Is U.S. CEO Equity and Cash Compensation Aligned with Agency Theory to Maximize Shareholder Returns?

Abstract

Recent international studies on CEO pay in Europe, Japan, and South Korea reveal significant differences from the U.S. in the use and effectiveness of equity-based CEO compensation, raising questions about the ability of conventional contracts based on agency theory to align with actual CEO compensation practices. Our study contributes to this debate by evaluating nine hypotheses from an extended principal–agent framework in which CEO equity and cash incentives are jointly determined in the shareholder return-maximizing contract. The extended model also incorporates the noisy market valuation relationship between firm income and its market equity value, and distinguishes between firm ‘business risk’ and ‘equity risk’. Our empirical results show that CEO cash incentives increase with firm growth prospects and equity risk and decline with firm business risk and firm scale as predicted by the model; meanwhile, CEO equity incentives are partially consistent. Overall, given the dominance of equity compensation in U.S. CEO pay, our results show that cash pay tied to firm business performance (e.g., operating cash flow) is efficient and plays an important role in aligning CEO and shareholder interests and reducing corporate governance risks associated with agency misalignment.

1. Introduction

While CEO equity compensation has risen in recent decades to become the dominant component of their pay in the United States, recent studies related to Europe, Japan, and South Korea reveal significant variation in the structure of CEO pay. For example, Pan and Zhou (2018) report that Japanese CEOs receive, on average, 71% of their compensation as salary, while the same for U.S. CEOs is 21%. Bettis et al. (2001) found that performance-based equity compensation increased dramatically from 20% to 70% in the largest 750 U.S. public firms over the 1998–2012 period. Lee and Wu (2022) report that chief executives in South Korean firms receive most of their pay as salary, and their pay-performance sensitivity is low. Smirnova and Zavertiaeva (2017) have found that CEO bonus pay in large European firms tied to ROA is more effective in enhancing firm performance than market-based compensation. This variation in the use of equity pay in advanced economies raises questions about the ability of conventional incentive contracts based on agency theory to align with actual CEO compensation practices.

The higher levels of CEO equity compensation in the U.S. are frequently justified by appealing to the principal–agent theory, which advocates the use of variable compensation as an efficient mechanism for aligning shareholder and CEO interests (e.g., Meckling & Jensen, 1976; Mirrlees, 1976; Grossman & Hart, 1983; Garen, 1994; Aggarwal & Samwick, 1999; Cheng et al., 2015). Another important question arising from the differences in pay structure between the U.S. and other economies is whether an extended principal–agent framework can explain higher cash incentives relative to equity incentives and whether the compensation received by U.S. CEOs is consistent with its predictions. The answer to this question can provide useful practical guidance on the design of more efficient CEO pay in the U.S. and reduce the risks associated with the agency misalignment of CEO and shareholder interests.

We contribute to this debate and provide new insights into the efficiency of U.S. CEO pay by evaluating nine hypotheses from an extended principal–agent framework that incorporates a broader set of firm characteristics (e.g., firm growth prospects, firm scale, equity risk, and business risk). This return-maximizing contract jointly determines the CEO’s equity and cash incentives. CEO cash incentives become more important in the extended model as the objective function includes a measure of firm income and its associated effect on equity value via a noisy market valuation mechanism. Additionally, the model distinguishes between business risk and equity risk, which the CEO is exposed to in the compensation contract. Firm business risk arises from interactions between firm stakeholders (e.g., customers, suppliers, and management) that impact firm revenues and costs, and ‘firm equity risk’ is related to assessments of the firm equity value by financial Fimarket participants.

Our empirical study uses data from Execucomp and Compustat to evaluate hypotheses on CEO cash and equity incentives using the extended principal–agent framework. In the pay regressions, we relate CEO cash and equity incentives to proxies of our key model variables (firm growth prospects, firm scale, equity risk, business risk), and the estimation controls for important firm characteristics, including firm leverage, return on equity, Tobin’s Q, equity return, cash flow changes, CEO age, and dividend yield. We also include fixed effects for firm and year to mitigate bias from potential omitted variables and endogeneity in the estimation, and the resulting pay regressions exhibit high R-squares (0.74–0.79).

The study also makes a methodological contribution by estimating CEO cash incentives or PPSC (pay-performance sensitivity of cash compensation) and firm business risk using quarterly firm operating cash flows and CEO pay from Compustat and Execucomp. The pay regression estimation shows that CEO cash incentives increase with the firm growth prospects and equity risk, and decline with firm scale and firm business risk, as predicted by the extended model, while CEO equity incentives are partially aligned. Overall, given the dominance of CEO equity compensation in the U.S., our empirical results show that CEO cash compensation tied to the firm business performance (e.g., firm operating cash flow) is efficient and plays a central role in aligning agency interests to maximize shareholder returns.

An important result from formal principal–agent models is that greater uncertainty in performance measures discourages effort and makes variable incentives more costly (e.g., Mirrlees, 1976; Grossman & Hart, 1983; Holmstrom & Milgrom, 1987). Many empirical studies evaluate the efficiency and agency alignment of CEO pay by studying the relationship between CEO pay incentives and firm equity risks, and report mixed results. While J. Core and Guay (1999), Oyer and Schaefer (2005), and Coles et al. (2006) find a positive relationship between the pay-performance sensitivity of CEO compensation incentives and firm equity risk, Lambert and Larcker (1987), Aggarwal and Samwick (1999), and Jin (2002) report a negative relationship. Garen (1994), Yermack (1995), Ittner et al. (1997), Conyon and Murphy (2000), and Cheng et al. (2015) find neither mixed results nor a significant relationship between CEO incentives and firm equity risk. Garen (1994) evaluates whether the pay-performance sensitivity of total CEO compensation and salary compensation increases with the standard deviation of firm equity returns, and the results do not provide empirical support for this prediction using the standard agency model. Aggarwal and Samwick (1999) report a negative relationship between the total equity variance (the product of percent return variance and firm market value) and the pay-performance sensitivity of CEO pay. J. E. Core and Guay (2002) include firm market value and the percent return variance as separate explanatory variables in the pay regressions and find a positive association between CEO incentives and equity return variance. Cheng et al. (2015) report a significant positive relationship between total CEO compensation and the return volatility for financial firms.

We also note that results from previous studies are not fully comparable to our study as the extended model’s objective function, contract structure, and valuation mechanism differ, as discussed above (please see Section 2 for details). These extensions provide additional testable hypotheses that relate jointly determined CEO equity and cash incentives to important firm characteristics, including growth prospects, firm scale, business risk, and firm equity risk. Many earlier CEO studies infer empirical hypotheses from the standard principal–agent model, where firm owners maximize expected profits with a contract that includes salary and variable cash compensation but not equity compensation.

Another stream of the CEO pay literature extends the standard principal–agent framework to study the relationship between equity incentives, firm investment, and firm size. Hermalin (2005) shows that tighter corporate governance increases both the level of effort that the CEO must exert and the risk of dismissal, and thus managers require greater pay as compensation. Gervais et al. (2011) show that managerial overconfidence reduces the incentives required to induce a manager to undertake risky but profitable projects. Giannetti (2011) shows that the potential for job-switching (due to transferable skills) induces CEOs to select short-term projects that increase their external marketability over long-term projects. To prevent this, shareholders must promise a greater share of profits to managers from a long-term project, which raises expected compensation.

