Audit committee equity incentives and stock price crash risk

Abstract

This paper theoretically and empirically investigates whether and how audit committee (AC) equity incentives affect future stock price crash risk. Consistent with our model prediction that equity incentives for ACs contribute to reducing the skewness of return distributions, we document evidence of a negative relationship between AC equity incentives and expected crash risk for a merged sample of 6550 US-listed firms over the 2001–2018 period, even after controlling for a wide range of other firm characteristics, using alternative variable specifications, and addressing potential endogeneity concerns. On average, a one-standard-deviation increase in AC equity incentives is associated with a reduction of 14.09–15.46% in stock price crash risk. Further analysis shows that AC equity incentives affect crash risk through financial reporting quality, the negative relationship between AC equity incentives and future stock price crash risk is more pronounced for firms with weaker external governance and for firms with more financial expertise in the AC, and this negative relationship is mainly driven by option-based equity incentives. Taken together, these findings are consistent with the view that equity-based compensation is critical for inducing greater monitoring efforts from AC members and mitigating managerial incentives to withhold bad news.

Appendices

Appendix 1: Variable definitions

This table provides the names and definitions of all variables used in the empirical analysis.

Variable	Definition
Dependent variables
NCSKEW	Negative skewness of firm-specific weekly returns, as defined in Eq. (3)
DUVOL	Natural logarithm of the ratio of the standard deviation in down weeks to the standard deviation in up weeks, as defined in Eq. (4)
CRASH	A dummy variable, equal to 1 if a firm-year observation experiences one or more firm-specific crash weeks over a year and 0 otherwise. Following Hutton et al. (2009), we define crash weeks as those with firm-specific weekly returns below the mean by over 3.09 standard deviations
CRASH2	A dummy variable, equal to 1 if a firm-year observation experiences one or more firm-specific crash weeks over a year and 0 otherwise. Following Kim et al. (2011), we define crash weeks as those with firm-specific weekly returns below the mean by over 3.20 standard deviations
COUNT	Number of firm-specific weekly returns below the mean by more than 3.09 standard deviations threshold in a given year
COUNT2	Number of firm-specific weekly returns below the mean by more than 3.20 standard deviations threshold in a given year
FREQUENCY	Percentage of crash weeks among all trading weeks in a given year, where crash weeks are defined as those with firm-specific weekly returns below the mean by over 3.09 standard deviations, following Hutton et al. (2009)
FREQUENCY2	Percentage of crash weeks among all trading weeks in a given year, where crash weeks are defined as those with firm-specific weekly returns below the mean by over 3.20 standard deviations, following Kim et al. (2011)
Independent variables
AC1	Ratio of AC’s equity-based compensation to AC’s total compensation
AC2	Average ratio of equity compensation to total compensation across all AC members of a firm
Control Variables
RET	Mean of firm-specific weekly returns over the fiscal year period times 100
SIZE	Natural logarithm of the market value of equity
MB	Market value of equity divided by the book value of equity
SIGMA	Standard deviation of idiosyncratic return for wi,t, as defined in Eq. (2)
DTURN	Difference between the average monthly turnover in year t and year t − 1
LEV	Ratio of total long-term debts to total assets
ROA	Incomes before extraordinary items divided by lagged total assets
ACCM	The prior three years’ moving sum of the value of discretionary accruals, where discretionary accruals are estimated based on Kothari’s performance-adjusted discretionary accruals
BDSIZE	Natural logarithm of the number of directors on the board
BDIND	Percentage of independent directors on the board
CEODELTA	Dollar change in the CEO’s equity holdings for a 1 percent change in stock price
CEOVEGA	Dollar change in the CEO’s equity holdings for a 1 percent change in stock return volatility
CFODELTA	Dollar change in the CFO’s equity holdings for a 1 percent change in stock price
CFOVEGA	Dollar change in the CFO’s equity holdings for a 1 percent change in stock return volatility
CEOTENURE	Natural logarithm of the number of years as CEO of the firm
CEOCHAIRMAN	A dummy which takes the value of 1 if AC chairman is also the company’s CEO, and 0 otherwise
Variables used in further analysis
ANADISP	Log of the standard deviation of analyst’s forecasts based on the last forecast issued by analysts over the 90-day period ending on the fiscal year-end date, divided by the stock price at the beginning of the fiscal year
INTERCONTR	A dummy variable which takes the value of 1 if a company’s internal control is effective and 0 otherwise
AC_EXPERTISE	Ratio of the number of AC members with financial expertise to the total number of AC members. Following Dhaliwal et al. (2010), the scope of financial expertise includes accounting experts with work experience as a CPA, CFO, vice president of finance, financial controller, or any other major accounting position
AC_CHAIR	An indicator that equals 1 if the AC chair has working experience as a CPA, CFO, vice president of finance, financial controller, or any other major accounting position and 0 otherwise
INSTITUTIONAL_OWN	Sum of all ownership positions greater than 5% held by institutional investors
OPTIONAWD	Natural logarithm of the value of annual option awards provided to the audit committee
STOCKAWD	Natural logarithm of the value of annual stock awards provided to the audit committee

Appendix 2: Derivations

Equation (1) The first-order condition for the program $\underset{\alpha }{{\text{max}}}\alpha x-{\text{ln}}{(1-\alpha )}^{-k\gamma \theta }$ is $x=\frac{\overline{T} }{1-\alpha }$, which implies $\alpha =0$ for $x<\overline{T }$ and $\alpha =1-\frac{\overline{T}}{x }$ for $x\ge \overline{T }$. Thus, the nondiverted earnings flow to the shareholders is $x$ below the threshold value $\overline{T }$ and $\overline{T }$ above, which equals ${\text{min}}(x,\overline{T })$.

