives long-term capital gain treatment, if: • The stock acquired upon exercise is not sold within two years from the date of the grant of the ISO and one year from the date of exercise of the ISO, and • The employee remains in the employ of the company up to three months before exercising the option (one year if termination is due to disability). Employer: If the holding period requirements are met, the company would not receive a tax deduction. Nonqualified Stock Options: Employee: In the case of NQSOs, the employee is generally not taxed when the option is granted, but, upon exercise, the employee recognizes ordinary income equal to the excess of the fair market value of the stock acquired (at exercise) over the exercise price paid. Upon sale of the acquired shares, the employee recognizes long-term capital gain or loss (provided that more than one-year holding period requirement is met) in an amount equal to any difference between the amount received on sale and the fair market value of the stock at exercise. Employer: At the time of exercise, the company is entitled to an income tax deduction corresponding to the amount of ordinary income realized by the employee. 65 Wage: Employer: top executives wages may not be fully tax-deductible in the United States since 1993, when public pressure forced the SEC to issue its Section 162(m) of the Internal Revenue Code (Section 162(m)). According to Section 162(m) the deduction for compensation (other than performance-based compensation) paid to top executives of publicly held corporations is limited to $1 million per year. Perry and Zenner (2001) investigate whether companies increasingly use ESOs in favor of cash payment after the introduction of Section 162(m) in 1993. They find that, although the regulations did not reach its prime stated objective of reducing compensation, the regulations do change the structure of the compensation contracts. Specifically, they find that firms with compensation packages of more than $1 million increasingly shift towards performance-based compensation, with firms citing Section 162(m) as a key reason for the shift. A4.2.3. Advantages and Disadvantages of Stock Options Advantages • ISOs 1. Taxation of the employee is deferred until the underlying shares are sold, and the executive’s entire gain on sale of the shares is taxed at capital gain rate. (However, the alternative minimum tax may well apply.) 66 • NQSOs 2. The company receives an income tax deduction equal to the gain at exercise realized by the employee. Disadvantages • ISOs 1. The company does not receive a corresponding tax deduction 2. The spread at exercise may well be considered alternative minimum taxable income for the employee. • NQSOs 3. NQSOs do not receive the preferential tax treatment ISOs receive and, thus, are less attractive to the employee than ISOs. The last disadvantage mentioned along with the requirement that ISOs may not be issued “in-the-money” provides one more reason why we observe mostly “at-the-money” contracts. We need to add here, that ISOs are mostly granted to the executives, while more flexible NQSOs are used for compensation of both executives and broad based employees. To show that a board of directors stresses the possible tax benefits of a plan, we will quote, for example, the 1982 proxy statement of Federal Signal Corporation: 67 The purpose of the amended plan is to make such changes as are required to permit options granted under the plan to qualify as ”incentive stock options” under the Internal Revenue Code…which provides more favorable income tax treatment for persons exercising options. One more consequence of tax issues could be that agents optimally exercise NQSO’s immediately after vesting (i.e. long before maturity) even for non- dividend-paying stocks (for the “economic” reasons, see Appendix 6). Due to different tax treatment of income and capital gain, the agent could find herself better-off realizing income earlier and paying lower income tax, and increasing the capital gain, paying more capital gain tax, but, hopefully, less total tax. To summarize, for the economic modeling, three main points are important: 1) The ISO creates tax expense (for executive) of difference between the price the stock was sold and strike price, multiplied by “capital gain rate” (which is normally lower than ordinary income rate and is 20% as of the moment of writing the dissertation). 