EXECUTIVE COMPENSATION PORTFOLIO SENSITIVITIES AND THE COSTOF EQUITY CAPITAL

Abstract
Executive compensation portfolio sensitivities to change in stock price (deltas) and stock
return volatility (vegas) influence managerial risk-taking decisions. Large deltas discouragerisk-taking while large vegas encourage risk-taking. In this paper, we examine the relation
between executive compensation portfolio deltas and vegas and the implied cost of equity
capital. We show that managerial risk incentives, as captured by executive compensation
portfolio deltas and vegas, determine the rate of return expected by shareholders. Higher
deltas (vegas) are associated with a lower (higher) implied cost of equity capital. In a changein-variable specification, we find that an increase (decrease) in delta (vega) results in adecrease (increase) in the implied cost of equity capital. We also show that higher deltas areassociated with lower external equity financing costs as deltas and the underpricing of
seasoned equity offerings are inversely related. Taken together, our findings demonstrate thatshareholders understand managerial risk incentives embedded in executive compensation andprice these risks into the cost of equity capital accordingly.

JEL: G30; G322
Keywords: Executive compensation; Deltas; Vegas; Implied cost of equity capital; SEO
underpricing.

EXECUTIVE COMPENSATION PORTFOLIO SENSITIVITIES AND THE COSTOF EQUITY CAPITAL

1. Introduction

In response to the significant increase in the use of stocks and options in executive
compensation over the past few decades, a large body of literature has devoted considerable
attention to understanding the role of executive compensation in corporate governance andfirm performance. 1 Furthermore, recent studies have also examined how executive
compensation affects managerial behavior, risk-taking decisions and their impacts on thefirm‟s overall risk. There is mounting evidence that executive compensation portfolio deltas,
the sensitivity of the stock and option compensation portfolio value to company stock prices,
lower managerial risk preferences (Lambert et al., 1991; Carpenter, 2000; Knopf et al., 2002)
while executive compensation portfolio vegas, the sensitivity of the option compensation
portfolio to company stock return volatility, increase managerial risk preferences (Knopf etal., 2002; Coles et al., 2006; Brockman et al., 2010; Armstrong and Vashishtha, 2011).
Prior research has investigated the effects of deltas and vegas on managerial risk
preferences to firm choices of risky investment and financing policies (Coles et al., 2006),
firms‟ hedging activities (Rogers, 2002; Knopf et al., 2002), firms‟ risk-taking in merger andacquisition activities (Hagendorff and Vallascas, 2011), firm‟s choices of financial reporting(Cheng and Warfield, 2005; Grant et al., 2009; Chava and Purnanandam, 2010), firm‟s shortterm debt (Brockman et al., 2010), and firm‟s cash holdings (Liu and Mauer, 2011). Given
that deltas and vegas determine several risk-taking aspects of a firm, this study aims toinvestigate whether shareholders price managerial risk incentives. Specifically, we examine
1Over the period 1993-2003, executive pay increased sharply with the aggregate compensation to the top fiveexecutives of each of the S&P 1500 firms doubling from 5 percent to 10 percent of the aggregate earnings ofthose firms (Bebchuk and Grinstein, 2005).

1

the relation between executive compensation portfolio deltas and vegas and the ex-ante
measure of cost of equity capital, namely the implied cost of equity capital. We focus on thecost of equity capital because of its paramount importance in a firm‟s financing and operating
decisions. Furthermore, while several prior studies have shown that management aims to
reduce the cost of equity capital by adopting voluntary disclosure (Diamond and Verrecchia,
1991; Botosan, 1997; Leuz and Verrecchia, 2000; Botosan and Plumlee, 2002; Graham et al.,2005; Dhaliwal et al., 2010) or smoothing earnings (Francis et al., 2004; Verdi, 2006), no
study has examined the relation between managerial risk incentives embedded in executive
compensation and shareholders‟ perception of these risk incentives.
We employ a sample of 11,041 firm-year observations from the S&P1500 over theperiod 1992-2009 and construct CEO compensation portfolio sensitivities as in Core andGuay (2002) to study the association between CEO risk incentives and the implied cost ofequity capital. In undertaking this analysis, we employ four ex-ante measures of the cost ofequity capital, deduced from the valuation models of Claus and Thomas (2001), Gebhardt etal. (2001), Gode and Mohanram (2003), and Easton (2004). Following Dhaliwal et al. (2005,
2006), Hail and Leuz (2006), and Dhaliwal et al. (2010), we also consider an average-based
measure of the implied cost of equity capital by taking the equally weighted average of thefour individual implied cost of equity capital estimates. Our basic hypothesis is that when a
CEO has an incentive to increase the firm‟s overall risk by adopting riskier corporate policies
and investment projects, shareholders demand compensation for bearing this excessive risk
by increasing the cost of equity capital.2 The reverse happens when the CEO has an incentive
to reduce the firm‟s overall risk. In testing these hypotheses, we compute CEO deltas and2

The adoption of riskier corporate policies and investment projects can increase a firm‟s systematic risk andidiosyncratic risk. While we do not aim to disentangle the effects of risk incentives on systematic risk andidiosyncratic risk, our basic assumption is that the cost of equity capital is an increasing function of the firm‟soverall risk. The extant empirical literature still has not reached consensus on whether idiosyncratic risk is
priced (Botosan, 1997; Botosan and Plumlee, 2002; Botosan et al., 2004) or not priced (Cohen, 2004; Chen etal., 2004; Nikolaev and van Lent, 2005; Hughes et al., 2007).

2

vegas as proxies for risk-taking incentives based on the CEO‟s personal holdings of thefirm‟s stocks and options. CEOs with higher deltas are likely to decrease the firm‟s overallrisk and thus lower the cost of equity capital because they have a large exposure to the firm‟stotal risk which is not diversifiable (Fama, 1980; Stulz, 1984; Smith and Stulz, 1985). In
addition, higher deltas can reduce the cost of equity capital through the outcome of the
incentive alignment effect. Higher deltas motivate CEOs to work towards increasing
shareholders‟ wealth, thereby reducing the agency cost between shareholders and managers.
CEOs with high vegas stand to gain from higher volatility and thus have an incentive toincrease the firm‟s overall risk, which leads to a higher cost of equity capital.
Our empirical findings offer three important new insights. First, we show that firms
with higher CEO compensation portfolio deltas are associated with a significantly lower
implied cost of equity capital while firms with higher CEO compensation portfolio vegas areassociated with a significantly higher implied cost of equity capital. The lower implied costof equity capital among high CEO compensation portfolio delta firms and the higher implied
cost of equity capital among high CEO compensation portfolio vega firms are observed
consistently across all individual measures of the implied cost of equity capital as well as theaverage-based measure of the implied cost of equity capital. For the average-based measureof the implied cost of equity capital, the effect of CEO compensation portfolio deltas on thecost of equity capital is a reduction of 60 basis points going from the 25th percentile to the75th percentile of CEO compensation portfolio deltas. The effect of CEO compensation
portfolio vegas on the average-based measure of the implied cost of equity capital issomewhat smaller with an increase of 16 basis points going from the 25th percentile to the75th percentile of CEO compensation portfolio vegas.
Second, using a change-in-variables regression specification, we show that the annualchange in CEO compensation portfolio deltas (vegas) is negatively (positively) and3

significantly related to the annual change in all of our implied cost of equity measures. When
we consolidate vega and delta into a ratio representing one overall measure of risk-incentive
as in Rogers (2002, 2005) and Grant et al. (2009), we find that a higher ratio of vega overdelta (i.e., a high risk incentive) is associated with a significantly higher cost of equity capital.
In addition, extending compensation sensitivity measures to reflect deltas and vegas of thecompensation package for the top five executives of a firm, we document that theircompensation portfolio deltas (vegas) are associated with a lower (higher) cost of equity
capital. When we decompose deltas into stock deltas and option deltas, we find that bothstock deltas and option deltas exert negative effects on the cost of equity capital with theeffect being exceedingly stronger for the latter.
Our empirical findings remain robust when we address endogeneity concerns by
including the lagged implied cost of equity capital in the regression analysis, or using delta
and vega measures that exclude the current year compensation, or adopting a two-stage
instrumental variable approach to investigate the relation between executive compensation
portfolio sensitivities and the cost of equity capital. In our final avenue of inquiry, we
examine the relation between managerial risk incentives and the underpricing of seasoned
equity offerings (SEOs) which is generally considered a measure of the cost of external
equity financing. We find that higher deltas are associated with significantly lower
underpricing of SEOs but do not find a significant relation between vegas and theunderpricing of SEOs.
Collectively, our findings are consistent with the proposition that managerial risk
incentives, as captured by compensation portfolio sensitivities to stock price and stock return
volatility, influence investors‟ perception of risk, leading to variation in the expected returnon equity. We make two significant contributions to the cost of equity capital and executive
compensation literature. First, our study is the first to show that shareholders understand and4price managerial risk-taking behavior as manifested by the negative (positive) relation
between executive compensation portfolio deltas (vegas) and the implied cost of equity
capital. Prior studies have shown that management can take a number of initiatives to reducethe cost of equity capital such as adopting voluntary disclosure, striving for a moretransparent information environment, or smoothing earnings (Francis et al., 2004; Verdi,
2006). We show that management can also influence shareholders‟ perception of risk, andthus the cost of equity capital, by conveying their risk appetite as embedded in executive
compensation. In addition, a large strand of literature focuses on identifying the crosssectional determinants of a firm‟s cost of equity capital (Dhaliwal et al., 2005; Dhaliwal et al.,2006; Lambert et al., 2007; Naiker et al., 2011). We make a significant contribution to thisliterature by establishing that executive risk incentives are important determinants, both
statistically and economically.
Second, we contribute to the literature on executive compensation by examining
market-based assessments of executive risk incentives. While a growing body of empirical
work analyzes the effects of risk incentives on corporate policies, investment choices, and thefirm‟s overall risk (Knopf et al., 2002; Rajgopal and Shevlin, 2002; Hanlon et al., 2004;
Coles et al., 2006; Brockman et al., 2010; Chava and Purnanandam, 2010), our analysis of
the implied cost of equity capital allows us to investigate whether the relation between risk
incentives and corporate policies drives market-based assessments of the firm‟s overall risk.
We establish a causal link between managerial risk incentives as embedded in thecompensation contract and the implied cost of equity capital, a measure of the risk premium
demanded ex-ante by shareholders. Our findings therefore have important implications for
optimal corporate compensation design and the regulation of executive compensation.
The rest of this study is organized as follows. Section 2 discusses related research anddevelops testable hypotheses. Section 3 describes the measurement of the main variables and5sample selection. Section 4 presents the descriptive statistics and Section 5 presents theempirical results. Section 6 concludes the study.

2. Related Literature and Testable Hypothesis
The separation of ownership and control in publicly held corporations has long beenrecognized as a major source of conflict between shareholders and management (Berle andMeans, 1932; Jensen and Meckling, 1976; Demsetz, 1983) and an extensive literature has
focused on the shareholder-value ramifications of this agency cost. While shareholders areoften considered risk-neutral with regard to firm specific risk as they can hold welldiversified investment portfolios, corporate managers whose human capital and money
capital are invested in the firm hold undiversified risk. As a consequence, managers may havean incentive to reduce firm risk more than what may be desirable to generally diversified
shareholders (Shavell, 1979; Smith and Stulz, 1985; Stiglitz, 1987; Guay, 1999; Fama andFrench, 1992; Beatty and Zajac, 1994). Risk-neutral shareholders would like to accept all
positive net present value (NPV) projects while risk-averse managers may pass on positive
NPV projects that are risky.
Executive compensation packages that align managers‟ wealth with corporate
performance or a firm‟s stock value have generally been considered a solution to the agency
problem (Holmstrom, 1979; Baker et al., 1988). In the past few decades, the use of stock
options as part of U.S. executive compensation has grown exponentially and beyond what
can be explained by changes in firm size, firm performance or industry classification(Bebchuk and Grinstein, 2005). 3 Stock options are an important mechanism to mitigate
managerial risk aversion to firm-specific risk because they create a convex relationship

3

Several studies have shown that grants of stock options represent the largest component of CEO compensationin large publicly listed corporations in the U.S. (Hall and Liebman, 1998; Murphy, 1999).