Equation (2) The remuneration to the AC is $w+\beta \left(1-\alpha \right)x-\frac{1}{2\gamma }{\theta }^{2}$, and the AC seeks to choose an effort to maximize the remuneration flow. First, consider that $x<\overline{T }$ so that the remuneration flow is $x+\beta x-\frac{1}{2\gamma }{\theta }^{2}$, which is maximized by minimizing effort. Second, consider that $x\ge \overline{T }$ so that the remuneration flow is $w+\beta \overline{T }-\frac{1}{2\gamma }{\theta }^{2}$, with first-order condition $\beta k\gamma =\frac{1}{\gamma }\theta$. Therefore, the optimal effort is to set $\theta$ so that it is the minimum of $\frac{x}{k\gamma }$ and $\beta k{\gamma }^{2}$.

Equation (5) The cash flow $\left(1-\alpha \right)x$ is equal to ${\text{min}}(\overline{T },x)$, which has a discounted value of $\frac{\overline{T}}{r }$ for the cash flow $\overline{T }$ and $\frac{x}{r-\mu }$ for the cash flow $x$. The value of this cash flow also contains optional elements that do not generate a cash flow but are associated with the transition of the cash flow through the barrier point $\overline{T }$. Denote the value of the optional cash flows by $v$, and it must be the case that $\frac{{\sigma }^{2}}{2}{x}^{2}{v}^{{\prime}{\prime}}+\mu x{v}{\prime}-rv=0$ to satisfy arbitrage-free pricing. The ODE has general solutions $v=A{x}^{{\lambda }_{1}}+B{x}^{{\lambda }_{2}}$, where the constants $A$ and $B$ are fitted to the boundary conditions for $v$. The boundary conditions are $\underset{x\to 0}{{\text{lim}}}v=0$, $\underset{x\to \infty }{{\text{lim}}}v=0$, $\underset{x\uparrow \overline{T}}{{\text{lim}} }v+\frac{x}{r-\mu }=\underset{x\downarrow \overline{T}}{{\text{lim}} }v+\frac{\overline{T}}{r }$, and $\underset{x\uparrow \overline{T}}{{\text{lim}}}{v }{\prime}+\frac{1}{r-\mu }=\underset{x\downarrow \overline{T}}{{\text{lim}} }v{\prime}$. The first boundary condition implies that $B=0$ for the region below the threshold value, and the second boundary condition implies that $A=0$ in the region above the threshold value. The third and fourth imply the following system:

$$A\overline{T}^{{\lambda_{1} }} + \frac{{\overline{T}}}{r - \mu } = B\overline{T}^{{\lambda_{2} }} + \frac{{\overline{T}}}{r},\quad A\lambda_{1} \overline{T}^{{\lambda_{1} - 1}} + \frac{1}{r - \mu } = B\lambda_{2} \overline{T}^{{\lambda_{2} - 1}} .$$

The system can be solved with respect to $A$ and $B$, and plugging these back into the value functions yields Eq. (5).

Equation (6) If $x$ follows a geometric Brownian motion with drift $\mu$ and volatility $\sigma$, then ${x}^{2}$ is another geometric Brownian motion with drift $2\mu +{\sigma }^{2}$ and volatility $2\sigma$. Therefore, the discounted value of ${x}^{2}$ is $\frac{{x}^{2}}{r-2\mu -{\sigma }^{2}}$, which requires that the denominator is positive to ensure convergence. The AC’s effort cost is $\frac{1}{2\gamma }{\theta }^{2}$, which has a value $\frac{\beta }{\overline{T}}\frac{{x }^{2}}{2(r-2\mu -{\sigma }^{2})}$ in the region below the threshold and $\frac{\beta \overline{T}}{2r }$ in the region above. As for the derivation of Eq. (5) above, there are optional elements associated with the transition through the threshold barrier, which take the value of $w=C{x}^{{\lambda }_{1}}+D{x}^{{\lambda }_{2}}$ for constants fitted to a similar set of boundary conditions as above. The constant $D=0$ for the region below the threshold value, and the constant $C=0$ for the region above. The smooth transition through the barrier implies the following system:

$$C\overline{T}^{{\lambda_{1} }} + \frac{{\beta \overline{T}}}{{2\left( {r - 2\mu - \sigma^{2} } \right)}} = D\overline{T}^{{\lambda_{2} }} + \frac{{\beta \overline{T}}}{2r},\quad C\lambda_{1} \overline{T}^{{\lambda_{1} - 1}} + \frac{\beta }{{r - 2\mu - \sigma^{2} }} = D\lambda_{2} \overline{T}^{{\lambda_{2} - 1}} .$$

The system can be solved with respect to $C$ and $D$, and plugging these back into the value functions yields Eq. (6).

Equation (9) We need to calculate the optimal shareholding at the contracting point, which involves maximizing the shareholders’ value (the net of the AC’s holding). The shareholders’ value at this point is given as the discounted value of all future nondiverted earnings minus the cost of effort for the AC. Therefore, for a given point below the threshold value for diversions, the program can be stated as follows:

$$\mathop {\max }\limits_{\beta } Ax^{{\lambda_{1} }} + \frac{x}{r - \mu } - Cx^{{\lambda_{1} }} - \frac{\beta }{{\overline{T}}}\frac{{x^{2} }}{{2\left( {r - 2\mu - \sigma^{2} } \right)}},$$

where we use the constants $A$ and $B$ from the previous derivations. This program can be written as $\underset{\beta }{{\text{max}}}A+B$, as the term ${x}^{{\lambda }_{1}}$ is just a positive constant and because in the term $\frac{\beta }{\overline{T} }$, the $\beta$ cancels out in the numerator and the denominator. Therefore, optimal shareholding does not depend on the contracting point if the program is carried out below the threshold value for benefit diversions. A straightforward derivation yields the results.