2) The NQSO creates the tax expense/deduction (for the executive and the firm in total) of difference between the fair market price the day the stock was acquired and strike price, multiplied by difference of marginal tax rates for the executive and for the firm (such that, if the rate is higher for the executive, the overall system “firm-executive” has tax expense, and if the rate is higher for the firm, the system “firm-executive” has tax deduction), plus tax expense (for executive) of difference between the price the stock 68 was sold and the price the stock was acquired, multiplied by “capital gain rate”. 3) Wage component of the executive compensation is limited to $1 million per year. 69 Appendix 5 The Basic Repeated Executive Stock Option Model The observed stock option grants present much lesser number of shares granted, than is predicted by most of existing academic works of agency problem. For example, the median annual CEO stock option grant in the new technology sector accounts for less than 0.03% of all shares outstanding (note, that new technology firms grant options much more generously than traditional firms). The following table presents the median overhang (unexercised “in-the-money” options plus unvested stock awards plus stock available for use, as a percentage of common shares outstanding) created by employee equity plan among 350 larger public companies for the years 1996-2000: Table 2 Median Overhang Created by Employee Equity Plan Year Median overhang 2000 13.3% 1999 11.8% 1998 11.3% 1997 10.7% 1996 10.7% 70 As mentioned in “Paying for performance” edited by Peter T. Chingos, “Today many institutional investors instruct portfolio managers to vote against equity plan when the total overhang created by managerial equity awards exceeds 10% to 15%.” Recall that such plans are accepted for 10-year period. It presents overall concern of shareholders over the diluting effect of CEO options. We will present the idea of a partial equilibrium model, which could incorporate such facts. For the beginning let assume that expected payoff of the principal is 0, if the agent does not apply effort (a=0). If the agent applies a high effort a=1, the principal gets extra unit of profit, i.e, 1 unit of profit. We could interpret it as an “abnormal” return. If it is 0, it means that the principal gets only “normal” return, which could be earned as well in outside investment. Some of that 1 unit of “abnormal” return should be transferred to the agent to cover her disutility of effort, and this payment must be performance contingent (in our case, they must be of the form of an option grant) to create the incentive for the agent. If the principal sells out the company to the agent, she could not expect “abnormal” future income from the company. So to be able to repeat the game in the future, it must sell only some part of the firm. In the period two the game is repeated, and so forth. The principal optimizes the discounted infinite “abnormal” income. But we need the assumption that the principal would not be able to control the firm after the controlling package M (for instance, M is equal to “50% plus one share”) of the stock outstanding goes out of her hand. After that moment she is no longer a “principal” and could expect 71 only normal return on her investment (in our settings it means 0 excessive income forever). The solution of the problem could induce lower level of stock grants, comparing to the one period model, and the lower (up to “at-the-money”) strike price. This is one of the possible ways to model the shareholder concern about future control over a corporation. Recall the basic model, but assume that K is a part of the contract, meaning, that the principal propose a contract (w,K,q). In that case the optimal contract is not unique. Consider a 2-period model (P2), such that in each period the problem looks exactly as in the 1-period model. If in the period “1” an optimal contract (w 1 ,K 1 ,q 1 ) was used and the expected profit was U(w 1 ,K 1 ,q 1 ;a H )= ∫ S Sf(S;a H )dS-C(w 1 ,K 1 ,q 1 ;a H ), in the next period the principal’s expected profit is U(w 2 ,K 2 ,q 2 ;a H )= ∫ S S(1-q 1 )f(S;a H )dS-C(w 2 ,K 2 ,q 2 ;a H ) (note that here q 2 =n 2 /{(1+n 1 )(1+n 1 +n 2 )}). Therefore, no matter which discount factor is used in multi-period maximization, to increase the second period profit, the principal would implement the optimal contract with the lowest possible q 1 (or in other words, n 1 ) in the previous period. The result obviously holds in any period, except the last one, in the model with any finite number of periods, as well as in the infinite-period model. This could be formalized as follows: Theorem A5.1: In any finite period model (P N ), where N>1, or infinite period model (P ∞ ), there exist a unique solution (w n ,K n ,q n ) for a one “n-th” period problem (n<N for a finite period model). 