Benmelech et al. (2010) consider a framework where the CEO privately observes that the firm has matured and its growth potential has declined. Reducing investment lowers the stock price, and managers with a large equity stake benefit from this by pursuing an inefficiently high investment policy. In a similar vein, Goldman and Slezak (2006) and Peng and Röell (2008) demonstrate that high equity incentives can encourage the manager to expend firm resources to manipulate the stock price upwards.

Cao and Wang (2008) present a market equilibrium model in which firms and CEOs search for optimal matches. Their theoretical and empirical results show that the growing performance of the macro-economy and firm-specific factors simultaneously generate an increase in CEO pay and firm size. The empirical study of Gayle and Miller (2009) shows that CEOs of larger complex firms face greater agency problems, thereby necessitating the need for higher equity incentives. Edmans et al. (2009) consider an agency model in which CEO effort affects the firm’s expected future equity value via a multiplicative effect and shows that the resulting CEO compensation is positively related to firm size. The extended agency model used in this study jointly determines both CEO cash and equity incentives in a setting where CEO effort affects the firm income measure and the firm equity value via the noisy market mechanism, and both components contribute to the shareholder return in the objective function of the principal.

We also discuss the relevance of our empirical findings to the managerial power perspective of CEO pay (e.g., Bertrand & Mullainathan, 2001; Bebchuk & Fried, 2003; Van Essen et al., 2015) and the ability of corporate executives to hedge the equity exposure in their compensation contracts using derivatives such as forward contracts and equity swaps (e.g., Bettis et al., 2001; Jagolinzer et al., 2007).

2. The Extended CEO Agency Framework and Hypotheses

We identify the study’s empirical hypotheses using an extended CEO principal–agent framework that incorporates three features leading to the joint determination of return-maximizing CEO equity and cash compensation. First, firm owners (the principal) maximize their expected total return from firm resources (inclusive of the relevant income measure and associated equity value change) by providing the CEO a contract that includes fixed salary, equity compensation, and variable cash compensation.1 Second, in jointly determining CEO equity and cash incentives, the extended model takes into account the noisy market valuation relationship between the firm equity value and income measure. Ignoring this relation leads to an underestimation of CEO cash incentives related to equity incentives (Pandher, 2022). Third, the model distinguishes between the two types of risks related to the generation of income and value from firm assets: ‘firm business risk’ and ‘firm equity risk’. Lastly, we make some modifications to enable the model’s empirical evaluation using firm-level data from Compustat and Execucomp.

A. 

The Extended CEO Agency Framework

In the extended agency framework, firm owners (the principal) provide the CEO with equity and cash incentives that will generate the effort (actions) required to maximize their complete return from investing in an income-producing business. At the start of the contracting period, firm owners offer the CEO a compensation contract $W=s+bY+mS$ where $s$ is the fixed salary, and $b$ and $m$ represent a fraction of the firm income measure $Y$ and firm equity value $S$, respectively, paid to the CEO as variable incentives. The CEO responds to the contract with effort $a$ over the contracting period.

Firm owners determine CEO equity and cash compensation to maximize the total expected return from firm resources over the contracting period, which is represented by2

$$r_s={\displaystyle \frac{\left(S_0+Y-w\right)-S_0}{S_0}}$$

(1)

where $Y$ represents the appropriate relevant measure of firm income (see below), $Y$ is the initial value of firm equity, $(S-S_0)$ is the change in the firm equity value over the period, and w is the CEO’s total compensation. It is useful to note that the exact specification of $Y$ is a modeling choice and may be adapted to different settings as discussed below.

We next consider how CEO actions affect the firm income measure $Y$, and the firm’s market equity value. The relationship between CEO effort $a$ and $Y$ is represented by

$$Y=\mu +\beta a+\epsilon , \epsilon ~N(0,{\sigma }_y^2)$$

(2)

where $\mu$ is the autonomous level of income unrelated to CEO actions, $\beta$ is the productivity of CEO effort $a$, and $\epsilon$ is a normally distributed shock in the current period. The shock $\epsilon$ represents uncertainty in the firm business performance resulting from interactions between firm stakeholders (e.g., customers, employees, and suppliers) and the economic environment.

The stock market essentially converts information and beliefs of market participants regarding future firm measures of income into a tradable value for buying and selling ownership shares. The firm’s total market value $S$ depends positively on expectations regarding $Y$, and this relationship can be expressed as

$$S=\theta E\left(Y\right)+\eta , \eta ~N(0,{\sigma }_s^2)$$

(3)

where θ is the valuation parameter, and the shock η represents uncertainty in market valuation. Investors are willing to pay higher stock prices (relative to current income levels) if they assess that future earnings will grow at a high rate (higher values of $\theta$ in (3) below). Hence, they are willing to pay more for firms with higher growth prospects in future periods.

The structure of the firm valuation in Equation (3) is also supported by finance theory. In financial investment analysis, the ratio of firm equity value to earnings and other firm performance measures (e.g., revenues and operating cash flow) is commonly used to value firms, and $\theta$ may be interpreted accordingly. For example, if $Y$ is viewed as firm earnings or operating cash flows (OCF), then the valuation parameter $\theta$ may be interpreted as the firm’s price-to-earnings (PE) or price-to-OCF ratio. Alternatively, the valuation parameter $\theta$ may be viewed as the growing perpetuity discount factor representing the present value of the future expected firm earnings $E\left(Y\right)$ in the residual income model (RIM)3. Further, the market shock $\eta$ represents ‘firm equity risk’ and the dispersion in the assessment of firm value by market participants.

In representing the agent’s preferences over compensation, it is a common practice in the principal–agent literature to use the constant absolute risk aversion (CARA) utility specification (e.g., Grossman & Hart, 1983; Jensen & Murphy, 1990; Garen, 1994; Dittman & Yu, 2008; Gao, 2010; and others). This utility yields tractable expressions for incentives and effort that are independent of the CEO’s initial wealth. The CEO’s utility function is

$$U\left(w, a\right)=-exp\left(-\alpha \left(w-{\displaystyle \frac{1}{2}}g{a}^2\right)\right)$$

where $\alpha$ is the manager’s coefficient of risk aversion, and the parameter $g$ represents the manager’s aversion to effort.