6

between pay and performance (Smith and Stulz, 1985; Lambert, 1986; Guay, 1999; Lambertand Larcker, 2004). Specifically, managers who hold company stock options are shieldedfrom the downside risk when the stock price falls below the option strike price but enjoy
unlimited gain when the stock price exceeds the option strike price. Consequently, optioncompensation motivates managers to accept and take more risk.
While the primary use of stock options in executive compensation packages is to alignmanagement‟s wealth with firm performance, recent literature on executive compensation
recognizes that the use of stock options can incentivize executives to engage or disengage inrisk-taking behavior. Ross (2004) sums up the literature by stating: “The common folklorethat giving options to agents will make them more willing to take risks is false.” Overall,
Carpenter (2000), Lambert et al. (1991), Knopf et al. (2002), and Ross (2004) suggest two
opposing effects of stock option portfolio sensitivities on managerial incentives. First, thepayoff of an option ties a manager‟s wealth to the stock price and, as a result, reduces therisk-averse manager‟s willingness to take risk. This effect increases in option portfolio deltas,
the relative sensitivity of the option portfolio value to changes in stock price. Second, becauseof the convex payoff structure of an option, the value of a manager‟s option portfolio
increases in stock return volatility and this gives the manager an incentive to take more risk.
This effect increases in option portfolio vegas, the relative sensitivity of the option portfolio
value to stock return volatility. Collectively, these studies posit that the sensitivities inherent
in managers‟ stock and option portfolios to stock price and stock return volatility can cause
managerial risk preference and risk-taking to move in opposite directions.
Several studies have provided empirical evidence that executive compensation
portfolio sensitivities are important in assessing managerial incentives and firms‟ risk-taking
activities. Knopf et al. (2002) show that managers with high deltas conduct more corporaterisk hedging activities to reduce firms‟ exposure to risk while managers with high vegas

7conduct less corporate hedging activities. In a similar vein, Rajgopal and Shevlin (2002) findthat firms in the oil and gas industry engage in greater exploration risk and less corporate risk
hedging activities when their CEOs possess high vega option portfolios. Coles et al. (2006)
further show that CEOs with high vega option portfolios exhibit higher risk-taking behavior
through the choice of corporate investment policy and corporate financing policy. These
researchers find that CEOs with high vega option portfolios tend to use higher financial
leverage, larger research and development expenditures and less capital expenditures.
Armstrong and Vashishtha (2011) show that vegas give CEOs an incentive to increase firm‟ssystematic risk. Other studies such as Bliss and Rosen (2001), Minnick et al. (2009), De
Young et al. (2010), and Hagendorff and Vallascas (2011) document that high delta banks
engage in less risky banking activities while high vega banks engage in riskier types ofactivities. Grant et al. (2009) show that CEO risk-related incentives embedded incompensation contract, as captured by the ratio of CEO vega over delta, are positively related
to income smoothing. They conclude CEO risk-taking behavior is accompanied by financial
reporting decisions as manifested by managers employing income smoothing to reduce
unintended consequences of risk.4
Recent research documents that creditors take into account the effect of executive
compensation portfolio sensitivities on management risk-taking behavior. Billett et al. (2010)
find that bondholders react negatively upon new CEO stock options grant announcements andthe negative response is more pronounced with high vega stock option grants and milder withhigh delta options grants. Brockman et al. (2010) find a negative (positive) relation between
CEO compensation portfolio deltas (vegas) and short-maturity debt. They conclude that firms

4

Grant et al. (2009) posit that income smoothing can be used as a mechanism to avoid the undesirable
consequences of risk on reported earnings such as potentially large losses, wide fluctuations, and to serve
shareholder interests and institutional investors‟ preferences. Other studies that document a positive relation
between CEO risk-taking incentives embedded in compensation contracts and CEO risk-taking behavior include
Tufano (1996), Rogers (2002, 2005), Nam et al. (2003), Mehran and Rosenberg (2007), Billet et al. (2010), Liu
and Mauer (2011), and Tchistyi et al. (2011).

8

use short-maturity debt to mitigate the agency cost of debt because short-maturity debt canconstrain managerial risk preferences.5 These studies are generally in line with the theoreticalprediction in Barnea et al. (1980) that debt-holders discount debt value once they recognize
the management‟ incentive problem.
This study examines the relation between executive risk-related incentives embeddedin the compensation contract and the implied cost of equity capital, an ex-ante measure of thepremium demanded by shareholders. We primarily focus on the risk incentives of CEOs as
they are the most influential in a firm‟s policy choices and risk-taking. The effect of CEO
compensation portfolio deltas on the cost of equity capital is expected to be negative for two
reasons. First, Lambert et al. (1991), Carpenter (2000), and Ross (2004) argue that a riskaverse and under-diversified manager has a strong incentive to adopt risk-reducing policy
choices if the compensation has high pay-for-performance sensitivity, leading to lower
overall risk and expected stock returns for the firm. Second, if high deltas motivate managers
to work hard or more effectively to increase shareholders‟ wealth, we would expect a
reduction in the agency cost due to the enhanced alignment between managers‟ andshareholders‟ interests, leading to a lower cost of equity capital. This discussion leads to ourfirst testable hypothesis, which can be stated as follows.
H1: The implied cost of equity capital is negatively related to the sensitivity of CEO
compensation portfolios to stock price (deltas).
Coles et al. (2006) demonstrate that CEO compensation with higher vegas motivates
the CEO to pursue riskier investment and financing policies. This risk-taking behavior is
expected to result in higher firm‟s overall risk and higher expected stock returns. Strobl (2003)
theorizes risk-taking incentives as a source of non-diversifiable risk to shareholders and thus
shareholders may also demand compensation for bearing this risk in the form of higher cost5

Brockman et al. (2010) also document that short-maturity debt reduces the influence of vegas and deltas
incentives on corporate bond yields.

9

of equity capital. Moreover, risk-taking incentives can increase the cost of equity capital byincreasing a firm‟s cash flow volatility which is positively associated with the costs of both
debt and equity financing (Bernadette and Schrand, 1999). This discussion leads to our
second testable hypothesis, which can be stated as follows.
H2: The implied cost of equity capital is positively related to the sensitivity of CEO
compensation portfolios to stock return volatility (vegas).

3. Variable Measurement and Sample Selection
3.1 Dependent Variable: Implied Cost of Equity Capital
To empirically examine the association between the implied cost of equity capital and
CEO compensation portfolio sensitivities, we first estimate the cost of equity capital that is
implied in current stock prices and analysts‟ earnings forecasts. More specifically, we infer
estimates of the implied cost of equity using the methods of Claus and Thomas (2001),
Gebhardt et al. (2001), Gode and Mohanram (2003) and Easton (2004). The extant literature
adopts these methods to ex-ante infer an estimate of the implied cost of equity using theresidual income and growth valuation models developed by Ohlson (1995), Feltham andOhlson (1995), and Ohlson and Juettner-Nauroth (2005). We refer to the estimates based onthese methods as RCT, RGLS, RGM, and REAST, respectively.
Since there is little consensus in the extant literature on which model yields the best
performance and there is no guidance on how these models should be evaluated (see, e.g.,Gode and Mohanram, 2003; Guay et al., 2003; Botosan and Plumlee, 2005; Easton andMonahan, 2005), we follow Dhaliwal et al. (2005) and Hail and Leuz (2006, 2009) and also
report our results based on the equally-weighted average of the four implied cost of equity

10

measures (denoted as RAVE) to mitigate the effect of measurement errors from each model.6
We choose the stock price at the end of four months after the fiscal year-end to estimate theimplied cost of equity capital to ensure that financial data used to compute the independent
variables and data on executive compensation are publicly available and fully priced at thetime of the cost of equity computations.7 To correct for partial-year discounting, we discountthe stock price at the end of four months after the fiscal year-end by four months to thebeginning of the fiscal year using the corresponding implied cost of equity capital. The four
implied cost of equity models and the relevant variables are described in Appendix A.
3.2 CEO Compensation Portfolio Deltas and Vegas
We collect CEO compensation information from Standard and Poor‟s ExecuComp
database. We define CEO compensation portfolio price sensitivity (CEOPRICESEN or deltas)
as the change in the value of the CEO‟s stock and option portfolio in response to a 1 percent
increase in the firm‟s stock price. We define CEO compensation portfolio volatility
sensitivity (CEOVOLSEN or vegas) as the change in the value of the CEO‟s option portfolio
in response to a 0.01 increase in the annualized standard deviation of the firm‟s stock return.
We follow Guay (1999) and Core and Guay (2002) in calculating CEO compensation
portfolio deltas and vegas. Essentially, the partial derivatives of the option price with respect
to stock price (deltas) and stock return volatility (vegas) are based on the Black-Scholes(1973) option pricing model. A detailed discussion of the Core and Guay (2002) derivation of
CEO compensation portfolio deltas and vegas is presented in Appendix B.
3.3 Control Variables
6

In unreported tests, we also use the median of the estimates from the four models and our findings areinsensitive to the use of the median instead of the mean.
7
Most listed U.S firms publish their annual reports within four months after the fiscal year-end. The U.S.
Securities and Exchange Commission (SEC) has required publicly traded companies to disclose information
regarding executives‟ compensation to the market and also post compensation amounts on its website. Using thestock price four months after the fiscal year-end allows the market sufficient time to fully price informationfrom financial reports. However, in unreported tests, our findings and conclusions in this study are unaffected
when we replicate our analysis using cost of equity estimated at the fiscal year-end. The market appears to priceinformation on managerial risk incentives instantaneously.

11

Following prior research, we employ eight variables to control for the effects fromother known determinants of the cost of equity capital. We commence by including the three
Fama and French (1996) risk factor loadings (βMKT, βSMB, and βHML) employed in Dhaliwal etal. (2005) and Dhaliwal et al. (2006) to control for market risk, size risk, and book-to-market
risk. The three risk factor loadings are estimated using a maximum of 60 weekly returns prior
to the firm‟s fiscal year-end, and a minimum of 20 weeks.8 We follow Gebhardt et al. (2001)
and Gode and Mohanram (2003) and control for two properties of analysts‟ forecasts, Dispand LTG where Disp refers to dispersion in the one-year-ahead analysts‟ earnings forecast
obtained from I/B/E/S, and LTG is the natural logarithm of I/B/E/S analysts‟ long-term
growth in earnings forecasts.9 Gebhardt et al. (2001) also include the book value-to-market
ratio (BM) to control for undervalued stocks. They argue that undervalued stocks (high BM)
should earn an abnormally high implied risk premium until the mispricing is corrected. We
also control for the size effect by including Size in our model (Gebhardt et al., 2001; Godeand Mohanram, 2003; Dhaliwal et al., 2006), and Size is measured as the natural logarithm ofa firm‟s market capitalization. We include leverage (Leverage) as the ratio of long-term debt
over equity to control for the effect of financial leverage on the cost of equity capital. To
control for the effect of outliers, we winsorize all variables at the 1st and 99th percentiles.