72 If, due to accounting and, to some extent, tax issues, we add the constraint K n ≥ S n-1 , (i.e. the strike price could not be set lower than the fair market stock price at the beginning of the period), we could state, that the optimal one period solution (w n ,K n ,q n ) is either of form (w n ,S n-1 ,q n ) in the case of corner solution, or (w n ,K n ,q n ) and K n > S n-1 in case of interior solution. 73 Appendix 6 Retention Mechanism in Multi-Period Model with Stock- based and Accounting-based Compensation Up till now we have analyzed only attraction and motivation mechanisms of a compensation scheme, where (IR) constraint of our problem is thought as an attraction mechanism and (IC) as a motivation mechanism. Costs of renegotiation and finding a new agent for the principal consists a retention problem. To be able to model retention mechanism we need to expand the problem to multi-period problem. In that case, the motivation mechanism would be (IC) constraint for each period. If we denote (IR) 0,t,T for 0≤t≤T, an expected at the moment 0 “individual rationality” constraint for the inter-temporal agent’s utility from period t till the final period T; (IR) 0,0,T will represent an “attraction” mechanism, while (IR) 0,t,T for all 0<t≤T will represent retention mechanism. Let’s start from 2-period model. In the absence of the retention costs, the optimal compensation scheme should not differ from period to period (except for the reason mentioned in the Appendix 5). The principal does not have a reason to prefer payment scheme 2 to scheme 1 (presented below). Imposing additional inter- temporal risk on the agent is costly to the principal. In case of presence of the retention costs, scheme 2 may be preferable. 74 Scheme 1 Scheme 2 Payments in different periods Payments in later periods are the same: should be higher: Period 1 Period 2 Period 1 Period 2 This is natural task for the executive option (“long-term incentives”). Imposing inter-temporal “volatility” of compensation for an agent leads to the increase of total cost of the contract, but if the increase in the cost is lower then the costs of executive turnover, the principal would be better-off adopting scheme 2 (paying more at time 2) over scheme 1 (the same payment at time 1 and time 2). Therefore, even if executive options are not a part of the optimal one period problem, they are naturally a part of the optimal contract in the multi-period setting. The increase in the base salary as well as annual bonuses could not accomplish the retention goals if they are done year after year and not as scheduled at moment 0 over time increase in the salary and bonuses. We need some instrument, which is fixed at the moment 0, and takes care of all upcoming periods’ (IR) constraints. Now assume that market correctly infers from the observed stock price the effort (or a “talent” for observing “ex-ante uncertainty”) of the agent, and as the result reservation utility tracks the stock price (or the stock price “relative” to some market index). In that case the executive option grant will take care of the needed 75 change in the retention mechanism, due to the fact that the expected value of the grant will automatically adjust to the observed stock price. This conclusion is close in spirit to the Oyer’s (2004) arguments, that the broad-based option plan may provide efficient retention incentives if reservation wages are correlated with stock prices, and if direct wage adjustment is sufficient costly. If the stock price is not perfectly correlated with the reservation utility, principal could find herself “under-providing” or “over-providing” retention payment. In such case some adjustments are needed. While we do not observe in practice any decrease in