The shareholders’ objective is to maximize the total expected firm return $E\left(r\right)={\displaystyle \frac{1}{S_0}} E\left(S+Y-w\right)$ defined in (3) above by offering the contract $W=s+bY+mS$ to the CEO so that it induces the return-maximizing level of effort $a$. The contract will be accepted if it provides at least the same utility as the CEO’s outside opportunity $U(\overline{w})$ ($U\left(w^{\ast }\right)=-exp(-\alpha w^{\ast }))$, where $w^{\ast }$ is the outside certainty reservation pay). Hence, the shareholders’ problem can be formally stated as

$$\underset{s, b,\mathit{m}}{\mathrm{Max}}{\displaystyle \frac{1}{S_0}} E\left(S+Y-w(s,b,m)\right)=\underset{s,\mathit{b},\mathit{m}}{\mathrm{Max}}{\displaystyle \frac{1}{S_0}} E\left(S+Y-s-bY-mS\right)$$

(4)

subject to

$$\underset{a}{\mathrm{Max}}-E\left\{-exp\left(-\alpha \left(w(s, b,m)-{\displaystyle \frac{1}{2}}g{a}^2\right)\right)\right\}$$

(5)

$$-E\left\{-exp\left(-\alpha \left(w(s, b,m)-{\displaystyle \frac{1}{2}}g{a}^2\right)\right)\right\}\ge U(w^{\ast })$$

(6)

To incorporate the effect of firm scale on incentives and to frame the empirical hypotheses in terms of return volatilities, it is useful to normalize the profit and firm value components in the CEO contract by the firm’s start-of-period market value $S_0$. This converts the variances of firm value and profits into variances on equity returns and net income per dollar of firm equity. Accordingly, the contract can be written as

$$W=s+S_{0}b {\displaystyle \frac{Y}{S_0}}+S_{0}m {\displaystyle \frac{S}{S_0}}$$

where ${\sigma }_S^2=V\left({\displaystyle \frac{S}{S_0}}\right)={\displaystyle \frac{{\sigma }_s^2}{S_0^2}}$ is the stock return variance, ${\sigma }_Y^2=V\left({\displaystyle \frac{Y}{S_0}}\right)={\displaystyle \frac{{\sigma }_y^2}{S_0^2}}$ is the equity-normalized profit variance, and the volatility ${\sigma }_Y$ represents the uncertainty of profits per dollar value of firm equity. This provides a common metric for comparing the two firm risks across firms and over time in the empirical study (Section 3).

B. 

Return-Maximizing CEO Equity and Cash Incentives

The solution of the CEO agency model (4)–(6) involves two steps. First, given the contract $w$, the CEO best effort response $a$ to the contract, expressed in (5), is determined. Then, the principal determines $(s, b, m)$ by maximizing (4) subject to (6) and the best effort response $a$ (see Appendix A for details).

Proposition 1.

CEO Compensation Incentives and Effort

The CEO’s return-maximizing cash and equity incentives $b$ and $m$ are given by

$$b={\displaystyle \frac{{{\beta }^2(1+\theta )\sigma }_s^2}{{{\beta }^2({\theta }^2\sigma }_Y^2+{\sigma }_S^2)+{\sigma }_Y^2 S_0^2 {\sigma }_S^{2}g\alpha }}$$

(7)

$$m={\displaystyle \frac{{{\beta }^2\theta (1+\theta )\sigma }_s^2}{{{\beta }^2({\theta }^2\sigma }_Y^2+{\sigma }_S^2)+{\sigma }_Y^2 S_0^2 {\sigma }_S^{2}g\alpha }}$$

(8)

The CEO effort generated by these incentives is

$$a={\displaystyle \frac{{{\beta }^3(1+\theta )({\theta }^2\sigma }_Y^2+{\sigma }_S^2)}{\left({{\beta }^2({\theta }^2\sigma }_Y^2+{\sigma }_S^2)+{\sigma }_Y^2 S_0^2 {\sigma }_S^{2}g\alpha \right)g}}$$

(9)

Table 1. Sensitivities of CEO Incentives and Effort. The signs of the sensitivities of CEO equity and cash incentives and effort in (7)–(9) to firm characteristics are reported below. The “+” sign indicates that the column variable increases when the row parameter increases, while a “−” sign indicates that the column variable decreases.

	$b$	$m$	$m/b$	$a$
$\theta$	+	+	+	+
$\beta$	+	+	0	+
${\sigma }_S$	+	−	−	−
${\sigma }_Y$	−	+	+	−
$S_0$	−	−	0	−

(Expressions for the partial derivatives were obtained from Maple and omitted in the interest of space. They are available upon request from the authors.)

reports the signs of the sensitivities of CEO cash incentives $b$ and equity incentives $m$ (and their ratio $m/b$) to various firm–CEO characteristics, including firm valuation or growth prospects $\theta$; CEO productivity $\beta$; firm business risk ${\sigma }_Y$; firm equity risk ${\sigma }_S$; and firm size $S_0$ (the partial derivatives are reported in Appendix B).

C. 

Empirical Hypotheses

The extended CEO agency model—which incorporates both firm income and equity value in the principal’s objective function, the noisy market valuation mechanism, and distinguishes between business risk and equity risk—provides additional theoretical predictions regarding the relationship between CEO equity and cash incentives and a broader set of firm characteristics (growth prospects, business risk, equity risk and corporate scale), which are evaluated in our empirical study using Execucomp and Compustat data. For example, many studies on CEO compensation infer hypotheses from the standard principal–agent model whose objective function is to maximize profits with a contract that does not include equity compensation. Other models focus on firm equity value in the objective function, while the contract ignores cash incentives. Hence, the extended CEO agency model jointly determines both CEO equity and cash incentives that maximize the total shareholder returns in an arguably more “complete” agency model.

The response of CEO compensation incentives to various firm characteristics provides a number of testable empirical hypotheses regarding the agency alignment of CEO cash and equity compensation. Table 1 reports the signs of the sensitivities of CEO profit incentives $b$ and equity incentives $m$ (and their ratio $m/b$) to various firm-CEO characteristics including firm valuation $\theta$, CEO productivity $\beta$, firm business risk ${\sigma }_Y$, firm equity risk ${\sigma }_S$, and firm size $S_0$.

If CEO equity and cash compensation are found to be inconsistent with these predictions, then this implies a breakdown in the agency alignment of CEO and shareholder interests, and this poses additional risks for corporate governance.

Firm valuation (growth prospects) is an important new parameter in the extended model and plays an important direct and moderating role in CEO return-maximizing incentives and effort. The total return of firm owners (1) includes both the relevant income measure and the associated value change in firm value.

Casual reasoning suggests that CEOs of firms with higher growth prospects should receive higher equity incentives. The extended agency model predicts that both CEO equity and cash incentives should increase with growth prospects (see Table 1). This occurs because CEO equity and cash incentives impact the total return of firm owners via two channels (see Equation (1)). First, they encourage CEO actions that positively affect the firm income measure ($Y$ in (2)), and second, the noisy market valuation mechanism (3) generates a change in firm value ${(S-S}_0)$ in (1). The return-maximizing contract in (4)–(6) balances the benefit of increasing the total return via these two channels with the specific costs of providing equity vs. cash incentives to the CEO. As the contribution to the total return from value growth ${(S-S}_0)$ is higher in firms with a greater growth prospect (larger $\theta$), the increase in CEO equity incentives is larger than cash incentives (the ratio of equity-to-cash incentives increases).

Hypothesis 1.

Firm Growth Prospects

A. 

CEOs of firms with higher growth prospects (θ) receive higher equity incentives.

B. 

CEOs of firms with higher growth prospects (θ) receive higher cash incentives.

C. 

Equity incentives increase in relation to cash incentives in firms with higher growth prospects.