4. Descriptive Statistics
Table 1 reports descriptive statistics on the five implied cost of equity capital
measures (RAVE, REAST, RGLS, RCT, and RGM), control variables and CEO compensation
portfolio deltas and vegas. Our sample comprises of 11,041 firm-year observations spanning8

Our results are unaffected when we estimate the three risk factor loadings using a maximum (minimum) of 60(20) monthly returns prior to the firm‟s fiscal year-end.
9
Gebhardt et al. (2001) and Gode and Mohanram (2003) find that analysts‟ forecast properties explain crosssectional variation in the implied equity risk premium.

12the period 1992-2009 from which we compute CEO compensation portfolio deltas, vegas andthe implied cost of equity capital.
[ INSERT TABLE 1 ABOUT HERE]
The summary statistics for RAVE, which is deduced as the average of the four implied
cost of equity capital estimates, indicate that the mean (median) risk premium demanded byinvestors over our sample period is 9.5 percent (9.00 percent). Similar to other studies (e.g.,
Guay et al., 2005; Dhaliwal et al., 2006), statistics for the individual implied cost of equity
measures indicate that the Gode and Mohanram (2003) and Easton (2004) models produce
larger mean implied cost of equity estimates for our sample firms (9.87 and 11.14 percent
respectively) in comparison with the estimate from the Claus and Thomas (2001) model(mean RCT of 8.61 percent) and the estimate from the Gebhardt et al. (2001) model (mean
RGLS of 8.43 percent).
Other summary statistics indicate that our sample firms on average have a book-tomarket ratio (BM) of approximately 59.28 percent. The mean long-term growth rate fromanalyst forecasts from I/B/E/S is around 15.26 percent, suggesting that analysts expect
positive growth in investment opportunities for the sample firms. The average dispersion in
analysts‟ earnings forecasts is 12.47 percent, reflecting notable uncertainty in the analysts'
earnings forecasts. The average log of market capitalization of our sample firms is 7.72 andthe average leverage is 21 percent. The average Fama-French risk factor loading is 0.9405,
0.2085, and 0.0581, respectively, for market risk, size risk, and book-to-market risk.
The CEO compensation portfolio sensitivities in Table 1 are in thousands of dollars.
The mean (median) CEO‟s wealth increases by $719,000 ($140,000) for a 1 percent increasein stock price (CEOPRICESEN). The mean (median) CEO‟s wealth increases by $106,000($64,000) for a 0.01 increase in annual stock return volatility (CEOVOLSEN). The values of
the CEO compensation portfolio sensitivities in our study are much larger than those reported

13

in Guay (1999) and somewhat similar to those reported in Brockman et al. (2010) and Chavaand Purnanandam (2010). This is because Guay‟s sample ends in 1993 while Brockman etal.‟s sample and Chava and Purnanandam‟s sample span the period 1992 to 2005 and 1993 to2005, respectively. Our sample period is the most comprehensive, covering the period 19922009. The increasing trend in grant stock options as part of executive compensation in the
U.S markets over time explains the significant increase of CEO compensation portfolio
sensitivity values in our study relative to those in Guay (1999). CEOPRICESEN and
CEOVOLSEN exhibit positive skewness as their mean values are much higher than thecorresponding median values. This skewness will not impede our empirical findings as weapply the natural logarithm of these dollar value sensitivities in subsequent regression
analyses.

5. Empirical Results
5.1 Average Implied Cost of Equity Capital and CEO Compensation Portfolio Sensitivities
We commence our empirical analyses by employing a regression analysis to examine
the cross-sectional relation between the average implied cost of equity capital and CEO
compensation portfolio sensitivities.
In Table 2, we report the empirical results from various pooled regression models.
Here, we take the natural logarithm of CEO compensation portfolio sensitivities for the
regression analysis. We report two-way clustered t-statistics based on standard errors
clustered by firm and year. According to H1 and H2, we expect a negative (positive) relation
between the average cost of equity capital and the CEO compensation portfolio sensitivity tostock price (sensitivity to stock return volatility). In Table 2, we report the empirical results
for four models. The regression results in model (1) support both hypotheses by showing that
LCEOPRICESEN‟s estimated coefficient is negative at -0.006 and LCEOVOLSEN‟s
14

estimated coefficient is positive at 0.0016, and both are highly significant (t-statistic of -5.23
and 3.66, respectively). In model (2), in which we include year fixed effect and industry fixed
effect in the regression model, the estimated coefficients on LCEOPRICESEN and
LCEOVOLSEN retain their signs and statistical significance. These findings suggest that highCEO compensation portfolio sensitivity to stock prices (deltas) is associated with a lower
implied cost of equity capital while high CEO compensation portfolio sensitivity to stock
return volatility (vegas) is associated with a higher implied cost of equity capital.
Models (3) and (4) in Table 2 include other control variables in the regression analysis.
In both models, the estimated coefficients on LCEOPRICESEN and LCEOVOLSEN retain
their negative (positive) signs and are highly significant. In model (3), the estimatedcoefficient on LCEOPRICESEN is -0.0044 (t-statistic of -3.91) and the estimated coefficienton LCEOVOLSEN is 0.0012 (t-statistic of 3.59). In model (4), in which we include both year
fixed effect and industry fixed effect, the estimated coefficient on LCEOPRICESEN is 0.0035 (t-statistic of -4.14) and the estimated coefficient on LCEOVOLSEN is 0.0021 (tstatistic of 4.04). Thus, the negative (positive) relation between LCEOPRICESEN(LCEOVOLSEN) and the average implied cost of equity capital remains robust to theinclusion of other determinants of the cost of equity capital as well as fixed effects.
Besides results for our main variables of interest, the results reported in Table 2 also
show consistent findings for control variables. The majority of control variables show the
expected signs and are significant in explaining the average implied cost of equity capital.
Specifically, the estimated coefficients on BM, LTG, Disp, Leverage and risk factor loadings
are positive and the estimated coefficient on Size is negative. Model (4) with the inclusion of
all control variables and fixed effects yields the best explanatory power with an R-squared
value of 0.34.

15

The coefficients on LCEOPRICESEN and LCEOVOLSEN in Table 2 not only display
high statistical significance but also show important economic significance. In model (1), in
which we only include CEO compensation portfolio sensitivities as explanatory variables, theestimated effect on cost of equity capital, inferred from the estimated coefficients, suggeststhat there is a 60 basis point reduction in the average cost of equity capital, going from the25th to the 75th percentile of LCEOPRICESEN, and a 16 basis point increase in the average
cost of equity capital, going from the 25th to the 75th percentile of LCEOVOLSEN. In model(4), with the most comprehensive set of control variables and fixed effects, the effect on the
average cost of equity capital is a 35 basis point reduction from LCEOPRICESEN and a 21
basis point increase from LCEOVOLSEN. We conclude that there is an economicallysignificant relation between CEO compensation portfolio sensitivities and the average
implied cost of equity capital.
[ INSERT TABLE 2 ABOUT HERE ]5.2 Individual Implied Cost of Equity Capital and CEO Compensation Portfolio Sensitivities
Table 3 reports the regression results of model (4) in Table 2 (the full regression
model with the inclusion of both control variables and fixed effects) for each of our fourindividual implied cost of equity capital measures. The estimated effect of LCEOPRICESEN
on individual implied cost of equity ranges from a 21 basis point reduction (RGM) to a 55
basis point reduction (REAST), going from the 25th to the 75th percentile of LCEOPRICESEN.
The estimated coefficient on LCEOPRICESEN is highly significant in all regressions, with tstatistics ranging between -3.66 and -6.77.
The estimated effect on individual implied cost of equity capital from LCEOVOLSEN
ranges from a 10 basis point increase (RGLS) to a 26 basis point increase (REAST), going fromthe 25th to the 75th percentile of LCEOVOLSEN. The estimated coefficient on LCEOVOLSEN
16

is also highly significant in all regressions, with t-statistics ranging between 2.23 to 5.15. The
effects of LCEOPRICESEN and LCEOVOLSEN are strongest, as inferred from the size of thecoefficient estimates, for the implied cost of equity capital estimated from the PEG model by
Easton (2004) (REAST). The results for the control variables and the explanatory power of theregressions are comparable to those obtained with the average implied cost of equity capitalin Table 2. The explanatory power of regression analysis ranges between 20 and 34 percent inTable 3.
To summarize, the results in Table 3 document that the negative (positive) relation
between LCEOPRICESEN (LCEOVOLSEN) and the implied cost of equity capital isconsistent and robust across a broad set of individual cost of equity capital measures.
[ INSERT TABLE 3 ABOUT HERE ]5.3 Changes-in-Variables Analysis
In this section, we examine the robustness of the results obtained in the previous
section by investigating the changes in variables as opposed to the levels of variables. We
implement this analysis by regressing the annual change in the implied cost of equity capitalon the annual change in CEO compensation portfolio sensitivities, after controlling for annualchanges in the control variables. Weber (2006) suggests that the use of change-in-variables
regressions can help address endogeneity concerns. Moreover, change-in-variables
regressions are useful in mitigating problems with correlated omitted variables as we use thefirm as its own control. We estimate the pooled regression using 9,293 firm-year observations
over the period 1993-2009 for which annual changes in variables can be computed.
Table 4 presents the regression results for four models using the annual change in the
average implied cost of equity capital on the left-hand side. In model (1), in which we include

17

only annual changes in CEO compensation portfolio sensitivities as explanatory variables, wedocument a negative and significant estimated coefficient on ΔLCEOPRICESEN of -0.0233(t-statistic of -4.82) and a positive and significant estimated coefficient on ΔLCEOVOLSEN
of 0.0057 (t-statistic of 4.05). These findings support our prior testable hypotheses. In model(2), in which we include year fixed effect and industry fixed effect in the regression model,
we document a negative and significant estimated coefficient on ΔLCEOPRICESEN (-0.0134
with t-statistic of -6.67) and a positive and significant estimated coefficient on
ΔLCEOVOLSEN (0.004 with t-statistic of 3.90). In models (3) and (4), when changes in othercontrol variables and fixed effects are included in the regressions, both the estimatedcoefficients on ΔLCEOPRICESEN and ΔLCEOVOLSEN retain their signs and statisticalsignificance. The explanatory power of the changes-in-variable regressions ranges from 14
percent in model (1) to 21 percent in model (4). Taken together, the change-in-variables
analysis confirms the earlier findings based on the levels of variables and support both H1 andH2.
[ INSERT TABLE 4 ABOUT HERE ]We notice that the effects of the changes in ΔLCEOPRICESEN and ΔLCEOVOLSEN
on the changes in the average implied cost of equity capital, inferred from the size of theestimated coefficients, are even of a stronger magnitude compared with the effects from thelevels of variables. The magnitude of the estimated coefficient on ΔLCEOPRICESEN inmodel (4) of Table 4 (0.0146) is 4.17 times that of the estimated coefficient on
LCEOPRICESEN in model (4) of Table 2 (0.0035). Likewise, the magnitude of the estimatedcoefficient on ΔLCEOVOLSEN in model (4) of Table 4 (0.0045) is 2.14 times that of theestimated coefficient on LCEOVOLSEN in model (4) of Table 2 (0.0021). Thus, the results inTable 4 suggest that the link between CEO risk-related incentives and the average cost of18

equity capital is not only evident but also highly economically important in the change
specification.
Table 5 presents the regression results of annual change in individual implied cost ofequity capital to a set of annual change in control variables and annual change in sensitivitiesof CEO compensation portfolios to stock price and stock return volatility. We show that theestimated coefficient on ΔLCEOPRICESEN ranges from -0.0098 (RCT) to -0.0211 (REAST) andis significant across all four models (t-statistic ranging from -3.49 to -7.11). The estimatedcoefficient on ΔLCEOVOLSEN ranges from 0.0033 (RCT) to 0.0049 (REAST) and is alsosignificant across all four models (t-statistic ranging from 3.19 to 6.37). Here, the change-invariables analysis for individual implied cost of equity capital measures is also consistent
with that of the change-in-variables analysis for the average implied cost of equity capital.
Similar to the results in Table 3, we also document that the effects of ΔLCEOPRICESEN and
ΔLCEOVOLSEN on the cost of equity capital are strongest for REAST.
[ INSERT TABLE 5 ABOUT HERE ]5.4 Ratio of CEO Vega over Delta and the Cost of Equity Capital
Prior research has employed the ratio of the CEO vega over delta as a consolidated
measure of CEO risk-related incentive (see, e.g., Rogers, 2002, 2005; Grant et al., 2009).
Core et al. (2003) argue that risk taking is a second-order effect in a CEO option portfolio in
which the incentive to increase the stock price dominates the incentive to take risk. Therefore,
it is intuitively plausible to examine the proportion of the second-order effect with respect tothe first-order effect and its effect on the cost of equity capital. Here, the ratio of the CEOvega over delta, denoted as CEOSENRATIO, measures the proportion of incentives to takerisk with respect to the proportion of incentives to reduce risk. The higher the ratio, the higher