compensation due to total increase in stock market price, some firm reinforce their retention mechanism in case of “under water “ options through re-pricing of existing option or granting new options. We shell make a note here. Let’s compare the effect of increase of the stock price for the different risk levels. If we assume equal effort needed for $1 increase in earnings (perpetually) for both more risky and less risky firm, for the riskier firm (with higher market β) the increase in stock price will be lower than for less risky firm. Therefore, if the market observes the increase for both firms and correctly infers the effort (or ability) of the executive, the reservation utility increase would be the same for both executives. As the result, to keep the retention mechanism in place, the riskier firm needs more stocks granted. To finish our discussion of the role of the stock options, we would like to cite some results of iQuantic survey of 1999, presented by Ittner et al. (2003), which states that the highest rank among different objectives of option grants is 76 “retain employees” (90% of firms mentioned this as a goal). “Reward specific project milestones or goals” and “reward past contributions” were named as the second and fifth in the rank, with 69% and 38% respectively. We shell mention here, that due to arguments presented above we would think of those two objectives as a retention mechanism, because we expect that “specific project milestones or goals” and “past contributions” probably increased the reservation utility of agents, and therefore call for stronger retention mechanism. “Attract employees” is on the third place with 65%. “Provide competitive total compensation” (sixth place with 31% of responses) could be seen as a part of attraction mechanism, if it concerns new employees or retention mechanism if it concerns existing employees. The pure incentive mechanism of the stock options is ether among “other objectives” (2% of responses, seventh place), or partially as “encourage stock ownership”, with 51% of responses and fourth place. As we see, the incentive objective is not one of the important in the survey. To be able to capture the observed role of the stock option, the multi-period model is suitable. 77 Appendix 7 Some “Puzzles” of the Executive Compensation One of the puzzles the executive compensation is how to price the stock option correctly. The principal and the agent could assign different values for the same stock option. Normally, it is assumed that the principal will assign to the option the same value as selling the option to outside investor. This implicitly assumes that the principal treats the agent the same way as an outside investor and do not expect any incentive or retention results from the stock option (which could be perfectly true). In that case the only reason to grant options are, as mentioned by Murphy (2003), the low “perceived price” of the option. If we believe that options do carry some incentive, we need to compare the cost of the option to the principal with the benefit of the option to the principal, or in other word “net” cost, and to adopt the option only if the “net” cost is negative, or, in other words, it is positive net gain. Pricing of the option from the point of view of the agent must take into account non-diversification of the agent wealth and non-tradability of the options as well as possibility to influence the stock price by the agent (again, if we believe in the incentive mechanism of the options). An attempt to solve the first part was done by the “certainty equivalence” approach (see for example, Hall and Murphy (2002)). We need to mention here, that the “certainty equivalence” approach for a total grant will result in the “average pricing” of the options in the grant. We need to note, that the price of the option should be thought rather as the marginal utility, 78 or in more precise term the “marginal certainty equivalence” of the last option in the grant. It will further decrease the value of the option for the agent, compared to the case of the “certainty equivalence” valuation. On the other hand, if we believe in the incentives built in the options, the value for the agent could be substantially higher, comparing to the similar undiversified outside investor, because of the opportunity to influence the stock price