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.
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Acknowledgements
Xinming Liu greatly appreciates the financial support from the National Natural Science Foundation of China (NSFC-72002183). Zhe Shen greatly appreciates the financial support from the National Natural Science Foundation of China (NSFC-71572159).
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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:
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:
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:
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.
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Shen, Z., Li, H., Instefjord, N. et al. Audit committee equity incentives and stock price crash risk. Rev Quant Finan Acc 62, 1145–1190 (2024). https://doi.org/10.1007/s11156-023-01233-5
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DOI: https://doi.org/10.1007/s11156-023-01233-5