19the incentive to take risk. Hence, we expect a positive relation between CEOSENRATIO andthe cost of equity capital.
Table 6 presents the regression results of five measures (RAVE, REAST, RGLS, RCT, andRGM) of the cost of equity capital against CEOSENRATIO with the inclusion of control
variables and fixed effects. The estimated coefficient on CEOSENRATIO is 0.0086 andhighly significant (t-statistic of 4.10) in the regression using the average implied cost ofequity capital on the left-hand side. Thus, the effect on the average implied cost of equity
capital is an 86 basis point increase, going from the 25th percentile to the 75th percentile of theratio of the CEO vega over delta. When examining regressions of individual implied cost ofequity measures, we also find that the estimated coefficient on CEOSENRATIO is positive(ranging between 0.0055 to 0.0135) and highly significant (t-statistic ranging from 2.55 to3.95).
[ INSERT TABLE 6 ABOUT HERE ]Overall, the results confirm that when we consolidate risk-taking incentives and riskreducing incentives into one relative measure, there is a significant positive relation between
CEO risk taking incentives and the implied cost of equity capital. In unreported tests in which
we conduct change-in-variables analysis, we also find that the annual change in
CEOSENRATIO is positively and significantly associated with the annual change in theimplied cost of equity capital.
5.5 Robustness Analysis
In this section, we examine the relation between various alternative measures ofexecutive compensation portfolio sensitivities and the implied cost of equity capital. For
brevity, we only present regression results using the average implied cost of equity capital

20

with the inclusion of all control variables and fixed effects. We present these results in Table
7 where the results are presented for six models.
In model (1), we replace our main definition of CEO compensation portfolio
sensitivities with the top five managers‟ compensation portfolio sensitivities. We apply thisalternative definition as corporate decisions and policy choices are often made in teams(Aggarwal and Samwick, 2003), and thus it is worthwhile to investigate whether and how
aggregate managerial incentives influence the cost of equity capital. In model (1) the
calculation of deltas and vegas is an aggregate of the dollar sensitivities to stock price andstock return volatility of the top five managers‟ stock and option portfolios (denoted as
LMGMPRICESEN and LMGMVOLSEN, respectively). The estimated coefficient on
LMGMPRICESEN is negative at -0.0047 and significant (t-statistic of -3.73) and theestimated coefficient on LMGMVOLSEN is positive at 0.0028 and significant (t-statistic of3.70). The explanatory power of model (1) is 35 percent. Thus, results on the relation
between the top five management compensation portfolio sensitivities and the average
implied cost of equity capital are similar to earlier findings on the relation between CEO
compensation portfolio sensitivities and the cost of equity capital.
In model (2), we consolidate the top five managers‟ compensation portfolio
sensitivities into the ratio of top five managers‟ vega over delta and denote this variable as
MGMSENRATIO. We document a positive and significant estimated coefficient on
MGMSENRATIO (0.0162 with a t-statistic of 3.82). This finding is in line with prior findingson the relation between the CEO‟s vega over delta ratio and the cost of equity capital.
In model (3), we separate the CEO‟s delta into stock portfolio delta (denoted as
LCEOPRICESEN_STOCK)

andoptionportfolio

delta(denotedas

LCEOPRICESEN_OPTION). We find that both stock and option deltas are negatively related21

to the average implied cost of equity capital. The estimated coefficient on
LCEOPRICESEN_STOCK is -0.0007 and significant at the 10 percent level and the estimatedcoefficient on LCEOPRICESEN_OPTION is -0.0048 and significant at the 1 percent level.
Here, we notice that the effect of the option compensation portfolio delta on the cost ofequity capital is much more pronounced than that of the stock compensation portfolio delta.
The magnitude of the estimated coefficient on LCEOPRICESEN_OPTION is 6.8 times thatof the estimated coefficient on LCEOPRICESEN_STOCK.10
In

model

(4),

we

examinetheeffects

of

the

CEO

stock

delta

(LCEOPRICESEN_STOCK), exercisable option delta (LCEOPRICESEN_EXOPTION), andexercisable option vega (LCEOVOLSEN_EXOPTION) on the average implied cost of equity
capital. We continue to find a negative relation between deltas and the cost of equity capitaland a positive relation between vegas and the cost of equity capital. In model (5), we conduct
similar analysis as in model (4) using non-exercisable options and report similar findings. Inmodel (6), we include CEO stock delta, deltas and vegas from both exercisable options andnon-exercisable options in the regression model. The estimated coefficient is -0.0008 (tstatistic of -2.19) for CEO stock delta, -0.0025 (t-statistic of -3.19) for CEO exercisable
option delta, and -0.0036 (t-statistic of -3.29) for CEO non-exercisable option delta. Thus, allthree deltas are significantly and negatively related to the average cost of equity capital. The
effect on the average implied cost of equity capital is strongest for CEO‟s non-exercisable
option delta and smallest for CEO‟s stock portfolio delta. This finding is intuitively plausible
as non-exercisable options should impose the greatest incentive on CEO risk-taking behavior
and thus have the strongest effect on the implied cost of equity capital. The estimated10

We conduct a statistical test of the null hypothesis that the estimated coefficient on
LCEOPRICESEN_OPTION is equal to the estimated coefficient on LCEOPRICESEN_STOCK and reject thisnull hypothesis (p-value<0.001). Thus, option delta exerts effects of a different magnitude on the average costof equity capital as compared with stock delta.

22coefficient on CEO‟s vegas is 0.0017 and significant (t-statistic of 2.81) for exercisable
option vega and 0.0040 and significant (t-statistic of 3.34) for non-exercisable option vega.
Here, we also notice a higher effect on the average cost of equity capital from CEO‟s nonexercisable option vega than from CEO‟s exercisable option vega.11
In summary, the analysis in Table 7 consistently shows a negative and significant
relation between executive compensation portfolio deltas and the average cost of equity
capital and a positive and significant relation between executive compensation portfolio
vegas and the average cost of equity capital. Other notable results in Table 7 are that optiondeltas have a stronger effect on the cost of equity capital than stock deltas and that deltas andvegas from non-exercisable options have stronger effects on the cost of equity capital thanthose from exercisable options.
[ INSERT TABLE 7 ABOUT HERE ]5.6 Endogeneity
The analyses thus far treat CEO compensation portfolio sensitivities as exogenous inmodelling the implied cost of equity capital. It is possible, however, that CEO compensation
portfolio sensitivities are endogenous. This endogeneity might arise if an omitted variablecorrelated with CEO compensation portfolio sensitivities and the cost of equity capital drive
the results in the study or if the cost of equity capital determines how firms establish their

11

We conduct two statistical tests for model (6) in Table 7: i) whether the estimated coefficient on
LCEOPRICESEN_EXOPTION is equal to the estimated coefficient on LCEOPRICESEN_NONEXOPTION, andii) whether the estimated coefficient on LCEOVOLSEN_EXOPTION is equal to the estimated coefficient on
LCEOVOLSEN_NONEXOPTION. We reject the null hypothesis in both tests (p-value<0.001) and conclude thatthe sensitivities of non-exercisable options exert effects of a different magnitude on the average cost of equity
capital as compared with the sensitivities of exercisable options.

23CEO stock and option incentive contracts.12 In this section, we address endogeneity concerns
in three different ways.
First, we follow Klein (1998) to address the concern of reverse causality (i.e., CEOrisk incentives in the compensation contract might be affected by the cost of equity capital in
the previous period). We include the lagged cost of equity capital variable in the regression
analysis. If the estimated coefficient on LCEOPRICESEN (LCEOVOLSEN) remains
significantly negative (positive) after including the lagged cost of equity capital, we can reject
the possibility of reverse causality to a certain extent. Model (1) in Table 8 presents theresults of this analysis and confirms our findings reported in Table 2. More specifically,
although the estimated coefficient on LCEOPRICESEN (LCEOVOLSEN) is reduced by about
28 (14) percent from 0.0035 (0.0021) in model (4) in Table 2 to 0.0024 (0.0018) in model (1)in Table 8, it is still significant (t-statistic of -5.23 and 3.89, respectively) when the lagged
average cost of equity capital is included in the regression as a control variable.13[ INSERT TABLE 8 ABOUT HERE ]Second, we compute CEO compensation portfolio deltas and vegas from stocks andoptions previously granted and exclude stocks and options granted for the current fiscal year.
Using the CEO compensation portfolio sensitivity variables computed from data several
years before the current fiscal year makes it less likely that CEO compensation portfoliodeltas and vegas are determined simultaneously with the current implied cost of equity
capital. We present these results under model (2) in Table 8. We find that the estimated12

Larcker (2003) suggests that most studies employing a managerial choice variable as an explanatory variable
face endogeneity concerns. Bhagat and Black (2002) also claim that studies examining variables capturingcorporate ownership and other corporate aspects such as performance and capital structure are interrelated. In
equilibrium, it is likely that these variables are jointly determined based on several firm-specific factors (Johnand John, 1993).
13
The results on other control variables are consistent with earlier findings in this study. For brevity inpresentation, we do not report the estimated coefficients and t-statistics for other control variables.

24coefficient on LCEOPRICESENt-1 is negative at -0.0020 and significant (t-statistic of -3.43)
while the estimated coefficient on LCEOVOLSENt-1 is positive at 0.0018 and also significant(t-statistic of 2.78). While the magnitude of estimated coefficients drops considerably forboth variables, there remain statistically and economically significant relations between CEO
deltas and vegas from the prior year and the average cost of equity capital.14
In our final approach, we employ a two-stage least squares regression analysis andtreat CEO compensation portfolio sensitivities as endogenous variables to formally tackle
endogeneity concerns. We use a comprehensive set of instrumental variables suggested byprior studies (Himmelberg et al., 1999; Knopf et al., 2002; Coles et al., 2006; Ortiz-Molina,
2006; and Brockman et al., 2010) to model CEO compensation portfolio sensitivities. In
addition to using control variables for the implied cost of equity capital as exogenous
variables, our set of instrumental variables here includes: LTENURE as the natural logarithmof the CEO‟s tenure measured in years; SURCASH as the cash from assets-in-place;
VOL_RISK as the natural logarithm of monthly stock return variance during the fiscal year;
LCASHCOMP as the natural logarithm of the sum of the CEO‟s salary and bonus; SGR as thesales growth rate; LRD as the natural logarithm of research and development expenses
divided by sales; LCAPX as the natural logarithm of capital expenditure divided by total
assets and BHRET as the buy-and-hold stock return during the fiscal year. First, we can treat
these instrumental variables as exogenous as there is no theoretical link for the relation
between these instruments and the cost of equity capital. Second, we compute a test of overidentifying restrictions to evaluate the appropriateness of the instruments as recommended in
Larcker and Rasticus (2010) since we have multiple instruments for each endogenous
variable. The Sargan test of over-identifying restrictions does not reject the exogeneity of

14

In models (1) and (2) in Table 8, the sample size reduces to 9,293 firm-year observations due to therequirement of lagged data.