by the agent’s action. Second puzzle, which we would like to discuss here, is: Why executives almost always exercise options when they become vested, long time before the maturity? For the outside investor it would be optimal to keep an American Call Option to maturity (for non paying dividend stock). We will construct an example, when the agent would optimally exercise the option as soon as it becomes vested to eliminate the incentive (if any) and retention mechanism of the option grant. In other words, if there is no incentive, the agent will exercise option just hoping to get a new one from the principal to keep the retention mechanism alive. If we assume that the incentive mechanism of the option exists, but do not look at the retention mechanism of the options, we could still construct such an example, because the agent could be better of if she exercises the option earlier and do not apply costly effort after that: Example A7.1: For simplicity, let’s assume that the risk neutral agent do not discount future efforts and incomes. Let’s assume that the agent applying effort could increase the expected return, without any impact on the volatility of the return. Let the expected return μ be equal to 100%, if the agent does not apply an 79 effort (cash value of the zero effort), and μ = 200%, if the agent applies the effort a=1, proportional to value of the firm (as always we normalize the value of the firm at t=0 by 1: S 0 =1). Therefore, the distribution of the stock price at T=2 would be (4,σ) with no effort, and (9, σ) with the effort. So if the agent makes an effort, the value jumps immediately in expectation to be E(S 2 )=9 at time 2. Now, if the option was granted “at-the-money” at t=0, at T=2 the price per share is S 2 =(9+1)/2=5, and assuming that agent do not change volatility, at time t=1, the stock price S 1 =5/2=2.5, and at time t=0, the stock price S 0 =2.5/2=1.25, so there is immediate effect on the stock price. If the agent works two periods hard (i.e. a 1 =1, a 2 =3) her expected payoff is 0: (S 2 -K)-a 1 -a 2 =(5-1)-1-3. If the agent works hard one period and exercises the option after one period, her expected payoff at time t=1 is 0.5: (S 1 -K)-a 1 =(2.5-1)-1. After the exercise, the total value of the firm is 2*3+2*1=8 at time T=2, and therefore price per share is S 2 =4. Therefore, at time t=1, the stock price S 1 =2 (after the option is exercised), so the price adjusts immediately, dropping from S 2 =2.5 before exercise to S 2 =2 after the exercise. The agent’s total expected payoff for two periods is (S 2 -K)- a 1 =(4-1)-1=2. So, the agent would optimally exercise at time t=1 even in the case of absence of dividends. Note, even if we assume that effort at the second period is 1 (i.e. it does not depend on the size of the company), the total expected payoff with the effort in the second period is (5-1)-1-1=2 and without the effort at the second period it is (4-1)-1=2, so the agent is indifferent between exercising at t=1 and at t=T=2. 80 Appendix 8 Robust Regression In this appendix we briefly discuss Robust Regression used in our empirical analysis. In order to perform a Robust Regression we first use Hubert weight and later switches to biweight. Robust regression assigns a weight to each observation with higher weights given to better behaved observations. In fact, extremely deviant cases can have their weights set to missing so that they are not included in the analysis at all. For more information about Robust Regression in general, and Hubert estimator and Tukey biweight (or bisquare) estimator particularly, see John Fox (2002). Here we present basic facts about Robust Regression. Consider the linear model y i = α + β 1 x i1 + β 2 x i2 +···+ β k x ik + ε i = x’ i β + ε i for the ith of n observations. The fitted model is y i = a + b 1 x i1 + b 2 x i2 +···+ b k x ik + e i = x’ i b + e i The general M-estimator minimizes the objective function ∑ n i=1 ρ(e i ) =∑ n i=1 ρ(y i − x’ i b) where the function ρ gives the contribution of each residual to the objective function. For example, for least-squares estimation, ρ(e i ) = e 2 i Let ψ = ρ’ be the derivative of ρ. Differentiating the objective function with respect to the coefficients, b, and setting the partial derivatives to 0, produces a system of k +1 estimating equations for the coefficients: ∑ n i=1 ψ(y i − x’ i b)x’ i = 0 81 Define the weight function w(e) = ψ(e)/e, and let w i = w(e i ). Then the estimating equations may be written as ∑ n i=1 w i (y i − x’ i b)x’ i = 0 Solving the estimating equations is a weighted least-squares problem, minimizing ∑w 2 i e 2 i . The weights, however, depend upon the residuals, the residuals depend upon the estimated coefficients, and the estimated coefficients depend upon the weights. An iterative solution is therefore required: 1. Select initial estimates b(0), such as the least-squares estimates. 