The model further shows analytically that both CEO cash and equity incentives in the return-maximizing contract will decline with firm scale (Table 1). Firm size increases the variance of CEO equity and cash compensation. This discourages CEO actions and raises the cost of variable incentives, and the return-maximizing contract responds by reducing both variable incentives.

Hypothesis 2.

Firm Scale

A. 

CEO equity incentives decline with firm scale (S₀).

B. 

CEO cash incentives decline with firm scale (S₀).

Next, we consider the risk dynamics of the return-maximizing CEO contract and the response of CEO equity and cash incentives to firm business risk and equity risk. The response of CEO compensation incentives to firm risk has served as a key instrument for assessing agency alignment in many studies (e.g., Demsetz & Lehn, 1985; Garen, 1994; J. E. Core & Guay, 2002; Garvey & Milbourn, 2003; Gao, 2010). Higher firm risk discourages managerial effort as firm performance outcomes become more uncertain, while the cost of variable incentives to shareholders increases. Hence, standard agency theory predicts a negative causality between variable compensation and the risk of performance measures in the contract. It is common practice in this analysis to measure ‘firm risk’ as the variance of firm equity returns.

The extended agency model distinguishes between the two types of firm risks to which the CEO is exposed—‘firm business risk’ and ‘equity return risk’—and evaluates their impact on return-maximizing equity and profit incentives. The return-maximizing compensation incentives place more weight on the lower risk performance measure, as this tends to reduce the certainty equivalent cost of the contract. The extended model predicts that CEO cash incentives are negatively related to firm business risk ${\sigma }_Y$, while CEO equity incentives are negatively related to firm equity return volatility ${\sigma }_S$ (Table 1). CEO compensation incentives also display ‘cross-risk efficiency’, with equity incentives rising with business risk and cash incentives rising with equity return risk.

Hypothesis 3.

Firm Business Risk

A. 

CEO cash incentives are negatively related to firm business risk (σ_Y).

B. 

CEO equity incentives are positively related to firm business risk (σ_Y).

Hypothesis 4.

Equity Return Risk

A. 

CEO cash incentives are positively related to firm equity risk (σ_S).

B. 

CEO equity incentives are negatively related to firm equity risk (σ_S).

3. Empirical Methodology and Data

The empirical methodology and pay regressions used to evaluate the study’s nine hypotheses in Section 2 are discussed below.

A. 

CEO Compensation Incentives and Firm Business Risk

In empirical studies, CEO compensation incentives are defined as the sensitivity of pay to changes in the relevant firm performance measure (Jensen & Murphy, 1990; J. Core & Guay, 1999). We estimate the CEO’s pay-for-performance sensitivity of equity compensation (PPSE) as the dollar value change in stocks and options owned by the CEO relative to a $1000 change in shareholder value. PPSE is defined by J. Core and Guay (1999) as the ratio of the change in the dollar value of CEO total equity compensation (shares owned by the CEO times the change in stock price) to the change in shareholder value over the year (outstanding firm shares times the change in stock price), multiplied by $1000. As the price change cancels out in this ratio, the equity component of PPSE comprises the fraction of shares of stock owned by the CEO multiplied by $1000. The component of the stock options of PPSE is the fraction of firm shares on which the options are written, multiplied by the option delta (and then multiplied by $1000). The CEO’s PPSE is then the sum of these components of stocks and options. In our study sample from Execucomp (see below), the mean CEO equity incentive (PPSE) is $33.50 per $1000 increase in shareholder wealth (Table 1).

Our analysis further makes a methodological contribution by using data from Compustat and Execucomp to estimate firm business risk and CEO cash incentives (PPSC), which measures the sensitivity of CEO cash compensation to changes in business performance. We noted earlier that the selection of the appropriate firm income measure Y over the contracting period is a modeling choice; however, its selection should be coherent with the principal’s objective. In the extended agency framework, firm owners provide the CEO with equity and cash incentives required to maximize the complete return from investing in an income-producing business. Three potential candidates for the firm income measure in (1) include dividends, earnings, and operating cash flow (OCF). The use of firm dividends as the income measure is prone to two problems. It would exclude many firms that do not pay dividends and would underestimate the total return over the contracting period. Since the firm is a going concern, net income at the end of the current period may be retained for reinvestment or paid out as dividends. Including only dividends in (3) underestimates the current period return because reinvested earnings will generate additional incremental earnings in future periods, which are ignored.4

Firm operating cash flow (OCF) represents the income from the firm’s business operations available to firm owners. This measure of business income is obtained by adjusting net income for non-cash accrual items (e.g., depreciation and amortization) and changes in working capital, and it represents the revenue remaining after deducting cash flows for all firm inputs and resources. Further, investing and financing transactions, including borrowing, capital expenditures, and dividend payments, do not affect OCF. Given that firm operating cash flow is most closely related to firm business income, we use this measure in the estimation of firm business risk and the pay-for-performance sensitivity of CEO cash compensation, as discussed below.

An important difference between CEO equity and cash compensation is that the former is an asset (portfolio of stock and options) held by the CEO, while cash compensation is an annual flow variable. As noted above, PPSE (pay-for-performance sensitivity of CEO equity compensation) is defined by J. Core and Guay (1999) as the ratio of the change in the dollar value of CEO total equity compensation to the change in shareholder value over the year. It is estimated as the fraction of firm shares owned by the CEO (multiplied by $1000). As a counterpart to PPSE, we analogously estimate the pay-for-performance sensitivity of CEO cash compensation (PPSC) as the ratio of total CEO annual cash compensation to total annual firm operating cash flow multiplied by $1000. While the mean CEO equity incentive (PPSE) is $33.50 per $1000 increase in shareholder wealth, the corresponding mean CEO cash incentive (PPSC) is $11.63 per $1000 increase in firm operating cash flow.5

As mentioned earlier, ‘firm business risk’ is the uncertainty in the firm business performance arising from factors affecting revenues and costs. We measure firm business risk using variations in quarterly firm operating cash flow from normal business activity. To make this measure comparable across firms and over time, we normalize firm operating cash flow by its market equity value at the start of the year and compute the quarterly variance over three-year windows. The resulting measure of firm business risk represents the annual variation in firm operating cash flow per dollar of invested shareholder equity.

In the estimation of business risk measure, we first define “CashReturn” as the (annualized) quarterly firm operating cash flow (OCF) divided by prior end-of-year firm market capitalization. The variance of CashReturn, based on quarterly Compustat data, is the measure for firm business risk discussed above. In our sample, CashReturn has a mean of 17.4% and a standard deviation of 12.9%. The corresponding mean and standard deviation of firm equity returns are 9.3% and 38.0%, respectively.

B. 