25

instruments (χ2 =0.48 and p-value=0.43).15 The data requirements to compute instrumental
variables reduce the sample size in this analysis to 8,471 firm-year observations.
In the first-stage regressions, LCEOPRICESEN and LCEOVOLSEN are eachseparately regressed on the exogenous variables and the instrumental variables listed above.
The R-squared value from the first-stage regressions is 0.80 for LCEOPRICESEN and 0.77
for LCEOVOLSEN. In the second-stage regression, we use the predicted values of
LCEOPRICESEN and LCEOVOLSEN from each of these separate first-stage OLS
regressions. Model (3) in Table 8 presents the results of the second-stage regression. The
estimated coefficients on Pr(LCEOPRICESEN) and Pr(LCEOVOLSEN) in the second-stage
regression are of lower magnitude than, but comparable to, those in the OLS regression inmodel (4) of Table 2. These coefficients retain their signs and are statistically significant at
the 1 percent level.
Overall, while CEO risk incentives are firm‟s choices and may be determined byseveral firm-specific factors, the results from Table 8 generally indicate that the negative(positive) relation between CEO deltas (vegas) and the implied cost of equity capital in ourstudy does not appear to be driven by the endogeneity of these risk incentives.
5.7 Tests on the Cost of External Equity Financing
We investigate the effects of CEO risk incentives on the cost of equity capital in acontext in which we can directly measure the cost of raising equity capital, the documented
underpricing of seasoned equity offerings (SEOs). SEO underpricing occurs when the offer

15

The tests of the appropriateness of instrumental variables are based on the assumption that at least one of the
instruments is valid (Larcker and Rasticus, 2010). We acknowledge that there might be a possibility that all
instrumental variables are biased in the same direction and the test of over-identifying restrictions does not
reject the null of appropriateness of instruments even though the instrumental variable estimates are biased.

26

price is lower than the closing price on the day prior to the offer date and represents a
substantial cost of issuing new shares (Altinkilic and Hansen, 2003).
SEO underpricing offers an effective setting to examine the relation between CEO
risk incentives and the cost of equity capital for two reasons. First, prior research has shownthat the use of implied cost of equity capital is subject to measurement errors (Joos, 2000;
Easton and Monahan, 2005) because the valuation models rely on imperfect analyst earnings
forecasts and simplified assumptions regarding earnings forecasts beyond the analysts‟
forecast horizons. SEO underpricing is a direct measure of the cost of raising equity capitaland can be accurately and directly measured, thereby ruling out any measurement error
issue. 16 Second, investigation of SEO underpricing offers another powerful way to tackle
endogeneity concerns because the underpricing of SEOs occurs on the offer date and isunlikely to affect the CEO compensation contract prior to this date.17 Our hypothesis in thisanalysis is that CEO deltas (vegas) are negatively (positively) related to SEO underpricing.
We collect the initial sample of 8,294 SEOs of common shares in the period from1993 to 2009 from the Securities Data Company (SDC).18 We then apply various restrictions
on the sample as in Bowen et al. (2009) and also require that data on CEO risk incentives
from the prior year are available for each SEO.19 As a result, the final sample includes 1,112
SEO issues spanning the period 1993-2009.

16

We acknowledge that the underpricing of SEOs is only one of several components of the cost of raising equity
capital in SEOs. For example, underwriting fees and price changes around SEO announcements also represent
significant costs. Bowen et al. (2009), however, posit that SEO underpricing is the most representative of thecost of raising equity capital.
17
The final offer price for SEOs is often set after the stock market closes on the day prior to the offer date. The
underpricing of SEOs occurs when the offer price is less than the closing market price on the day prior to theoffer date, representing a cost of raising equity capital for the issuers (Altinkilic and Hansen, 2003).
18
We select the beginning sample period to be in year 1993 so that we can use CEO risk incentives in 1992 torelate to SEO underpricing in 1993.
19
Specifically, we require that i) SEO issues must include some primary offerings, ii) SEO issues must havedata available in CRSP, iii) the offer price is between $5 and $4000 to eliminate illiquid firms, and iv) SEO
issues have analyst coverage in the IBES Detailed Earnings Forecast file.

27

We compute CEO deltas and vegas from the year prior to the SEOs to relate to SEO
underpricing. Similar to prior studies, we define underpricing as the return from the closing
price on the day immediately before the offer date to the offer price. 20 We also employ a setof control variables as determinants of SEO underpricing: firm size (Size) as the natural logof the market value of equity at the end of the year before the SEOs, number of analysts
covering the firms (#N_Analyst) in the year before the SEO, idiosyncratic volatility (Idio_Vol)
as the natural log of the standard deviation of the residuals from the regression of monthly
returns on Fama and French (1996) risk factors in the five years before the SEOs, relative
offer size (Relative_Offer_Size) as the offer size relative to outstanding shares, positive preoffer abnormal return (CAR_Positive) as the cumulative abnormal return in the 10 days
leading to the offer date if this is a positive value, negative pre-offer abnormal return(CAR_Negative) as the cumulative abnormal return in the 10 days leading to the offer date if
this is a negative value, the rounding of the offer price to a $0.25 increment (Tick[0,0.25] ),stock price 10 days prior to the offer date (Price), and a dummy variable for NYSE stocks(NYSE).21
Table 9 presents the regression results of SEO underpricing on CEO compensation
portfolio sensitivities and control variables. In model (1), which excludes control variables
20

Safieddine and Wilhelm (1996) suggest that some offer dates in SDC are incorrect because the offers occur
after-hours. We employ the volume-based adjustment in Altinkilic and Hansen (2003) and Corwin (2003) tocorrect for possible errors in the SDC offer dates. Essentially, if we find that trading volume on the day after the
SDC offer date is more than twice that on the SDC offer date and more than twice the average daily trading
volume in the 250 days leading to the SDC offer date, we shift the „actual‟ offer date to the trading day
following the SDC offer date. Corwin (2003) confirms high accuracy in the adjustment of SDC offer dates using
trading volume.
21
Corwin (2003) suggests that firm size can act as a proxy for information asymmetry and is negatively related
to SEO underpricing. Bowen et al. (2009) document a negative relation between the number of analysts
covering the firm and SEO underpricing because asymmetric information risk is reduced. Beatty and Ritter(1986) suggest that underpricing is larger for firms with high return volatility. Corwin (2003) uses the offer size
relative to outstanding shares as a proxy for the price pressure and finds higher underpricing for firms with arelatively large offer size. Gerard and Nanda (1993) and Corwin (2003) use pre-offer cumulative returns tomeasure price manipulation by investors. Mola and Loughran (2004) suggest that the underpricing of SEOs
should be larger for firms with offer prices that are not at a $0.25 increment. Corwin (2003) and Bowen et al.
(2009) show some difference in underpricing for NYSE firms.

28and fixed effects, the estimated coefficient on LCEOPRICESEN is -0.0058 and significant (tstatistic of -3.17). Thus, there is strong evidence that CEO deltas are associated with a lower
cost of external equity finance as deltas are inversely related with SEO underpricing. The
estimated coefficient on LCEOVOLSEN is positive at 0.0013 but insignificant (t-statistic of0.91). Model (2) includes fixed effects but excludes control variables. Here, we find an evenstronger estimated coefficient on LCEOPRICESEN (-0.0079 with t-statistic of -3.97). The
estimated coefficient LCEOVOLSEN is positive and continues to be insignificant. In model (3)in which control variables are included and in model (4) in which both control variables andfixed effects are included, our main findings on LCEOPRICESEN and LCEOVOLSEN are
generally similar to those reported in models (1) and (2). The estimated coefficients oncontrol variables are generally in line with expected signs and prior studies. We find thatanalyst coverage and stock prices are significantly associated with lower SEO underpricing
while idiosyncratic volatility, relative offer size, and negative pre-offer cumulative abnormal
return are significantly associated with higher SEO underpricing. The explanatory power ofthe regression analysis of SEO underpricing in Table 9 varies from 2 percent in model (1) to19 percent in model (4).
[ INSERT TABLE 9 ABOUT HERE ]To summarize, in the setting of SEOs where the cost of raising external equity can bedirectly measured from SEO underpricing, we find that CEO deltas are negatively related to
SEO underpricing and thus lead to a lower cost of external equity financing. This result
echoes the negative relation between CEO deltas and the implied cost of equity capital fromearlier findings. We, however, do not document a significant relation between CEO vegas
and SEO underpricing.

29

6. Conclusion
Recent studies posit that managerial stock and option compensation portfolios exhibit
two opposing effects on managerial risk-taking behaviour (Knopf et al., 2002; Coles et al.,2006; Brockman et al., 2010). Deltas, the sensitivity of CEO compensation portfolio to stock
price, discourage managerial risk-taking behavior while vegas, the sensitivity of CEO‟scompensation portfolio to stock return volatility, encourage managerial risk-taking behavior.
A growing body of empirical research provides evidence that CEO compensation portfolio
sensitivities determine the risk-taking behavior of CEOs and the firm‟s overall risk (Knopf etal., 2002; Rajgopal and Shevlin, 2002; Coles et al., 2006; Grant et al., 2009; Brockman et al.,2010; Armstrong and Vashishtha, 2011). In this study, we investigate whether shareholders
price CEO risk-related incentives arising from CEO compensation portfolio sensitivities in
the implied cost of equity capital. We hypothesize that CEO compensation portfolio
sensitivity to stock price (stock return volatility) results in incentives to reduce (increase) the
overall risk of a firm and therefore is associated with a lower (higher) cost of equity capital.
To test our hypotheses, we employ a sample of 11,041 firm-year observations overthe period 1992 to 2009. We use four individual measures of implied cost of equity capitalfrom four valuation models in the literature: Claus and Thomas (2001), and Gebhardt et al.
(2001), Gode and Mohanram (2003) and Easton (2004) and an average-based measure of
implied cost of equity capital. We follow Core and Guay (2002) in estimating option
sensitivities of CEO compensation portfolio. Our findings show strong empirical support for
both hypotheses. We find a consistently negative relation between CEO compensation
portfolio sensitivity to stock price (deltas) and the cost of equity capital. We also find aconsistently positive relation between CEO compensation portfolio sensitivity to stock return
volatility (vegas) and the cost of equity capital.