2. At each iteration t, calculate residuals e i (t−1) and associated weights w i (t−1)=w[e i (t−1)] from the previous iteration. 3. Solve for new weighted-least-squares estimates b(t)=[X’ W(t−1)X] −1 X’W(t−1)y where X is the model matrix, with x’ i as its ith row, and W(t−1)= diag{w i (t−1)}is the current weight matrix. Steps 2 and 3 are repeated until the estimated coefficients converge. Objective functions for the Huber estimator and the Tukey bisquare (or biweight) estimator are: Huber: ρ H (e) =1/2e 2 for |e| ≤ k and ρ H (e) =k|e| −1/2k 2 for |e| > k Bisquare: 82 ρ B (e) =k 2 /6{1 −[1 −(e/k) 2 ] 3 }for |e| ≤ k and ρ B (e) = k 2 /6 for |e| > k The least-squares and Huber objective functions increase without bound as the residual e departs from 0, but the least-squares objective function increases more rapidly. In contrast, the bisquare objective function levels off (for |e| > k). Least-squares assigns equal weight to each observation; the weights for the Huber estimator decline when |e| > k; and the weights for the bisquare decline as soon as e departs from 0, and are 0 for |e| > k. The value k for the Huber and bisquare estimators is called a tuning constant; smaller values of k produce more resistance to outliers, but at the expense of lower efficiency when the errors are normally distributed. The tuning constant is generally picked to give reasonably high efficiency in the normal case; in particular, k = 1.345σ for the Huber and k = 4.685σ for the bisquare (where σ is the standard deviation of the errors) produce 95-percent efficiency when the errors are normal, and still offer protection against outliers. In an application, we need an estimate of the standard deviation of the errors to use these results. A robust measure of spread is employed in preference to the standard deviation of the residuals. A common approach is to take s = MAR/0.6745, where MAR is the median absolute residual. 83 Appendix 9 Table 3 Robust Regression of Stock Options Granted as a Percentage of Total Compensation Dependent Variable: OptionGrantedPart Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 22 298.80077 13.58185 263.70 <.0001 Error 17213 886.54423 0.05150 Corrected Total 17235 1185.34500 Root MSE 0.22695 R-Square 0.2521 Dependent Mean 0.32325 Adj R-Sq 0.2511 Coeff Var 70.20835 Parameter Estimates Parameter Standard Variable Label Estimate Error t Value Intercept Intercept -0.36395 0.01797 -20.25 LOG_MKTVAL 0.05113 0.00132 38.75 VOLAT Volatility (60mo) 0.43863 0.01260 34.80 SALECHG Sales 1 Year Percent Change 0.00011048 0.00007203 1.53 EPSEXCHG EPS 1 Year Percent Change -0.00000598 0.00000222 -2.69 ASSETCHG Assets 1 Year Percent Change0.00047111 0.00005709 8.25 ROA Return on Assets -0.00097356 0.00023368 -4.17 TOBINS_Q 0.00039366 0.00013342 2.95 DummyNewSIC 0.11793 0.00678 17.38 DummyOldSIC 0.03372 0.00385 8.75 Dummy1993 0.02472 0.01509 1.64 Dummy1994 0.07908 0.01469 5.38 Dummy1995 0.06395 0.01455 4.40 Dummy1996 0.10372 0.01458 7.11 Dummy1997 0.11377 0.01454 7.82 Dummy1998 0.18172 0.01469 12.37 Dummy1999 0.20305 0.01473 13.78 Dummy2000 0.17727 0.01474 12.03 Dummy2001 0.21172 0.01486 14.24 Dummy2002 0.13332 0.01492 8.94 Dummy2003 0.05999 0.01475 4.07 Dummy2004 0.04419 0.01467 3.01 Dummy2005 0.02792 0.01456 1.92 84 Table 4 Robust Regression of Bonus Paid as a Percentage of Total Compensation Dependent Variable: BonusPart Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 22 29.96438 1.36202 82.99 <.0001 Error 17190 282.10479 0.01641 Corrected Total 17212 312.06917 Root MSE 0.12811 R-Square 0.0960 Dependent Mean 0.18071 Adj R-Sq 0.0949 Coeff Var 70.88868 Parameter Estimates Parameter Standard Variable Label Estimate Error t Value Intercept Intercept 0.18052 0.01013 17.81 LOG_MKTVAL 0.00297 0.00074241 3.99 VOLAT Volatility (60mo) -0.08414 0.00633 -13.30 SALECHG Sales 1 Year