CEO Pay Regressions

The regression analysis used to evaluate the study hypotheses is discussed below. The pay regressions relate CEO equity and cash incentives, namely PPSE and PPSC, to proxies for primary model variables, including firm growth prospects, firm scale, business risk and equity return risk, and controls variables used in other CEO compensation studies (e.g., Garen, 1994; Aggarwal & Samwick, 1999; Jin, 2002; Garvey & Milbourn, 2003; Gao, 2010; Cheng et al., 2015). To mitigate against omitted variable bias and potential endogeneity, we also include firm and year fixed effects, and the resulting CEO pay regressions exhibit high R-squares of 74–79% (Tables 4 and 5). The complete CEO pay regressions are as follows:

$$\begin{array}{rr}\hfill Y_{it}=a_t& \hfill + {a_{1}FirmSize}_{it-1}+{a_{2}EquityReturn}_{it-1}+{a_{3}CDF\left(EquityVariance\right)}_{it-1}\\ & \hfill +{a_{4}CashReturn}_{it-1}+{a_{5}CDF\left(CashVariance\right)}_{it-1}+{a_6(M/B)}_{it-1}\\ & \hfill +{a_7(P/E)}_{it-1}+{a_{8}ROE}_{it-1}+{a_{9}Leverage}_{it-1}+{a_{10}Age}_{it-1}+{\epsilon }_{it}\end{array}$$

(10)

We follow Conyon et al. (2010) and define the dependent variable as $Y=\mathrm{l}\mathrm{n}\left(PPSE\right)\times 100$ for CEO equity incentives and $\mathrm{l}\mathrm{n}\left(PPSC\right)\times 100$ for cash incentives. Econometrically, the logarithm transformation improves the model’s empirical fit by reducing its non-linearity and heteroskedasticity. The scaling of 100 allows the coefficients to be interpreted as a percent change effect, and the testing is based on clustered errors. To address possible concerns of endogeneity among explanatory variables, we employ the general method of moments (GMM) estimation analysis of the pay regression model. As a further robustness check, we estimate quantile (median) regression models that fit the median (rather than average) level of CEO incentive. This estimation is less sensitive to outlier observations in the data or non-normal distribution.

The dependent variables in the regression (10) are discussed next. According to Hypothesis 1, firms with higher growth prospects will provide larger equity and cash incentives to CEOs. Since investors are willing to pay a higher price for these firms relative to earnings (higher θ), we use the firm’s price-to-earnings (PE) ratio as a reasonable market-based proxy for firm growth prospects. Hypothesis 2 predicts a negative relation between firm scale (FirmSize) and CEO cash and equity incentives, and we estimate it using firm market capitalization.

Hypotheses 3 and 4 involved the estimation of volatility in OCF and stock returns. EquityVariance measures the firm equity risk and is estimated as the variance of stock returns over the prior three years. CDF (EquityVariance) is the firm’s position in the cumulative distribution function of firm equity variances (Aggarwal & Samwick, 1999). As discussed above, CashReturn estimates the firm business performance and is measured as the annual firm business operating cash flow divided by the prior end-of-year firm market capitalization. CashVariance measures the firm business risk and is estimated as the variance of quarterly CashReturns over the prior three years, and CDF (CashReturn) represents the firm’s position in the cumulative distribution function of firm CashReturn variances.

EquityReturn is the annual shareholder return and is used to control for differences in firm performance. The Leverage ratio, calculated as the book value of long-term debt divided by the book value of assets, is used to control for differences in capital structure. The estimation also controls for CEO Age and DividendYield.

C. 

Study Data

CEO compensation data from U.S. firms is obtained from the Execucomp database for the period 1992–2018. The quarterly Compustat financial database is used to compute quarterly variance of cash returns and equity returns over rolling windows of three years, and is merged with the annual dataset on CEO compensation data. The resulting dataset includes firms in the S&P 500 large cap index, the S&P 400 mid cap index, and the S&P 600 small cap index. Following J. Core and Guay (1999), we exclude financial firms, and the data is winsorized at 2.5% in both tails of the distributions of our dependent variables, PPSE and PPSC. After creating lags of dependent variables and eliminating observations with missing data, the resulting sample has 13,667 firm–year observations.

Table 2. Summary Statistics. Annual CEO compensation data from U.S. firms is obtained from the Execucomp database (1992–2018) and merged with quarterly data from the Compustat database over rolling windows of three years to construct CEO compensation cash and equity incentives (PPSC, PPSE). After winsorizing 2.5% of observations in both tails of the distributions of PPSE and PPSC (J. Core & Guay, 1999) and eliminating observations with missing data, the resulting study sample has 13,667 firm–year observations.

Variable	Mean	Std. Dev.	10th Pct	Median	90th Pct
MV Equity (million USD)	8094	24,243	297	1764	16,810
Stock return (%)	9.3	38.0	−36.1	7.0	56.0
Stock return variance	2109	3684	106	902	5181
Cash return (%)	17.4	12.9	6.0	15.1	31.5
Cash return variance	190	108	39	188	340
M/B	2.6	2.9	1.0	2.1	5.4
P/E	12.6	92.1	−0.9	17.2	39.8
ROE (%)	9.1	7.0	0.2	11.0	23.0
Leverage (%)	46.4	18.5	20.2	47.9	69.9
Age	56.3	7.2	47.0	56.0	65.0
Dividend yield (%)	1.3	1.5	0.0	0.8	3.5
PPSE (USD)	33.50	61.40	2.16	12.45	85.43
PPSC (USD)	11.63	18.98	1.03	5.56	26.16
PPSE/PPSC	4.6	7.1	0.6	2.3	10.5

reports firm and CEO summary characteristics. The mean of firm market capitalization (MV Equity) is $8094 million, and the median is $1764 million. Firm equity returns per share (Stock Return) have a mean of 9.3% and a standard deviation of 38.0% (the median return is 7.0%). Operating cash per dollar of equity value (CashReturn) has a mean of 17.4% and a standard deviation of 12.9%, with a median of 15.1%.

The pay-performance sensitivity of CEO equity compensation (PPSE) has a mean of $33.50 per $1000 increase in shareholder wealth, and a median of $12.45 per $1000. The pay-performance sensitivity of CEO cash compensation (PPSC) has a mean of $11.63 per $1000 increase in firm operating cash flow, with a median of $5.56 per $1000.

Table 3. Correlations. The correlations among variables described in Table 2 are reported below. The correlations are reported for variable averages across firms in the three-year estimation windows across firms.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)
(1) MV Equity	1.00
(2) Stock return	−0.01	1.00
(3) Stock return variance	−0.06	0.09	1.00
(4) Cash return	−0.05	0.25	−0.01	1.00
(5) Cash return variance	−0.18	0.07	0.19	0.39	1.00
(6) M/B	0.03	0.02	0.01	−0.07	−0.07	1.00
(7) P/E	0.00	0.02	0.00	0.00	−0.03	0.00	1.00
(8) ROE	0.03	0.02	−0.01	0.03	−0.06	0.93	0.02	1.00
(9) Leverage	0.07	−0.02	−0.09	0.30	0.27	−0.04	−0.03	−0.06	1.00
(10) Age	0.05	0.00	−0.04	0.04	−0.01	−0.02	0.01	0.00	0.03	1.00
(11) Dividend yield	0.11	−0.08	−0.22	0.15	0.07	−0.04	0.00	0.03	0.28	0.08	1.00
(12) PPSE	−0.14	−0.02	0.07	−0.07	0.01	0.02	0.02	0.00	−0.15	0.12	−0.22	1.00
(13) PPSC	−0.17	−0.02	0.14	−0.20	0.06	0.03	−0.03	−0.03	−0.20	−0.04	−0.26	0.36	1.00
(14) PPSE/PPSC	0.02	−0.02	0.00	0.04	−0.04	0.00	0.02	0.01	−0.04	0.14	−0.08	0.52	−0.15	1.00

Table 3. Correlations. The correlations among variables described in Table 2 are reported below. The correlations are reported for variable averages across firms in the three-year estimation windows across firms.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)
(1) MV Equity	1.00
(2) Stock return	−0.01	1.00
(3) Stock return variance	−0.06	0.09	1.00
(4) Cash return	−0.05	0.25	−0.01	1.00
(5) Cash return variance	−0.18	0.07	0.19	0.39	1.00
(6) M/B	0.03	0.02	0.01	−0.07	−0.07	1.00
(7) P/E	0.00	0.02	0.00	0.00	−0.03	0.00	1.00
(8) ROE	0.03	0.02	−0.01	0.03	−0.06	0.93	0.02	1.00
(9) Leverage	0.07	−0.02	−0.09	0.30	0.27	−0.04	−0.03	−0.06	1.00
(10) Age	0.05	0.00	−0.04	0.04	−0.01	−0.02	0.01	0.00	0.03	1.00
(11) Dividend yield	0.11	−0.08	−0.22	0.15	0.07	−0.04	0.00	0.03	0.28	0.08	1.00
(12) PPSE	−0.14	−0.02	0.07	−0.07	0.01	0.02	0.02	0.00	−0.15	0.12	−0.22	1.00
(13) PPSC	−0.17	−0.02	0.14	−0.20	0.06	0.03	−0.03	−0.03	−0.20	−0.04	−0.26	0.36	1.00
(14) PPSE/PPSC	0.02	−0.02	0.00	0.04	−0.04	0.00	0.02	0.01	−0.04	0.14	−0.08	0.52	−0.15	1.00

The ratio of equity to cash incentives (PPSE/PPSC) has a mean of 4.6 and a median of 2.3, indicating that the pay-performance sensitivity of equity compensation dominates the pay-performance sensitivity of operating cash. The mean and median ages of CEOs are 56.3 years and 56.0 years, respectively. The mean firm market-to-book ratio (M/B) is 2.6, the mean price-to-earnings ratio is 12.6, and the mean return-on-equity (ROE) is 9.1%. Firms in the sample have a mean debt-to-asset ratio (Leverage) of 46.4% and the mean dividend yield is 1.3%.

4. Empirical Results and Discussion

Results from the estimation of pay regressions for CEO cash and equity compensation are discussed below. Column (3) in

Table 4. Pay Regression—CEO Cash Compensation Incentives. The estimation of the pay regression for CEO cash incentives (10) is reported below. The dependent variable is the natural logarithm of annual CEO equity incentives, defined as $\ln (PPSC)\times 100$ (the scaling by 100 allows the regression coefficients to be interpreted as a percent change effect of a unit change in the dependent variable). Column (4) reports the full model using quantile (median) regression methods. Estimates denoted with “**” represent estimates significant at the 1% level.

	Dependent Variable
	Ln(PPSC)		Ln(PPSC)		Ln(PPSC)		Ln(PPSC)
	(1)		(2)		(3)		(4)
	OLS		OLS		OLS		Median
Intercept	1116.909	**	1074.952	**	1128.144	**	1128.187	**
	(22.45)		(21.83)		(22.30)		(25.38)
FirmSize	−42.097	**	−40.891	**	−43.098	**	−43.764	**
	(−38.72)		(−38.84)		(−38.55)		(−53.73)
EquityReturn			0.009		0.009		−0.001
			(0.66)		(0.65)		(−0.01)
CDF(EquityVariance)			13.153	**	17.739	**	17.463	**
			(3.43)		(4.45)		(8.05)
CashReturn	0.000				0.000		0.000
	(0.39)				(0.32)		(0.02)
CDF(CashVariance)	−13.448	**			−19.341	**	−17.517	**
	(−2.93)				(−4.05)		(−6.46)
M/B					0.000		0.000
					(1.25)		(0.08)
P/E	0.040	**	0.041	**	0.038	**	0.034	**
	(4.05)		(4.05)		(3.77)		(6.07)
ROE					0.000		0.000
					(0.00)		(0.00)
Leverage					−7.831	**	−11.471	**
					(−2.65)		(−3.56)
Age					0.042		0.564	**
					(0.29)		(7.17)
DividendYield					−5.439	**	−3.177
					(−3.63)		(−0.38)
Firm indicators	Yes		Yes		Yes		Yes
Year indicators	Yes		Yes		Yes		Yes
Observations	13,667		13,667		13,667		13,667
Adjusted R-squared	0.79		0.79		0.79		0.74

,

Table 5. Pay Regression—CEO Equity Compensation Incentives. The estimation of the pay regression for CEO equity incentives (10) is reported below, where the dependent variable is the natural logarithm of annual CEO equity incentives defined as $\ln (PPSE)\times 100$. Column (4) reports the full model using median regression estimation, which minimizes the absolute regression error. Estimates denoted with “**” represent estimates significant at the 1% level, and “*” represents significance at the 5% level.

	Dependent Variable
	Ln(PPSE)		Ln(PPSE)		Ln(PPSE)		Ln(PPSE)
	(1)		(2)		(3)		(4)
	OLS		OLS		OLS		Median
Intercept	970.057	**	1053.521	**	863.534	**	869.836	**
	(20.12)		(21.58)		(18.01)		(29.19)
FirmSize	−26.028	**	−28.331	**	−29.381	**	−29.275	**
	(−25.25)		(−26.56)		(−27.73)		(−39.75)
EquityReturn	0.007				0.007		−0.010
	(0.54)				(0.55)		(−0.10)
CDF(EquityVariance)	32.713	**			42.656	**	24.445	**
	(8.72)				(11.29)		(12.04)
CashReturn			0.000		0.000		0.000
			(0.47)		(0.47)		(−0.01)
CDF(CashVariance)			−22.191	**	−37.237	**	−19.038	**
			(−4.93)		(−8.22)		(−7.44)
M/B					0.000		0.000
					(0.77)		(0.11)
P/E	0.018	*	0.018	*	0.019	*	0.016	**
	(1.91)		(1.94)		(2.01)		(2.68)
ROE					0.000		0.000
					(0.00)		(0.00)
Leverage					−0.430		−1.512
					(−0.15)		(−0.59)
Age					3.676	**	3.658	**
					(27.02)		(45.97)
DividendYield					−7.184	**	−4.662
					(−5.06)		(−0.57)
Firm indicators	Yes		Yes		Yes		Yes
Year indicators	Yes		Yes		Yes		Yes
Observations	13,667		13,667		13,667		13,667
Adjusted R-squared	0.78		0.78		0.79		0.76

and

Table 6. Pay Regression—Ratio of CEO Equity-to-Cash Compensation Incentives. Estimation of the CEO pay regression (10) is reported for the ratio of CEO equity-to-cash incentives, where the dependent variable is defined as $\ln (PPSC)/\ln (PPSE)$. Estimates denoted with “**” represent estimates significant at the 1% level, and “*” represents significance at the 5% level.

	Dependent Variable
	Ln(PPSE)/ Ln(PPSC)		Ln(PPSE)/ Ln(PPSC)		Ln(PPSE)/ Ln(PPSC)		Ln(PPSE)/ Ln(PPSC)
	(1)		(2)		(3)		(4)
	OLS		OLS		OLS		Median
Intercept	−795.671	**	−754.164	**	−955.386	**	−863.873	**
	(−12.55)		(−11.77)		(−14.90)		(−19.70)
FirmSize	14.863	**	13.766	**	13.717	**	10.341	**
	(10.97)		(9.83)		(9.68)		(13.02)
EquityReturn	−0.002				−0.002		−0.012
	(−0.10)				(−0.10)		(−0.19)
CDF(EquityVariance)	19.561	**			24.917	**	13.247	**
	(3.97)				(4.93)		(5.09)
CashReturn			0.000		0.000		0.000
			(0.05)		(0.10)		(−0.04)
CDF(CashVariance)			−8.743	*	−17.896	**	−11.367	*
			(−1.88)		(−2.95)		(−3.82)
M/B					0.000		0.000
					(−0.42)		(−0.06)
P/E	−0.023		−0.022		−0.019		−0.015	*
	(−1.78)		(−1.74)		(−1.47)		(−2.14)
ROE					0.000		0.000
					(0.00)		(0.00)
Leverage					7.401	*	10.095	**
					(1.98)		(3.21)
Age					3.635	**	3.464	**
					(19.98)		(34.69)
DividendYield					−1.745		−1.921
					(−0.92)		(−0.43)
Firm indicators	Yes		Yes		Yes		Yes
Year indicators	Yes		Yes		Yes		Yes
Observations	13,667		13,667		13,667		13,667
Adjusted R-squared	0.66		0.65		0.67		0.60

reports the full model, while columns (1) and (2) introduce business risk and equity return risk separately. Column (4) reports estimation from the quantile (median) regression.

A. 

Firm Growth Prospects

Pay regression estimation reveals that the relationship between CEO cash and equity and firm growth prospects is consistent with predictions from the extended agency model. The estimated coefficient for price-to-earnings ratio (PE) in the pay regressions for CEO cash and equity incentives in Table 4 and Table 5 is strongly positive and significant, and it supports both Hypotheses 1A and 1B. It implies that as the PE ratio increases by one unit, CEO equity and cash incentives increase by 3.8% and 1.9%, respectively, and these estimates are strongly significant (Column (2)).

As discussed earlier, firms with higher growth prospects (higher θ) will have a higher valuation in the equity market as investors anticipate higher future earnings growth and are willing to pay a higher share price relative to other firms with lower anticipated growth. While intuitive reasoning may suggest that CEOs of these firms should receive higher equity incentives, the extended model predicts that CEO cash incentives should also increase. This occurs because CEO pay incentives impact the total return of firm owners via two channels: first, they encourage CEO actions that positively impact business income, and secondly, this leads to an associated gain in firm value via the noisy market valuation mechanism (3). The return-maximizing contract solving (4)–(6) balances the benefit and costs of providing equity and cash incentives of these two effects on the total shareholder return, given the firm’s growth opportunities.

B. 

Firm Scale

The extended model further predicts that both CEO equity and cash incentives should decline with firm scale (Hypothesis 2). We find strong empirical support for Hypothesis 2 as the pay-performance sensitivity of both CEO cash and equity compensation declines with FirmSize (firm market capitalization). Across all regression models (columns (1)–(4)), the coefficients for firm size (Size) are negative and significant. The estimate for cash incentives is −43.10 (column (3) of Table 4), while the coefficient for equity incentives is −29.38 (column (3) of Table 5). Since both the dependent variable and FirmSize are on the log scale, the regression coefficient can be interpreted as an elasticity (the percentage change in incentives in response to a percentage change in firm size). The estimate implies that a 10% increase in firm size results in a −4.31% decline in cash incentives and a −2.93% decline in equity incentives. Therefore, cash incentives decrease more than equity incentives with firm market capitalization.

While firm size amplifies the impact of CEO actions on firm value, it also increases the variability of CEO compensation outcomes. This discourages managerial effort and makes the provision of variable incentives more costly for risk-averse CEOs. The return-maximizing contract responds by reducing both incentives as firm scale increases.

Table 6 reports how the ratio of equity-to-cash incentives is affected by firm growth prospects, firm scale, equity risk, and business risk. The positive and significant coefficient for FirmSize means that, as firm size increases, the use of CEO equity incentives increases more rapidly relative to cash incentives, as predicted by the extended model (Hypothesis 2).

C. 

Firm Business Risk and Equity Risk

Hypotheses 3 and 4 state that an increase in firm business risk reduces CEO cash incentives (but increases equity incentives), while an increase in equity risk reduces equity incentives (but raises cash incentives). Both risks increase the uncertainty in firm and CEO compensation outcomes and discourage effort, leading to a negative own-risk effect but a positive cross-risk effect on incentives.

The estimated pay regressions show that CEO cash incentives are negatively related to business risk (cash return variance) and positively related to equity valuation risk (stock return variance), providing strong support for Hypotheses 3A and 4A. In column (3) of Table 3, the estimated coefficient for the CDF of cash return variance is −17.52. This indicates that CEO cash incentives decrease by about 17.5% from the firm with the lowest cash return risk (CDF of cash return variance = 0) to the firm with the highest cash return risk (CDF of cash return variance = 1). Further, the estimation confirms that CEO cash incentives are positively related to firm equity risk, with a coefficient of 17.46, indicating that these incentives increase by 17.5% from the firm with the lowest to the highest equity return variance.

In the response of CEO equity incentives to firm equity risk, the coefficient for the CDF of equity return variance in column (3) of Table 5 is 42.66. This suggests that CEO equity incentives increase by 42.7% between the firm with the lowest equity return risk (CDF of equity return variance = 0) and the firm with the highest equity return risk (CDF of equity return variance = 1). The estimation further shows that, instead of declining, equity incentives increase when firm equity returns become more volatile. The estimated coefficient for the CDF of cash return variance (proxy for business risk) is −19.04, suggesting that the pay-performance sensitivity of equity pay decreases by 19% between the firm with the lowest business risk and the highest business risk. These results show that CEO equity incentives do not respond efficiently to either equity risk or business risk and do not support Hypotheses 3B and 4B.

A number of previous studies also report a positive (as opposed to negative) relationship between CEO equity incentives and the variance of stock returns (e.g., Demsetz & Lehn, 1985; J. Core & Guay, 1999; J. E. Core & Guay, 2002; Garvey & Milbourn, 2003; Gao, 2010). An alternative explanation for the positive relation is that stock options provide greater incentives for managerial risk-taking by providing asymmetric upside gains (Coles et al., 2006; Low, 2009).

D. 

Robustness and Implications for Hedging and Managerial Power

The estimates in column (3) of Table 4 and Table 5 show that the CEO pay regression estimates remain stable when additional control variables are added (e.g., ROE, Leverage, DividendYield, and M/B). To further confirm the robustness of the study results, median regression estimation is reported in column (4). The median regression minimizes the absolute difference in regression errors (as opposed to the squared error in OLS), and extreme observations have less effect on the estimated coefficients. The coefficients for equity return risk and cash return risk are somewhat larger in the full OLS model in column (3) of Table 4 and Table 5; however, they retain their direction and significance.

To address possible concerns of endogeneity among explanatory variables, we employ the general method of moments (GMM) estimation analysis of our model, as shown in

Table 7. GMM Estimation of CEO Pay Regressions. Estimation of the CEO pay regression (10) is reported using the General Method of Moments (GMM) analysis to address endogeneity of explanatory variables. The dependent variable is the natural logarithm of annual CEO equity incentives defined as $\ln (PPSC)\times 100$ in column (1), the natural logarithm of annual CEO equity incentives defined as $\ln (PPSE)\times 100$ in column (2), and the ratio of CEO equity-to-cash incentives defined as $\ln (PPSC)/\ln (PPSE)$ in column (3). Estimates denoted with “**” represent estimates significant at the 1% level, and “*” represents significance at the 5% level.

	Dependent Variable
	Ln(PPSC)		Ln(PPSE)		Ln(PPSE)/ Ln(PPSC)
	(1)		(2)		(3)
	GMM		GMM		GMM
Intercept	1457.874	**	870.913	**	−1289.100	**
	(48.57)		(24.05)		(−29.61)
FirmSize	−59.988	**	−43.972	**	16.376	**
	(−45.66)		(−32.53)		(8.49)
EquityReturn	0.079		0.041		−0.0381
	(1.73)		(1.67)		(−1.05)
CDF(EquityVariance)	23.624	**	72.440	**	52.597	**
	(4.68)		(8.99)		(5.46)
CashReturn	−0.483		−0.432	**	0.049
	(−1.44)		(−2.42)		(0.24)
CDF(CashVariance)	−31.152	**	−43.841	**	−12.018	*
	(−6.32)		(−5.87)		(−1.83)
M/B	0.046		0.032		−0.031
	(1.20)		(0.96)		(−0.76)
P/E	0.005		0.017		0.012
	(1.30)		(2.25)	*	(1.23)
ROE	−0.480		−0.359		0.328
	(−1.05)		(−0.91)		(0.67)
Leverage	−51.694	**	−56.648	**	−4.647
	(−7.98)		(−7.01)		(−0.49)
Age	0.259		3.840		3.556	**
	(1.60)		(14.16)	**	(11.38)
DividendYield	−0.506		−5.931		−5.353	*
	(−1.66)		(−2.92)		(−2.76)
Firm indicators	Yes		Yes		Yes
Year indicators	Yes		Yes		Yes
Observations	13,667		13,667		13,667
Adjusted R-squared	0.55		0.31		0.10

. The GMM results are consistent with our main OLS results for the relations between CEO compensation and business risk and equity risk. Specifically, columns (1) and (2) of Table 7 show a positive relation between both cash and equity compensation with respect to equity valuation risk (stock return variance), and both cash and equity compensation have a negative relation with respect to business risk (cash return variance). Similarly, column (3) of Table 7 is also consistent with our main OLS results, showing that the ratio of equity to cash compensation is positively related to equity risk and negatively related to business risk. It may be noted that the GMM results show a similar magnitude of coefficients for equity and business risk compared to OLS, but the adjusted R-squared fit is lower.

The study results discussed above also have relevance to executives’ ability to hedge equity exposure in their compensation contracts using derivatives such as forward contracts and equity swaps that allow exposure to the stock price to be converted to a fixed level or return. Jagolinzer et al. (2007) find that hedging positions by senior executives account for 30% of their firm-specific wealth. Bettis et al. (2001) report that the use of financial derivatives to hedge their equity exposure by corporate insiders has increased, and further show that these activities reduce their stock ownership by an average of 25%. CEO cash incentives tied to firm business performance (e.g., operating cash flow) are difficult to hedge using derivatives based on the stock price, and our empirical results show that these incentives are fully agency-aligned to four important firm resource characteristics.

Our empirical findings also provide additional insights into the discussion of the role of managerial power in CEO pay. Proponents of managerial power theories (Bertrand & Mullainathan, 2001; Bebchuk & Fried, 2003) argue that powerful CEOs can ‘capture’ the remuneration-setting process through compliant boards to push their own rewards beyond levels that are not efficient for shareholders. Further, Bertrand and Mullainathan (2001) show that CEOs can reap windfall gains from market-wide or sector-driven changes in equity prices as opposed to their firm performance. Abernethy et al. (2014) find that firms with powerful CEOs adopt performance-vested stock option (PVSO) plans early and attach less challenging targets in initial PVSOs when CEO compensation systems are changed in response to regulatory or public pressure. The meta-analytic study of Van Essen et al. (2015) finds that CEOs receive significantly higher levels of cash and total compensation when they have greater power relative to the board and that, while managerial power theories can better explain the level of CEO compensation, they are less able to predict the sensitivity of pay to performance. Our results show that the pay-performance sensitivity of CEO cash compensation is fully agency-aligned with four important firm characteristics in the extended model, while equity pay is not efficient.

5. Conclusions

Recent international studies on CEO pay in Europe, Japan and South Korea reveal significant differences from the U.S. in the use and effectiveness of equity-based CEO compensation (e.g., Smirnova & Zavertiaeva, 2017; Pan & Zhou, 2018; Lee & Wu, 2022), raising questions about the ability of conventional incentive contracts based on agency theory to align with actual CEO compensation practices. Our study contributes to this debate and provides new empirical and practical insights into the design of efficient U.S. CEO pay by evaluating nine hypotheses from an extended principal–agent framework. CEO cash incentives become more important in the extended agency model, as the objective function includes a measure of firm income and its associated effect on equity value via a noisy market valuation mechanism, while separating firm business risk from equity risk.

To estimate the pay regressions for CEO cash incentives, the paper also makes a methodological contribution by using data from Compustat and Execucomp to estimate firm business risk and CEO cash incentives (PPSC) using quarterly operating cash flows. Overall, given the dominance of CEO equity pay in the United States, our empirical results show that CEO cash incentives related to firm business performance (e.g., operating cash flow) are efficient and can play a critical role in aligning agency interests for maximizing shareholder returns, while equity compensation exhibits mixed alignment. The pay regression estimates show that CEO cash incentives are positively related to firm growth prospects and equity return risk and negatively related to firm business risk and firm scale, as predicted by the model. Meanwhile, CEO equity incentives exhibit agency alignment with firm growth and scale, but not with business risk and equity risk. The regression estimation exhibits higher R-squares (0.74–0.79), controls for important firm characteristics, and includes fixed effects for firm and year to mitigate omitted variable bias and endogeneity.

Lastly, our study results also have implications for the hedging of equity exposure by corporate executives and for the managerial power perspective on CEO pay, both of which pose additional risks to corporate governance due to misaligned interests between shareholders and executives. Here, CEO cash incentives linked to firm operating performance have the benefit that they cannot be directly hedged using derivative instruments, and we find that CEO cash incentives are aligned with all four important firm characteristics in the extended agency model.