30

In a change-in-variables analysis, we document that the annual change in CEO‟sdeltas (vegas) is significantly and negatively (positively) associated with the annual change inthe cost of equity capital. When consolidating vegas and deltas into a ratio that measures theoverall CEO risk-taking incentive as in Rogers (2002, 2005) and Grant et al. (2009), we findthat the ratio of the CEO vega over delta is significantly and positively related to the cost ofequity capital. The negative (positive) relation between deltas (vegas) and the cost of equity
capital is also robust to the examination of the top five managers‟ compensation portfolio
sensitivities, the break-down of deltas into stock delta and option delta, and the separation of
option deltas and vegas between exercisable options and non-exercisable options. Our main
findings are also robust to various tests of endogeneity on the relation between CEO risk
incentives and the cost of equity capital. In a setting of SEOs, we document that CEO deltas
are inversely related to SEO underpricing and conclude that high deltas are associated with alower cost of external equity financing. We find a positive but insignificant relation between
CEO vegas and the cost of external equity financing.
Our study offers significant contributions to the literature on the executive
compensation and the cost of equity capital. We show that CEO compensation portfolio
sensitivities affect the implied cost of equity capital in opposite directions. These findings are
consistent with the notion that CEO compensation portfolio sensitivities exert opposite
effects on the firm‟s overall risk. Our findings also add new evidence to the literature on thecost of equity capital, namely that CEO compensation portfolio sensitivities are significant
determinants, both statistically and economically. These findings highlight the important rolethat CEO risk-taking behavior plays in market-based assessments of firms.

31

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35

Appendix A
Implied Cost of Equity Capital Measures
To estimate the implied cost of equity capital, we apply the four following models
developed by Easton (2004), Gode and Mohanram (2003), Claus and Thomas (2001), andGebhardt et al. (2001):
Pt= Stock price after the latest fiscal year-end at time t. We use stock price four months
after the latest fiscal year-end (Pt+4) to compute Pt. To account for partial year discounting,
we estimate stock price at time t by discounting Pt+4 by (1+R) 4/12 where R is the implied costof equity capital.
BVt= Book value of equity from the most recent available financial statement at time t.
FEPSt+i= Analyst forecasted earnings per share from IBES for the next i years.
k= Forecasted dividend payout ratio where is the dividend payout ratio calculated as theactual dividends per share at the beginning of year () divided by the actual earnings
per share at the beginning of fiscal year ().
1. The Modified Price-Earnings Growth (PEG) Model by Easton (2004)
FEPS t 1  REAST  k  FEPS t 1  FEPS t  2
(A.1)
Pt 
2
REAST
REAST= cost of equity capital.
We use a numerical binary search to equate the right-hand side to the left-hand side ofequation A.1 within a difference of $0.001.
2. Gode and Mohanram (2003)

 FEPS t 1 
  g 2  g 
RGM  A  A2  
 Pt


A

(A.2)

1 
k  FEPS t 1   g 
2 
Pt


g2 

FEPS t  2  FEPS t 1 

FEPS t 1
g  rf  0.03
RGM= cost of equity capital.
Here, growth rate (g) is calculated using the contemporaneous risk-free rate (rf is the yield on
10-year Treasury bonds) minus 3 percent.
3. Claus and Thomas (2001)

FEPS t  i  RCT  BVt  i 1 FEPS t  6  RCT  BVt  5   (1  g )
( RCT  g )  (1  RCT )51  RCT ii 1
6Pt  BVt  (A.3)

RCT= cost of equity capital.
We use a numerical binary search to equate the right hand side to the left hand side ofequation A.3 within a difference of $0.001.
4. Gebhardt et al. (2001)
FROEt 1  RGLS   BVt  FROEt  2  RGLS   BVt 1  TV
Pt  BVt (A.4)
1  RGLS (1  RGLS ) 2

FROEt i  RGLS   BVt i 1  FROEt T  RGLS   BVt T 1
RGLS  (1  RGLS )T 1
1  RGLS i
i 3

T 1

TV  

FROE is calculated as income available to shareholders scaled by the lagged total book value of36

equity. From the 3rd year to the Tth year, FROE is assumed to decline linearly to an
equilibrium return on equity (ROE). The equilibrium return on equity is determined by ahistorical 10-year industry median ROE. We use Fama and French (1997) to classify 48
industries. If the industry ROE is less than the risk-free rate, we set the industry ROE to be therisk-free rate.
RGLS= cost of equity capital.
We use a numerical binary search to equate the right-hand side to the left-hand side ofequation A.4 within a difference of $0.001.

37

Appendix B
CEO Compensation Portfolio Delta and Vega Measures
Data used to construct management price and volatility sensitivity come frommultiple sources. More specifically, we obtain management compensation and ownershipdata from the S&P ExecuComp database. Financial information is from Compustat annual
files and stock return information is from CRSP monthly files. Yields on long-term
government bonds are obtained from the Federal Reserve Bank.
The theoretical framework used to construct management compensation sensitivities
to stock price and stock return volatility originates from the Black-Scholes option pricing
model adjusted for dividends. The model is presented as follows:
( )

(

√ )

(B.1)

with
( )

(

)

√
where
N = cumulative probability function for the normal distribution
S = price of underlying stock
X = exercise price of the option
σ = expected stock return volatility of the underlying stock over the life of the optionr = risk-free interest rate
T = time to maturity of the optiond = expected dividend yield over the life of the option
Option delta is the partial derivative of the option price with respect to stock price and option
vega is the partial derivative of the option price with respect to stock return volatility as
follows:
( )
(B.2)
( ) √
(B.3)
where
N' = density function for the normal distribution
To capture option delta and vega, we use six variables, namely, stock price, dividend
yield, stock return volatility, risk-free rate, exercise price and time to maturity. The variables
are estimated following Core and Guay (2002):
Stock price
We use the closing price at the end of the fiscal year as the stock price. Stock pricedata are from Compustat annual files.
Dividend yield
Dividend yield is estimated as the firm's average dividend ratio over the preceding
three years. Dividend ratio is the ratio of common dividend over the market value of equity.
Dividend yield data are from the Compustat annual files.
Stock return volatility
Stock return volatility is defined as the annualized monthly volatility of stock returns
over the preceding five years. Monthly stock return data are from CRSP monthly files.
Risk-free rate38

We adopt the yield of 10-year US Treasury bonds as the proxy for the risk-free rate.
Treasury yield data are from the Federal Reserve Bank.
Exercise price and time to maturity
We partition a CEO‟s option portfolio into three parts: new option grants, previous
exercisable option grants and previous non-exercisable option grants. Full information about
the exercise price and time to maturity is available from ExecuComp for new grants, whichmakes the calculation for new grants much easier. However, no data are available on theexercise price and time to maturity for previous option grants. We therefore rely on theapproximation method developed by Core and Guay (2002).
To estimate the average exercise price for previous option grants, we divide therealizable value of the options by the number of options to find the average difference
between stock price and exercise price. We then subtract the difference from the stock priceto get the exercise price. For the time to maturity of previous option grants, we set thematurity of exercisable (non-exercisable) options as four (one) years less than that of new
grants. If there are no new grants in the current year, we set the time to maturity of
exercisable (non-exercisable) options to nine (six) years. Therefore, the maturity of
exercisable options is always three years less than that of non-exercisable options.
We first estimate delta and vega for each type of option grant and then calculate thestock price and stock return volatility sensitivities of the management's option and stock
holdings as follows:() (B.4)() (B.5)where S is the stock price and N is the number of options/stocks in thousands. The subscript
NG stands for new option grants; the subscript PGEX stands for previous exercisable option
grants; the subscript PEUNEX stands for previous non-exercisable option grants; and thesubscript STK stands for stock holdings.

39

Table 1. Descriptive Statistics
Variable Name

Mean

Q1

Q3

MedianStd. Dev.

RAVE

0.09480.07580.10630.09030.0339REAST

0.11140.07900.12680.09890.0600RGM

0.09870.07930.11150.09570.0373RCT

0.0861

0.06470.10020.08180.0400RGLS

0.08430.0656

0.09920.08090.0305BM

0.59280.17790.88420.48570.5123LTG

0.1526

0.10950.19100.14460.8350Disp

0.12470.04000.13000.07000.2593Size

7.7202

6.68958.67907.6073

1.5258

Leverage

0.21030.06530.31830.19910.1669BMKT

0.94050.64751.09000.97780.5227

BSMB

0.20850.05700.6001

0.1986

0.6786

BHML

0.05810.02700.40080.11670.8043

CEOPRICESEN ($000)

719.72749.384388.373

139.8426646.130

CEOVOLSEN ($000)
106.063
38.277101.988
63.711297.506
This table present descriptive statistics for variables used in this study. The sample comprises of 11,041 firmyear observations spanning the period 1992-2009 for which data to compute CEO compensation portfolio
sensitivities and the implied cost of equity capital are available. The average implied cost of equity capital(RAVE ) is the equally-weighted average of the four implied cost of equity measures: REAST from Easton (2004),
RGM from Gode and Mohanram (2003), RCT from Claus and Thomas (2001), and RGLS from Gebhardt et al.
(2001). BM is the ratio of the book value over the market value of equity; LTG is the analyst long-term growthin earnings forecast from I/B/E/S; Disp is the forecast dispersion defined as the coefficient of variation of
I/B/E/S earnings forecasts; Size is the natural logarithm of the market value of equity (in millions); Leverage isthe ratio of long-term debt over total assets; BMKT, BSMB, and BHML are factor loadings from the Fama and French(1996) three-factor model on risk factors. CEOPRICESEN is the change in the dividend-adjusted Black-Scholes
value of the CEO‟s stock options plus the change in the CEO‟s common stockholdings for a 1 percent change inthe value of the firm‟s stock price. CEOVOLSEN is the change in the dividend-adjusted Black-Scholes value of
the CEO‟s option portfolio for a 0.01 change in the annualized standard deviation of the firm‟s stock returns.

40

Table 2. The Relation between the Average Implied Cost of Equity Capital (RAVE) and CEO
Compensation Portfolio Sensitivities to Stock Price and Stock Return Volatility
Variable Name
Intercept

Predicted
Sign?

LCEOPRICESEN-LCEOVOLSEN

+

BM

+

LTG

+

Disp

+

Size

-

Leverage

+

BMKT

+

BSMB

+

BHML

+

Model 1Model 2Model 3Model 40.1243(14.29)***-0.0060(-5.23)***0.0016(3.66)***

0.1208(13.39)***-0.0054(-6.89)***0.0018(4.38)***

0.1169(15.85)***-0.0044(-3.91)***0.0012(3.59)***
0.0099(10.77)***0.0280(1.75)*
0.0206(2.12)**-0.0014(-2.96)***0.0236(6.17)***
0.0063(3.62)***
0.0014(1.25)
0.0020(2.26)**

0.1081(14.07)***-0.0035(-4.14)***0.0021(4.14)***
0.0100(9.17)***
0.0739(5.85)***
0.0276(2.35)**-0.0021(-3.27)***0.02556(7.11)***
0.0040(3.68)***
0.0006(1.18)
0.0026(4.15)***

Year Fixed Effect
No
Yes
No
Yes
Industry Fixed Effect
No
Yes
No
Yes
Adj. R2
0.06
0.15
0.20
0.34
N
11,041
11,041
11,041
11,041This table presents results from regression models of the average implied cost of equity capital to a set of control
variables and sensitivities of CEO compensation portfolios to stock price and stock return volatility. The
average implied cost of equity capital (RAVE ) is the equally-weighted average of the four implied cost of equity
measures: REAST from Easton (2004), RGM from Gode and Mohanram (2003), RCT from Claus and Thomas (2001),
and RGLS from Gebhardt et al. (2001). BM is the ratio of the book value over the market value of equity; LTG isthe analyst long-term growth in earnings forecast from I/B/E/S; Disp is the forecast dispersion defined as thecoefficient of variation of I/B/E/S earnings forecasts; Size is the natural logarithm of the market value of equity(in millions); Leverage is the ratio of long-term debt over total assets; BMKT, BSMB, and BHML are factor loadings
from the Fama and French (1996) three-factor model on risk factors. CEOPRICESEN is the change in thedividend-adjusted Black-Scholes value of the CEO‟s stock options plus the change in the CEO‟s common
stockholdings for a 1 percent change in the value of the firm‟s stock price. CEOVOLSEN is the change in thedividend-adjusted Black-Scholes value of the CEO‟s option portfolio for a 0.01 change in the annualized
standard deviation of the firm‟s stock returns. Industry fixed effect is defined by the Fama and French (1997)
industry classifications. Two-way clustered t-statistics are based on standard errors clustered by firm and year.
***, **, and * denote statistical significance at the 1, 5, and 10 percent level.

41

Table 3. The Relation between Individual Implied Cost of Equity Capital Measure and CEO
Compensation Portfolio Sensitivities to Stock Price and Stock Volatility
Variable Name
Intercept

Predicted
Sign?

LCEOPRICESEN-LCEOVOLSEN

+

BM

+

LTG

+

Disp

+

Size

-

Leverage

+

BMKT

+

BSMB

+

BHML

+

REAST

RGM

RCT

RGLS

0.1505(16.87)***-0.0055(-6.77)***0.0026(3.76)***
0.0096(4.69)***
0.0033(4.87)***
0.0788(5.29)***-0.0066(-4.89)***0.0392(6.34)***
0.0178(5.78)***
0.0057(3.04)***-0.0003(-0.22)0.1037(11.25)***-0.0021(-5.49)***0.0018(5.15)***
0.0078(7.71)***
0.1054(4.86)***
0.0084(2.65)**-0.0015(-2.17)**0.0105(6.01)***
0.0011(0.74)
0.0007(0.03)
0.0013(2.05)**

0.1164(14.31)***-0.0027(-3.66)***0.0025(3.65)***
0.0058(6.70)***
0.0016(1.41)
0.0069(2.95)***-0.0029(-4.20)***0.0175(4.88)***
0.0054(2.94)***
0.0009(0.73)
0.0012(1.47)

0.0972(20.23)***-0.0030(-4.74)***0.0010(2.23)**
0.0122(9.78)***
0.0001(0.30)
0.0153(2.97)**-0.0008(-2.12)**0.0270(4.95)***
0.0056(3.78)***
0.0022(2.38)**
0.0031(2.73)***

Year Fixed Effect
Yes
Yes
Yes
Yes
Industry Fixed Effect
Yes
Yes
Yes
Yes
Adj. R2
0.32
0.21
0.20
0.34
N
11,041
11,041
11,041
11,041This table presents results from regression models of individual implied cost of equity capital to a set of control
variables and sensitivities of CEO compensation portfolios to stock price and stock return volatility. REAST isfrom Easton (2002), RGM is from Gode and Mohanram (2003), RCT is from Claus and Thomas (2001), and RGLS
is from Gebhardt et al. (2001). BM is the ratio of the book value over the market value of equity; LTG is theanalyst long-term growth in earnings forecast from I/B/E/S; Disp is the forecast dispersion defined as thecoefficient of variation of I/B/E/S earnings forecasts; Size is the natural logarithm of the market value of equity(in millions); Leverage is the ratio of long-term debt over total assets; BMKT, BSMB, and BHML are factor loadings
from the Fama and French (1996) three-factor model on risk factors. LCEOPRICESEN is the natural logarithmof the change in the dividend-adjusted Black-Scholes value of the CEO‟s stock options plus the change in theCEO‟s common stockholdings for a 1 percent change in the value of the firm‟s stock price. LCEOVOLSEN is
the natural logarithm of the change in the dividend-adjusted Black-Scholes value of the CEO‟s option portfolio
for a 0.01 change in the annualized standard deviation of the firm‟s stock returns. Industry fixed effect is definedby the Fama and French (1997) industry classifications. Two-way clustered t-statistics are based on standard
errors clustered by firm and year. ***, **, and * denote statistical significance at the 1, 5, and 10 percent level.

42

Table 4. The Relation between Annual Change in the Average Cost of Equity Capital (ΔRAVE) and Annual
Change in CEO Compensation Portfolio Sensitivities to Stock Price and Stock Return Volatility
Variable Name
Intercept

Predicted
Sign?

ΔLCEOPRICESEN-ΔLCEOVOLSEN

+

ΔBM

+

ΔLTG

+

ΔDisp

+

ΔSize

-

ΔLeverage

+

ΔBMKT

+

ΔBSMB

+

ΔBHML

+

Model 1Model 2Model 3Model 40.0046(1.36)-0.0233(-4.82)***0.0057(4.05)***

0.0170(1.48)-0.0134(-6.67)***0.0044(3.90)***

0.0045(1.39)-0.0239(-5.20)***0.0056(3.79)***
0.0026(1.09)
0.0339(1.73)*
0.0069(0.93)-0.0014(-2.36)**0.0098(1.49)
0.0053(1.41)
0.0032(1.20)
0.0017(1.67)*

0.0131(1.47)-0.0146(-4.28)***0.0045(4.02)***
0.0052(2.17)**
0.069(2.05)**
0.0171(1.35)-0.0021(-2.27)**0.00175(1.11)
0.0021(1.40)
0.0006(0.64)
0.0011(1.37)

Year Fixed Effect
No
Yes
No
Yes
Industry Fixed Effect
No
Yes
No
Yes
Adj. R2
0.14
0.16
0.15
0.21
N
9,293
9,293
9,293
9,293
This table presents results from regression models of annual change in the average implied cost of equity capital
to a set of annual change in control variables and annual change in sensitivities of CEO compensation portfolios
to stock price and stock return volatility. The average implied cost of equity capital (RAVE ) is the equallyweighted average of the four implied cost of equity measures: REAST from Easton (2002), RGM from Gode andMohanram (2003), RCT from Claus and Thomas (2001), and RGLS from Gebhardt et al. (2001). BM is the ratio of
the book value over the market value of equity; LTG is the analyst long-term growth in earnings forecast from
I/B/E/S; Disp is the forecast dispersion defined as the coefficient of variation of I/B/E/S earnings forecasts; Sizeis the natural logarithm of the market value of equity (in millions); Leverage is the ratio of long-term debt overtotal assets; BMKT, BSMB, and BHML are factor loadings from the Fama and French (1996) three-factor model onrisk factors. LCEOPRICESEN is the natural logarithm of the change in the dividend-adjusted Black-Scholes
value of the CEO‟s stock options plus the change in the CEO‟s common stockholdings for a 1 percent change inthe value of the firm‟s stock price. LCEOVOLSEN is the natural logarithm of the change in the dividendadjusted Black-Scholes value of the CEO‟s option portfolio for a 0.01 change in the annualized standard
deviation of the firm‟s stock returns. Industry fixed effect is defined by the Fama and French (1997) industry
classifications. Two-way clustered t-statistics are based on standard errors clustered by firm and year. ***, **,and * denote statistical significance at the 1, 5, and 10 percent level.

43

Table 5. The Relation between Annual Change in the Individual Implied Cost of Equity Capital Measure
and Annual Change in CEO Compensation Portfolio Sensitivities to Stock Price and Stock Return
Volatility
Variable Name
Intercept

Predicted
Sign?

ΔLCEOPRICESEN-ΔLCEOVOLSEN

+

ΔBM

+

ΔLTG

+

ΔDisp

+

ΔSize

-

ΔLeverage

+

ΔBMKT

+

ΔBSMB

+

ΔBHML

+

ΔREAST

ΔRGM

ΔRCT

ΔRGLS

0.0148(1.47)-0.0211(-7.11)***0.0046(3.19)***
0.0052(1.82)*
0.0018(3.71)***
0.0046(1.86)*-0.0056(-2.29)**0.0235(2.19)**
0.0074(1.28)
0.0049(1.26)
0.0026(1.92)**

0.0123(1.18)-0.0099(-3.59)***0.0034(3.31)***
0.0071(3.47)***
0.0051(1.68)*
0.0160(1.78)*-0.0042(-1.93)**0.0054(0.48)
0.0048(1.30)
0.0029(1.07)
0.0029(2.02)**

0.0169(1.64)*-0.0098(-3.49)***0.0033(3.32)***
0.0021(0.80)
0.0041(3.73)***-0.0020(-0.22)-0.0011(-0.21)0.0068(0.80)
0.0028(0.52)-0.0019(-0.60)0.0008(0.51)

0.0140(1.16)-0.0153(-6.64)***0.0049(6.37)***
0.0019(0.80)
0.0001(0.44)
0.0062(1.55)-0.0011(-2.03)**0.0133(2.47)**-0.0003(-0.15)-0.0004(-0.24)0.0013(2.28)**

Year Fixed Effect
Yes
Yes
Yes
Yes
Industry Fixed Effect
Yes
Yes
Yes
Yes
Adj. R2
0.14
0.14
0.12
0.21
N
9,293
9,293
9,293
9,293
This table presents results from regression models of annual change in individual implied cost of equity capital
to a set of annual change in control variables and annual change in sensitivities of CEO compensation portfolios
to stock price and stock return volatility. REAST is from Easton (2002), RGM is from Gode and Mohanram (2003),
RCT is from Claus and Thomas (2001), and RGLS is from Gebhardt et al. (2001). BM is the ratio of the bookvalue over the market value of equity; LTG is the analyst long-term growth in earnings forecast from I/B/E/S;
Disp is the forecast dispersion defined as the coefficient of variation of I/B/E/S earnings forecasts; Size is thenatural logarithm of the market value of equity (in millions); Leverage is the ratio of long-term debt over total
assets; BMKT, BSMB, and BHML are factor loadings from the Fama and French (1996) three-factor model on risk
factors. LCEOPRICESEN is the natural logarithm of the change in the dividend-adjusted Black-Scholes value of
the CEO‟s stock options plus the change in the CEO‟s common stockholdings for a 1 percent change in thevalue of the firm‟s stock price. LCEOVOLSEN is the natural logarithm of the change in the dividend-adjusted
Black-Scholes value of the CEO‟s option portfolio for a 0.01 change in the annualized standard deviation of thefirm‟s stock returns. Industry fixed effect is defined by the Fama and French (1997) industry classifications.
Two-way clustered t-statistics are based on standard errors clustered by firm and year. ***, **, and * denotestatistical significance at the 1, 5, and 10 percent level.

44TABLE 6. The Relation between Implied Cost of Equity Capital and the Ratio of CEO Compensation Portfolio Sensitivities
Variable Name
Intercept

Predicted Sign?

CEOSENRATIO

-

BM

+

LTG

+

Disp

+

Size

-

Leverage

+

BMKT

+

BSMB

+

BHML

+

RAVE
0.0976(16.85)***0.0086(4.10)***
0.0098(9.45)***
0.0240(1.60)*
0.0206(2.20)**-0.0033(-5.35)***0.0241(5.86)***
0.0062(3.66)***
0.0009(0.88)
0.0025(2.66)***

REAST
0.1338(18.52)***0.0135(3.95)***
0.0092(4.31)***
0.0012(0.88)
0.0579(2.21)**-0.0079(-6.52)***0.0401(6.04)***
0.0174(5.85)***
0.0046(2.74)***
0.0007(0.41)

RGM
0.0963(13.28)***0.0079(2.55)**
0.0077(7.70)***
0.0418(1.80)*
0.0053(1.53)-0.0013(-2.01)**0.0107(2.99)***
0.0011(0.70)
0.0002(0.24)
0.0015(2.29)

RCT
0.1066(16.81)***0.0101(3.39)***
0.0073(6.19)***
0.0015(1.39)
0.0054(1.64)*-0.0033(-4.51)***0.0192(3.78)***
0.0052(2.99)***
0.0004(0.35)
0.0016(1.82)*

RGLS
0.0977(24.48)***0.0055(3.26)***
0.0121(8.99)***
0.0002(0.63)
0.0151(2.83)***-0.0020(-3.51)***0.0230(4.84)***
0.0054(3.81)***
0.0018(2.23)**
0.0034(2.91)***

Year Fixed Effect
Yes
Yes
Yes
Yes
Yes
Industry Fixed Effect
Yes
Yes
Yes
Yes
Yes
Adj. R2
0.33
0.32
0.20
0.18
0.37
N
11,041
11,041
11,041
11,041
11,041This table presents results from regression models of implied cost of equity capital to a set of control variables and the ratio of the sensitivity of CEO option portfolio to stockvolatility over the sensitivity of CEO option and stock portfolio to stock price (CEOSENRATIO). The average implied cost of equity capital (RAVE ) is the equally-weighted
average of the four implied cost of equity measures: REAST from Easton (2002), RGM from Gode and Mohanram (2003), RCT from Claus and Thomas (2001), and RGLS from
Gebhardt et al. (2001). BM is the ratio of the book value over the market value of equity; LTG is the analyst long-term growth in earnings forecast from I/B/E/S; Disp is theforecast dispersion defined as the coefficient of variation of I/B/E/S earnings forecasts; Size is the natural logarithm of the market value of equity (in millions); Leverage isthe ratio of long-term debt over total assets; BMKT, BSMB, and BHML are factor loadings from the Fama and French (1996) three-factor model on risk factors. Industry fixed
effect is defined by the Fama and French (1997) industry classifications. Two-way clustered t-statistics are based on standard errors clustered by firm and year. ***, **, and *denote statistical significance at the 1, 5, and 10 percent level.

45

TABLE 7. The Relation between the Average Implied Cost of Equity Capital (RAVE) and Alternative Measures of Compensation Portfolio Sensitivities to Stock
Price and Stock Return Volatility
Variable Name
Intercept

Predicted Sign?

LMGMPRICESEN-

LMGMVOLSEN+MGMSENRATIO+LCEOPRICESEN_STOCK-LCEOPRICESEN_OPTION-LCEOVOLSEN+LCEOPRICESEN_EXOPTION-LCEOVOLSEN_EXOPTION+LCEOPRICESEN_NONEXOPTION-LCEOVOLSEN_NONEXOPTION+

Model 10.1162(17.81)***-0.0047(-3.73)***0.0028(3.70)***

Model 2
0.09871(17.78)***Model 30.1043(16.93)***Model 40.1041(18.59)***Model 50.1017(19.45)***Model 60.1037(19.96)***-0.0007(-1.77)*-0.0048(-3.67)***0.0041(3.45)***-0.0007(-1.74)*-0.0010(-2.29)**-0.0008(-2.19)**-0.0057(-3.52)***0.0052(3.98)***-0.0025(-3.19)***0.0017(2.81)***-0.0036(-3.29)***0.0040(3.34)***

0.0162(3.82)***-0.0032(-3.21)***0.0019(2.93)***

Control Variables Included
Yes
Yes
Yes
Yes
Yes
Yes
Year Fixed Effect
Yes
Yes
Yes
Yes
Yes
Yes
Industry Fixed Effect
Yes
Yes
Yes
Yes
Yes
Yes
Adj. R2
0.35
0.34
0.34
0.34
0.34
0.36
N
11,041
11,041
11,041
11,041
11,041
11,041This table presents results from regression models of implied cost of equity capital to a set of control variables and alternative measures of compensation portfolio to stock
price and stock return volatility. The average implied cost of equity capital (RAVE) is the equally-weighted average of the four implied cost of equity measures: REAST from
Easton (2002), RGM from Gode and Mohanram (2003), RCT from Claus and Thomas (2001), and RGLS from Gebhardt et al. (2001). BM is the ratio of the book value over themarket value of equity; LTG is the analyst long-term growth in earnings forecast from I/B/E/S; Disp is the forecast dispersion defined as the coefficient of variation of I/B/E/S
earnings forecasts; Size is the natural logarithm of the market value of equity (in millions); Leverage is the ratio of long-term debt over total assets; BMKT, BSMB, and BHML arefactor loadings from the Fama and French (1996) three-factor model on risk factors. LMGMPRICESEN is the natural logarithm of the change in the dividend-adjusted BlackScholes value of the top five managers‟ stock options plus the change in their common stockholdings for a 1 percent change in the value of the firm‟s stock price.

46

LMGMVOLSEN is the natural logarithm of the change in the dividend-adjusted Black-Scholes value of the top five managers‟ option portfolio for a 0.01 change in theannualized standard deviation of the firm‟s stock returns. MGMSENRATIO is the ratio of LMGMVOLSEN over LMGMPRICESEN. LNCEOPRICESEN_STOCK is the natural
logarithm of the change in the CEO‟s stock portfolio for a 1 percent change in the value of the firm‟s stock price. LNCEOPRICESEN_OPTION is the natural logarithm of thechange in the dividend-adjusted Black-Scholes value of the CEO‟s stock options for a 1 percent change in the value of the firm‟s stock price.
LNCEOPRICESEN_EXOPTION (LNCEOPRICESEN_NONEXOPTION) is the natural logarithm of the change in the dividend-adjusted Black-Scholes value of the CEO‟s
exercisable (non-exercisable) stock options for a 1 percent change in the value of the firm‟s stock price. LNCEOVOLSEN_EXOPTION (LNCEOVOLSEN_NONEXOPTION)
is the natural logarithm of the change in the dividend-adjusted Black-Scholes value of the CEO‟s exercisable (non-exercisable) stock options for a 0.01 change in theannualized standard deviation of the firm‟s stock returns. Industry fixed effect is defined by the Fama and French (1997) industry classifications. Two-way clustered tstatistics are based on standard errors clustered by firm and year. ***, **, and * denote statistical significance at the 1, 5, and 10 percent level.

47

Table 8. Robustness Tests of Endogeneity on the Relation between the Average Implied Cost of Equity
Capital (RAVE) and CEO Compensation Portfolio Sensitivities to Stock Price and Stock Volatility
Variable Name

Predicted Sign

Intercept?

LCEOPRICESEN-LCEOVOLSEN+LCEOPRICESEN t-1-

LCEOVOLSEN t-1+

Pr(LCEOPRICESEN)-

Pr(LCEOVOLSEN)+

RAVE t-1+

Model 1
Regression with
LaggedRAVE
0.0579(6.34)***-0.0025(-5.23)***0.0018(3.89)***

Model 2
Regression with
LaggedSensitivities
0.1086(11.25)***Model 3Two-stage Least
Squares (2 SLS)
Regression
0.1082(14.31)***-0.0020(-3.42)***0.0018(2.78)***-0.0024(-3.92)***0.0020(2.61)***

0.4466(5.29)***
Control Variables Included
Yes
Yes
Yes
Year Fixed Effect
Yes
Yes
Yes
Industry Fixed Effect
Yes
Yes
Yes
Adj. R2
0.51
0.34
0.34
N
9,293
9,293
8,471
This table presents results from various robustness tests of endogeneity on the relation between CEO
compensation portfolio sensitivities and the average implied cost of equity capital. The average implied cost ofequity capital (RAVE) is the equally-weighted average of the four implied cost of equity measures: REAST from
Easton (2002), RGM from Gode and Mohanram (2003), RCT from Claus and Thomas (2001), and RGLS from
Gebhardt et al. (2001). LCEOPRICESEN is the natural logarithm of the change in the dividend-adjusted BlackScholes value of the CEO‟s stock options plus the change in the CEO‟s common stockholdings for a 1 percent
change in the value of the firm‟s stock price. LCEOVOLSEN is the natural logarithm of the change in thedividend-adjusted Black-Scholes value of the CEO‟s option portfolio for a 0.01 change in the annualized
standard deviation of the firm‟s stock returns. Pr(LCEOPRICESEN) and Pr(LCEOVOLSEN) are the predictedvalues of CEO compensation portfolio sensitivities from the first-stage regression. Industry fixed effect isdefined by the Fama and French (1997) industry classifications. Two-way clustered t-statistics are based onstandard errors clustered by firm and year. ***, **, and * denote statistical significance at the 1, 5, and 10
percent level.

48

Table 9. SEO Underpricing and CEO Compensation Portfolio Sensitivities to Stock Price and Stock
Return Volatility
Variable Name
Intercept

Predicted
Sign?

Model 1Model 2

0.0537(6.12)***-0.0058(-3.17)***0.0013(0.91)

0.0655(4.18)***-0.0079(-3.97)***0.0011(0.90)

Model 3Model 40.02080.0266(5.35)***(3.56)***
LCEOPRICESEN-0.0037-0.0051(-3.12)***(-3.63)***LCEOVOLSEN+
0.00110.0010(0.87)(0.71)
Size-0.0009-0.0010(-0.67)(-1.11)#N_Analyst-0.0038-0.0042(-3.23)***(-3.37)***
Idio_Vol+
0.34710.4423(4.25)***(3.47)***
Relative_Offer_Size+
0.0321
0.0429(2.77)***(2.66)***
CAR_Positive?
0.00910.0086(1.55)(1.12)
CAR_Negative+
0.02470.0288(1.88)*(2.01)**
Tick[0,0.25]
0.00050.0006+(0.45)(0.23)
Price-0.0054-0.0067(-3.11)***(-3.44)***
NYSE-0.0001-0.0001(-0.17)(-0.16)
Year Fixed Effect
No
Yes
No
Yes
Industry Fixed Effect
No
Yes
No
Yes
Adj. R2
0.02
0.16
0.12
0.19
N
1,112
1,112
1,112
1,112
This table presents results from regression models of SEO underpricing on a set of control variables and CEO
compensation portfolio sensitivities to stock price and stock return volatility. SEO underpricing is the returnfrom the closing price on the day immediately before the offer date to the offer price. LCEOPRICESEN is thenatural logarithm of the change in the dividend-adjusted Black-Scholes value of the CEO‟s stock options plus
the change in the CEO‟s common stockholdings for a 1 percent change in the value of the firm‟s stock price.
LCEOVOLSEN is the natural logarithm of the change in the dividend-adjusted Black-Scholes value of theCEO‟s option portfolio for a 0.01 change in the annualized standard deviation of the firm‟s stock returns. Firm
size (Size) is the natural log of the market value of equity at the end of the year before the SEOs; number ofanalysts (#N_Analyst) is the number of analysts covering the firms in the year before the SEO; idiosyncratic
volatility (Idio_Vol) is the natural log of the standard deviation of the residuals from the regression of monthly
returns on Fama and French (1996) risk factors in the five years before the SEOs; relative offer size
(Relative_Offer_Size) is the offer size relative to outstanding shares; positive pre-offer abnormal return(CAR_Positive) is the cumulative abnormal return in the 10 days leading to the offer date if this is a positive
value; negative pre-offer abnormal return (CAR_Negative) is the cumulative abnormal return in the 10 days
leading to the offer date if this is a negative value; Tick[0,0.25] is the rounding of the offer price to a $0.25
increment; stock price (Price) is the stock price 10 days prior to the offer date, and NYSE is a dummy variable
for NYSE stocks. Industry fixed effect is defined by the Fama and French (1997) industry classifications. Twoway clustered t-statistics are based on standard errors clustered by firm and year. ***, **, and * denotestatistical significance at the 1, 5, and 10 percent level.

49