Percent Change 0.00027327 0.00004075 6.71 EPSEXCHG EPS 1 Year Percent Change 0.00000755 0.00000135 5.59 ASSETCHG Assets 1 Year Percent Change-0.00007058 0.00003016 -2.34 ROA Return on Assets 0.00314 0.00014599 21.49 TOBINS_Q -0.00034633 0.00007739 -4.47 DummyNewSIC -0.03491 0.00374 -9.34 DummyOldSIC 0.00296 0.00221 1.34 Dummy1993 0.00358 0.00868 0.41 Dummy1994 0.00902 0.00844 1.07 Dummy1995 0.00910 0.00837 1.09 Dummy1996 -0.00125 0.00838 -0.15 Dummy1997 -0.00124 0.00836 -0.15 Dummy1998 -0.01978 0.00843 -2.35 Dummy1999 -0.02404 0.00845 -2.85 Dummy2000 -0.03119 0.00844 -3.69 Dummy2001 -0.04506 0.00849 -5.30 Dummy2002 -0.01138 0.00854 -1.33 Dummy2003 0.00749 0.00846 0.88 Dummy2004 0.02208 0.00843 2.62 Dummy2005 0.01187 0.00837 1.42 85 Table 5 Robust Regression of Stock Option Granted Dependent Variable: BLK_VALU Options Granted ($ Black-Scholes value) Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 22 5555202568 252509208 532.41 <.0001 Error 15496 7349311425 474272 Corrected Total 15518 12904513992 Root MSE 688.67374 R-Square 0.4305 Dependent Mean 708.23038 Adj R-Sq 0.4297 Coeff Var 97.23866 Parameter Estimates Parameter Standard Variable Label Estimate Error t Value Intercept Intercept -53.55584 42.27659 -1.27 MKTVAL Market Value (Fiscal Year-End) 0.06061 0.00061102 99.20 VOLAT Volatility (60mo) 282.00290 34.13387 8.26 SALECHG Sales 1 Year Percent Change -0.34888 0.24514 -1.42 EPSEXCHG EPS 1 Year Percent Change -0.00206 0.00696 -0.30 ASSETCHG Assets 1 Year Percent Change 2.20207 0.23193 9.49 ROA Return on Assets -0.28380 0.75674 -0.38 TOBINS_Q 0.32940 0.43038 0.77 DummyNewSIC 183.34201 23.34809 7.85 DummyOldSIC 90.82728 12.51869 7.26 Dummy1993 60.63985 46.63584 1.30 Dummy1994 163.46196 45.39300 3.60 Dummy1995 126.38112 45.00596 2.81 Dummy1996 219.87211 45.36935 4.85 Dummy1997 240.40530 45.50423 5.28 Dummy1998 492.43032 46.24247 10.65 Dummy1999 575.29306 46.72892 12.31 Dummy2000 572.47085 46.75571 12.24 Dummy2001 663.86658 47.57330 13.95 Dummy2002 532.34617 47.31009 11.25 Dummy2003 406.75236 46.38719 8.77 Dummy2004 402.73261 46.28626 8.70 Dummy2005 343.41498 45.84111 7.49 86 Table 6 Robust Regression of Bonus Paid Dependent Variable: BONUS Bonus ($Thous) Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 22 1557225793 70782991 668.29 <.0001 Error 16446 1741891072 105916 Corrected Total 16468 3299116864 Root MSE 325.44706 R-Square 0.4720 Dependent Mean 435.09404 Adj R-Sq 0.4713 Coeff Var 74.79925 Parameter Estimates Parameter Standard Variable Label Estimate Error t Value Intercept Intercept 228.68511 18.46961 12.38 MKTVAL Market Value (Fiscal Year-End) 0.02738 0.00025746 106.36 VOLAT Volatility (60mo) -210.48383 15.76293 -13.35 SALECHG Sales 1 Year Percent Change 0.79144 0.10458 7.57 EPSEXCHG EPS 1 Year Percent Change 0.02466 0.00363 6.79 ASSETCHG Assets 1 Year Percent Change -0.07379 0.08393 -0.88 ROA Return on Assets 5.69484 0.37804 15.06 TOBINS_Q -0.62069 0.21654 -2.87 DummyNewSIC -57.22473 9.83978 -5.82 DummyOldSIC 36.79899 5.80129 6.34 Dummy1993 15.02804 20.64082 0.73 Dummy1994 44.26796 19.95983 2.22 Dummy1995 52.69343 19.80589 2.66 Dummy1996 66.40046 19.91327 3.33 Dummy1997 97.91018 19.89631 4.92 Dummy1998 100.89919 20.17983 5.00 Dummy1999 123.86479 20.30307 6.10 Dummy2000 118.92959 20.32995 5.85 Dummy2001 105.38143 20.52105 5.14 Dummy2002 204.24514 20.69480 9.87 Dummy2003 216.99888 20.50481 10.58 Dummy2004 306.84786 20.48831 14.98 Dummy2005 308.62692 20.35238 15.16 87 Table 7 Multivariate Regression of Stock Option Granted and Bonus Paid as a Percentage of Total Compensation, Option Part Dependent Variable: OptionGrantedPart Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 22 243.36534 11.06206 169.34 <.0001 Error 17224 1125.14632 0.06532 Corrected Total 17246 1368.51167 Root MSE 0.25559 R-Square 0.1778 Dependent Mean 0.32824 Adj R-Sq 0.1768 Coeff Var 77.86626 Parameter Estimates Parameter Standard Variable Label Estimate Error t Value Intercept Intercept -0.23452 0.01915 -12.24 LOG_MKTVAL 0.04218 0.00140 30.15 VOLAT Volatility (60mo) 0.27996 0.01134 24.68 SALECHG Sales 1 Year Percent Change 0.00016108 0.00007271 2.22 EPSEXCHG EPS 1 Year Percent Change -0.00000598 0.00000241 -2.48 ASSETCHG Assets 1 Year Percent Change0.00038208 0.00005704 6.70 ROA Return on Assets -0.00086237 0.00024936 -3.46 TOBINS_Q 0.00035508 0.00013938 2.55 DummyNewSIC 0.12024 0.00704 17.07 DummyOldSIC 0.03059 0.00417 7.33 Dummy1993 0.02506 0.01652 1.52 Dummy1994 0.07655 0.01607 4.76 Dummy1995 0.06065 0.01593 3.81 Dummy1996 0.09783 0.01595 6.13 Dummy1997 0.11068 0.01590 6.96 Dummy1998 0.17388 0.01606 10.83 Dummy1999 0.19565 0.01610 12.15 Dummy2000 0.17859 0.01607 11.11 Dummy2001 0.21493 0.01619 13.28 Dummy2002 0.14182 0.01625 8.73 Dummy2003 0.07276 0.01609 4.52 Dummy2004 0.05262 0.01603 3.28 Dummy2005 0.03315 0.01592 2.08 88 Table 8 Multivariate Regression of Stock Option Granted and Bonus Paid as a Percentage of Total Compensation, Bonus Part Dependent Variable: BonusPart Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 22 32.60575 1.48208 54.72 <.0001 Error 17224 466.52460 0.02709 Corrected Total 17246 499.13035 Root MSE 0.16458 R-Square 0.0653 Dependent Mean 0.19963 Adj R-Sq 0.0641 Coeff Var 82.44052 Parameter Estimates Parameter Standard Variable Label Estimate Error t Value Intercept Intercept 0.17385 0.01233 14.10 LOG_MKTVAL 0.00451 0.00090077 5.00 VOLAT Volatility (60mo) -0.04847 0.00731 -6.63 SALECHG Sales 1 Year Percent Change 0.00035345 0.00004682 7.55 EPSEXCHG EPS 1 Year Percent Change 0.00000616 0.00000155 3.97 ASSETCHG Assets 1 Year Percent Change-0.00006509 0.00003673 -1.77 ROA Return on Assets 0.00306 0.00016057 19.05 TOBINS_Q -0.00027492 0.00008975 -3.06 DummyNewSIC -0.04182 0.00453 -9.22 DummyOldSIC -0.00192 0.00269 -0.72 Dummy1993 0.00637 0.01064 0.60 Dummy1994 0.00855 0.01035 0.83 Dummy1995 0.01015 0.01026 0.99 Dummy1996 0.00384 0.01027 0.37 Dummy1997 0.00320 0.01024 0.31 Dummy1998 -0.01821 0.01034 -1.76 Dummy1999 -0.02297 0.01037 -2.22 Dummy2000 -0.03106 0.01035 -3.00 Dummy2001 -0.04802 0.01042 -4.61 Dummy2002 -0.00857 0.01046 -0.82 Dummy2003 0.01030 0.01036 0.99 Dummy2004 0.02353 0.01032 2.28 Dummy2005 0.01582 0.01025 1.54 89 Table 9 Correlation Coefficients of Dependent Variables Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum OptionGrantedPart 21526 0.32489 0.28951 6994 0 1.00000 BonusPart 21526 0.19179 0.17251 4128 -1.3998E-7 1.00000 Pearson Correlation Coefficients, N = 21526 Prob > |r| under H0: Rho=0 Option Granted Bonus Part Part OptionGrantedPart 1.00000 -0.40891 <.0001 BonusPart -0.40891 1.00000 <.0001 Variable N Mean Std Dev Sum Minimum Maximum BLK_VALU 21568 2206 8925 47587478 0 600347 BONUS 21772 704.29971 1603 15334013 -0.0010000 102015 Simple Statistics Variable Label BLK_VALU Options Granted ($ Black-Scholes value) BONUS Bonus ($Thous) Pearson Correlation Coefficients Prob > |r| under H0: Rho=0 Number of Observations BLK_VALU BONUS BLK_VALU 1.00000 0.14317 Options Granted ($ Black-Scholes value) <.0001 BONUS 0.14317 1.00000 Bonus ($Thous) <.0001

Abstract (if available)

Abstract In the dissertation we consider the Executive Compensation problem with the compensation plan restricted to the fixed cash salary, short-term bonuses (based on the accounting performance data) and long-term incentives (executive stock option (ESO) contract). We model executive effort and performance measure as multi-dimensional. We propose a model of asymmetric information flow, when the uncertainty about relationship between two performance measures is revealed to the agent after the contracting but before an action is taken. We provide empirical evidence that not only overall risk of companies has opposite effect on bonuses and ESO's, but also different types of risk are primary determinants of different parts of executive compensation.

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Asset Metadata

Creator Marynets, Yuri (author)

Core Title Stock options and short term bonuses in executive compensation contracts

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 07/30/2009

Defense Date 06/14/2007

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag executive compensation,OAI-PMH Harvest

Language English

Advisor Fygenson, Mendel (committee chair), Cvitanic, Jaksa (committee member), Pevnitskaya, Svetlana (committee member)

Creator Email marynets@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m723

Unique identifier UC1221488

Identifier etd-Marynets-20070730 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-534728 (legacy record id),usctheses-m723 (legacy record id)

Legacy Identifier etd-Marynets-20070730.pdf

Dmrecord 534728

Document Type Dissertation

Rights Marynets, Yuri

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu