Accruals and price crashes

Abstract

I investigate the relation between accruals and firm-level price crashes, representing extreme price decreases in weekly returns. I find that high accruals predict a higher price crash probability than low accruals. This finding can be explained by managers’ use of income-increasing accrual estimates to hoard bad news. Once accumulated bad news crosses a tipping point, it is released all at once and results in a price crash. Consistent with this explanation, I find the observed relation to be the strongest for operating assets (the least reliable accrual components). Cross-sectional analyses further support the bad news hoarding explanation.

1 Introduction

The recent financial crisis has renewed interest in understanding tail risk. In particular, a growing stream of finance and accounting literature attempts to link firm characteristics to the probability of price crashes, representing extreme negative observations in the distribution of firm-level weekly returns (e.g., Hutton et al. 2009).¹ Motivation for examining price crashes includes equity valuation (Conrad et al. 2013) and option pricing (Cox and Ross 1976; Merton 1976). Firm characteristics indicative of future price crashes include proxies for (a) risk of operations (Chen et al. 2001), (b) properties of investor beliefs (Cao et al. 2002; Hong and Stein 2003), and (c) attributes of financial reporting (e.g., Hutton et al. 2009; Kim et al. 2011b).

Hutton et al. (2009) provide the first piece of evidence that establishes an association between the opacity of financial reporting and crash risk. Using earnings management as the proxy for reporting opacity, they show that the sum of absolute discretionary operating accruals over the past 3 years is positively associated with subsequent price crashes. They interpret this finding as suggesting that both positive and negative discretionary operating accruals are associated with hidden bad news. This interpretation, however, contradicts the conventional wisdom in the accruals literature that firms with negative discretionary accruals are associated with less hidden bad news than those with positive discretionary accruals (Dechow et al. 1995; Xie 2001).² To reconcile these two seemingly conflicting points of view, I conduct a comprehensive investigation of the relationship between accruals and future price crashes.

To reconcile the above contrasting predictions for the relation between negative accruals and hidden bad news, I consider two opposing mechanisms, suggested in the literature, that relate accruals to future price crashes. Under the first mechanism, managers seeking to suppress or hoard bad news tend to make aggressive income-increasing accrual estimates (Dechow et al. 1995, 2011; Richardson et al. 2006), which in turn leads to more hidden bad news among high accruals firms in comparison to low accruals firms.³ Therefore, when accumulated bad news crosses a tipping point, it is released all at once and results in a price crash (Jin and Myers 2006; Benmelech et al. 2010). Under the second mechanism, extreme negative accruals reflect severe performance deterioration due to financial distress and consequently high default risk (Ng 2005; Khan 2008). Firms with higher default risk are more likely to fail, leading to more price crashes for low accruals firms relative to high accruals firms.

Following prior literature, I measure the probability of price crashes in two ways. The first measure is a continuous variable that equals the number of standard deviations by which the most extreme negative weekly return over the year falls below its mean (Bradshaw et al. 2010). The mean and standard deviation are based on firm-specific weekly return distributions for that year. The second measure is an indicator variable that equals one if the firm experiences one or more extreme negative weekly returns that are more than 3.09 standard deviations below the mean over the year and zero otherwise (Hutton et al. 2009). As the results for these two measures are similar, I refer to them collectively as price crashes for brevity. Following Richardson et al. (2006) and Dechow et al. (2008), I define accruals as growth in net operating assets, deflated by average total assets. This comprehensive measure reflects the notion that all operating assets and liabilities accounts are products of the accrual accounting system.

I find a strong positive association between total accruals and future price crashes. For example, the probability of observing price crashes (defined as weekly returns that are more than 3.09 standard deviations below the mean) over the next year increases from 12.88 % for the lowest decile of the current year’s accruals to 17.27 % for the highest decile. The monotonic increase of crash risk across the increasing accruals portfolios is the highest for the current year’s accruals but also holds for accruals of the past 2 years. This remains true after I control for variables considered in prior research to predict price crashes. In multivariate regression models forecasting price crashes, accruals in the most recent year are among the strongest predictors in both economic and statistical significance. These findings are consistent with the hidden bad news explanation.⁴

I continue to examine variation in the association between accruals and price crashes across components of accruals. Following Richardson et al. (2005), I decompose accruals into four components according to their relative reliability in accrual estimation, with current and non-current operating asset accruals being the least reliable, non-current operating liability accruals being more reliable, and current operating liability accruals being the most reliable.⁵ Less reliable components of accruals provide managers with greater discretion when attempting to hoard bad news and therefore are expected to have a stronger positive association with future price crashes. Consistent with this prediction, I find that current operating asset accruals and non-current operating asset accruals are significantly positively associated with price crashes, while non-current operating liability accruals are not significantly related to crashes over the next year. Surprisingly, current operating liability accruals turn out to be negatively associated with price crashes. Finding that firms with increased current operating liabilities are more likely to experience future price crashes is consistent with the default risk explanation but inconsistent with the bad news hoarding explanation. The collective evidence from accrual decomposition suggests that the relation between different accrual components and subsequent price crashes depends on the relative reliability of that component.

To further validate the bad news hoarding explanation for the positive association between operating asset accruals and price crashes and the default risk explanation for the negative association between current operating liability accruals and price crashes, I examine the implications of bad news hoarding (default risk) for cross-sectional variation in the positive (negative) association.⁶ Consistent with the predictions of the bad news hoarding mechanism, the positive association between operating asset accruals and future price crashes is stronger in three instances: (1) when CFOs have a stronger incentive to hide bad news, as captured by a higher option incentive ratio (Core and Guay 2002; Coles et al. 2006); (2) when it is more difficult for investors to unravel hidden bad news, as captured by a high-tech firm or a higher sales growth rate; and (3) when external monitoring is weaker, as captured by a higher level of transient institutional holding or a shorter auditor tenure. In contrast, and inconsistent with the prediction of the default risk mechanism, I do not find the negative association between current operating liability accruals and future price crashes to be stronger among firms with higher default risk, as captured by a lower Altman (1968) Z score, a higher Shumway (2001) bankruptcy score, or a higher Vassalou and Xing (2004) default probability. This finding suggests that neither bad news hoarding nor default risk explains the negative association between current operating liability accruals and future price crashes.

Despite its puzzling nature, the negative relation between current operating liability accruals and price crashes helps to explain the U-shaped relation between discretionary operating accruals and price crashes documented by Hutton et al. (2009). This U-shaped relation results from nonlinearities in the relations between future price crashes and accruals derived from current operating assets and current operating liabilities. The likelihood of a price crash declines as current operating asset accruals decrease from high to medium levels but remains constant between medium and low levels. In contrast, the likelihood of a price crash declines as current operating liability accruals increase from low to medium levels but remains constant between medium and high levels.⁷ As working capital accruals are simply current operating asset accruals plus current operating liability accruals, the above nonlinearities result in a U-shaped relation between the level of working capital accruals and future price crashes, which in turn leads to the U-shaped relation between discretionary operating accruals and price crashes.⁸ My evidence suggests that, while the positive association observed when discretionary operating accruals are positive is consistent with the bad news hoarding explanation, the negative association when discretionary operating accruals are negative is inconsistent with both the bad news hoarding explanation and the default risk explanation.

My study contributes mainly to two literatures. It adds to the growing body of work on price crashes by comprehensively examining the link between accruals and price crashes. I find that high total accruals in the most recent year best predict future price crashes. The focus in Hutton et al. (2009) on reporting opacity, measured as the absolute value of discretionary operating accruals summed over the past 3 years, masks this dominant relation. I also show that the exact pattern of the association between accruals and future price crashes hinges critically on the definition of accruals. This is because different accrual components have different degrees of reliability in accrual estimation and consequently are associated with different levels of hidden bad news.

My study also contributes to the literature on the accruals anomaly by helping to differentiate two competing explanations for the lower mean returns observed for high accruals firms (Sloan 1996). One explanation argues that investors fail to recognize the lower persistence of accruals caused by hidden bad news (Xie 2001; Richardson et al. 2006) and consequently overprice firms with high accruals.⁹ The other explanation maintains that high accruals firms have lower default risk and therefore are compensated with lower returns (Ng 2005; Khan 2008). While both explanations make the same prediction on the relation between accruals and the mean of returns distribution, they make opposing predictions on the association between accruals and the left tail of returns distribution. The fact that total accruals and all major accrual components, except for current operating liability accruals, are positively associated with price crashes implies that the accruals anomaly is mainly driven by investors’ accrual mispricing due to a failure to recognize the hidden bad news reflected in the accruals.

2 Literature review on firm-level price crashes

2.1 Crash risk and asset pricing

There is growing interest in understanding the role of crash risk (i.e., the likelihood of sudden but infrequent large price decreases) in asset pricing. At the market level, crash risk explains a significant fraction of the equity premium (Barro 2006; Gabaix 2012). At the firm level, crash risk is an important determinant of expected returns in the cross-section (Yan 2011; Conrad et al. 2013). Crash risk also determines option prices, incrementally to stock return volatility (Cox and Ross 1976; Merton 1976; Pan 2002). These important economic consequences call for a deeper understanding of the causes of price crashes.

2.2 Explanations of price crashes

2.2.1 Bad news hoarding

Prior literature has proposed a number of explanations for the origin of firm-level price crashes. The two explanations most relevant to my study are bad news hoarding and default risk. The bad news hoarding explanation comes from theories of managers hoarding bad news (Jin and Myers 2006; Bleck and Liu 2007; Benmelech et al. 2010). In these models, managers attempt to hide bad news because they have a higher discount rate than shareholders and their personal wealth is tied to stock and accounting performance.¹⁰ When accumulated bad news crosses a tipping point in the future, it will be released all at once and result in a price crash.

There is ample evidence consistent with bad news hoarding. Using earnings management as the proxy for financial reporting opacity, Hutton et al. (2009) show that more opaque firms experience more price crashes over the next year. To measure earnings management, they sum the absolute value of discretionary operating accruals from the modified Jones model (Dechow et al. 1995) over the past 3 years. They interpret this finding as suggesting that firms with consistently large values of discretionary accruals, both positive and negative, are more likely to be managing reported earnings to conceal bad news.

Hutton et al. (2009) inspires a handful of other proxies for bad news hoarding as price crash predictors. Kim et al. (2011a) show that the CFO’s option incentive ratio is positively associated with future price crashes. This finding suggests that a higher sensitivity of the value of the options portfolio to stock price increase creates a stronger incentive for CFOs to hide bad news, consistent with the prediction by Benmelech et al. (2010). Other predictors of price crashes include tax avoidance (Kim et al. 2011b), internal control weakness (Kim et al. 2013a, b), accounting conservatism (Kim and Zhang 2013), management forecast frequency (Hamm et al. 2012), and CEO overconfidence (Kim et al. 2013a, b).

2.2.2 Default risk

Price crashes also could result from corporate failure (i.e., the failure to meet financial obligations). Firms with higher default risk are more likely to suddenly release extremely bad news (resulting in a price crash) or extremely good news (resulting in a price jump), because they have a more extreme bimodal outcome: failure or continuance as a going concern.

So far, prior literature has failed to provide evidence consistent with the above prediction using proxies like firm size and leverage. Hutton et al. (2009) and Kim et al. (2011a, b) find a positive relationship between firm size and future price crashes, which contradicts the observation that larger firms have a lower bankruptcy probability than smaller firms (Campbell et al. 2008).¹¹ As explained by Hutton et al. (2009), this surprising result could stem from the definition of a price crash: a tail event of sufficient magnitude to fall in the lower 0.1 % of normal distribution. As larger firms have lower standard deviations of returns than smaller firms, the absolute magnitude of a return needed to qualify as a crash is thus lower for larger firms. This mechanical positive association between firm size and price crashes overwhelms the negative relation predicted by the default risk explanation.

The above studies also document a negative association between leverage and future price crashes, which is inconsistent with the observation that high leverage firms have a higher probability of failures than low leverage firms (Campbell et al. 2008). One potential explanation for this surprising result is that investors underprice high leverage firms, making it less likely to observe price crashes for these firms ex post. Consistent with this explanation, Campbell et al. (2008) show that high leverage firms generate higher future mean returns than low leverage firms.

2.2.3 Other explanations

Other price crash explanations in the literature include differences of opinion (Hong and Stein 2003) and information blockage (Cao et al. 2002).¹² Consistent with these explanations, Chen et al. (2001) document that share turnover (the proxy for differences of opinion) and past stock returns (the proxy for information blockage) positively predict the likelihood of future price crashes, measured as the negative returns skewness.

2.3 Predictability of price crashes and market inefficiency

It is worth noting that the predictability of price crashes does not require market inefficiency of price crash predictors. Consider the following example, where X is a noisy signal of hidden bad news. For simplicity, I assume that the amount of hidden bad news equals 20 % of market value, and 15 % (0 %) of firms with a high (low) value of X are hiding bad news.¹³ Holding everything else constant, rational investors would value firms with a high X 3 % less than those with a low X. When future news arrives, half of the high X firms will be hit with another piece of bad news, and a sudden price drop of at least 17 % (20–3 %) will occur when the hidden bad news is released all at once. This example illustrates the existence of price crash predictability, even if the market correctly prices the noisy signal X of bad news hoarding. In fact, all theoretical models of price crashes reviewed above assume market efficiency.

On the other hand, market inefficiency could reinforce the likelihood and magnitude of price crashes. Ak et al. (2015) show that mean stock returns over the next 6 months are significantly lower for high crash risk portfolio than low crash risk portfolio, which suggests market inefficiency of price crash predictors. Continuing the above example, I assume instead that investors fail to understand the signal X. Under this assumption, irrational investors value high X and low X firms at the same price. When future news arrives, half of the high X firms will be hit with another piece of bad news, and a sudden price drop of at least 20 % will occur when the hidden bad news is released all at once. This example suggests that we could find stronger evidence of price crash predictability when the market fails to adjust for bad news hoarding.

3 Hypothesis development

In my study, I conduct a comprehensive investigation of the link between accruals and price crashes. I first examine the association between total accruals and price crashes, and then explore the variation in this association across accrual components and across firms.

3.1 Accruals and price crashes

The price crash theories discussed earlier suggest two opposing mechanisms that relate accruals to future price crashes. Under the first, accruals predict price crashes because of the hidden bad news reflected in the accruals. The accruals literature has provided robust evidence that accruals are less reliable than the cash component of earnings because of the greater subjectivity involved in the identification and measurement of non-cash assets and liabilities (Dechow and Dichev 2002; Richardson et al. 2005). The subjectivity in accrual estimation provides managers with room to hide bad news by over-estimating accruals (Dechow et al. 1995; Richardson et al. 2006; Dechow et al. 2011). For example, managers could conceal negative product market shocks by delaying inventory write-offs. Firms also tend to over-invest when hiding bad news (Kedia and Philippon 2009; McNichols and Stubben 2008), which likewise results in a positive association between bad news hoarding and the level of accruals.¹⁴ When accumulated bad news crosses a tipping point, it will be released all at once and will result in more price crashes for high accruals firms compared to low accruals firms.

Under the second mechanism, accruals predict price crashes because of the default risk reflected in accruals. Ng (2005) and Khan (2008) analyze the characteristics of firms with different levels of accruals. They find that low accruals firms generate less income, lower sales growth, and lower Altman Z scores (Altman 1968) than do high accruals firms and that all three attributes are symptoms of higher default risk. As firms of higher default risk are more likely to fail, the default risk explanation predicts more price crashes for low accruals firms.

In light of the opposing predictions from the bad news hoarding and default risk explanations, my first research hypothesis is stated as follows:

(H1)

The level of accruals is positively (negatively) related to the probability of weekly price crashes over the next year under the bad news hoarding (default risk) mechanism.

Even though hidden bad news and default risk predict opposing signs of the association between accruals and the left-tail of firm-specific returns distribution, both have been used to explain the negative relation between accruals and the mean of firm-specific returns distribution first documented by Sloan (1996). Xie (2001) shows that the accruals anomaly is driven by the discretionary portion of accruals. He interprets this finding as suggesting that the lower returns associated with high accruals are due to the market’s failure to recognize hidden bad news reflected in accruals. In contrast, Ng (2005) and Khan (2008) show that hedge returns from buying low accruals firms and shorting high accruals firms significantly decrease after controlling for distress risk. They interpret this finding as suggesting that low accruals firms have higher default risk and therefore are compensated with higher expected returns. My examination of hypothesis H1 could help to differentiate between these competing explanations of the accruals anomaly.

3.2 Accrual components and price crashes

Richardson et al. (2005) provide a comprehensive accrual categorization and detailed analysis of the degrees of subjectivity involved in estimating different components. Components that involve a higher degree of discretion are expected to have more intentional and unintentional estimation errors and hence be less reliable. Less reliable accruals offer more freedom for opportunistic managers to overstate accrual estimates; therefore these accruals are expected to be more associated with hidden bad news. Assuming a constant level of default risk across accrual components, the above variation in reliability leads to my second research hypothesis:

(H2)

A less reliable accrual component is more positively associated with the probability of weekly price crashes over the next year under the bad news hoarding mechanism.

Empirical results consistent with hypothesis H2 corroborate the bad news hoarding explanation for the association between accruals and future price crashes.

3.3 Cross-sectional variation in the association between accruals and price crashes

Under the bad news hoarding explanation, accruals positively predict future price crashes due to the use of positive accruals to conceal bad news. Such aggressive use of accruals is expected to be elevated in instances when the incentive to hide bad news is stronger, the constraint on hiding bad news is weaker, and it is more difficult for investors to unravel hidden bad news. Under the default risk explanation, accruals negatively predict future price crashes because of higher default risk reflected in low accruals. As corporate failure is a low probability event, the noise in the proxies for default risk is expected to be larger when the level of default risk is sufficiently low. Consequently, the association between accruals and default risk is expected to be stronger when default risk is higher.¹⁵ This leads to a more negative, or less positive, association between accruals and future price crashes among firms with higher default risk. The above discussion leads to my third research hypothesis:

(H3a)

Under the bad news hoarding mechanism, the association between the level of accruals and the probability of weekly price crashes over the next year is more positive when the incentive to hide bad news is stronger, when the constraint on hiding bad news is weaker, and when it is more difficult for investors to unravel hidden bad news.

(H3b)

Under the default risk mechanism, the association between the level of accruals and the probability of weekly price crashes over the next year is more negative when the default risk is higher.

Cross-sectional variation consistent with hypothesis H3a (H3b) corroborates the bad news hoarding (default risk) explanation for the association between accruals and future price crashes.

4 Variable definition and research design

4.1 Variable definition

Following prior literature, I use one continuous variable VCRASH _t+1 (Bradshaw et al. 2010) and one indicator variable CRASH _t+1 (Hutton et al. 2009) to measure the probability of weekly price crashes over year t + 1, where year t + 1 is defined as the 12 months starting from the fifth month after the end of fiscal year t.¹⁶ (Please refer to the “Appendix” for variable definitions.) To calculate these measures, I first estimate firm-specific weekly returns for year t + 1. The firm-specific weekly return is defined as the log of one plus the residual ɛ _i,w from the following expanded market model regression¹⁷:

$$\begin{aligned} Ret_{i,w} &= \alpha_{i,0} + \beta_{i, - 1} *MRet_{w - 1} + \beta_{i,0} *MRet_{w} + \beta_{i,1} *MRet_{w + 1} \\ & + \gamma_{i, - 1} *IRet_{w - 1} + \gamma_{i,0} *IRet_{w} + \gamma_{i,1} *IRet_{w + 1} + \varepsilon_{i,w} , \\ \end{aligned}$$

(1)

where Ret _i,w represents the returns of firm i for week w of year t + 1, MRet _w represents the market returns for week w of year t + 1, and IRet _w represents the industry returns for week w of year t + 1.

I define VCRASH _t+1 as the absolute value of the difference between minimum firm-specific weekly return and its mean over year t + 1, divided by its standard deviation for year t + 1 (Bradshaw et al. 2010; Kim et al. 2013a, b). To define CRASH _t+1, I first define price crash weeks in year t + 1 for a given firm as those weeks during which firm-specific weekly return is at least 3.09 times the standard deviation below the mean, with 3.09 chosen to generate a frequency of 0.1 % in the normal distribution. Following Hutton et al. (2009), the indicator variable CRASH _t+1 equals one if the firm experiences one or more crash weeks over year t + 1 and zero otherwise. Compared with CRASH _t+1, VCRASH _t+1 captures both the frequency and the magnitude of extreme negative returns and does not depend on the choice of a distribution cut-off. Nevertheless, I report results for both measures.

Following Richardson et al. (2006) and Dechow et al. (2008), I define accruals (ΔNOA) as the growth in net operating assets deflated by average total assets. This definition of accruals is arguably the most comprehensive one because it includes changes in all operating assets and liabilities, all of which reflect the accounting accrual system’s estimate of firm value.

4.2 Research design

4.2.1 Test of hypothesis H1

To test hypothesis H1, I estimate the following regression model that links the probability of price crashes in year t + 1, VCRASH _t+1 and CRASH _t+1, to accruals of the most recent 3 years and a set of control variables:

$$VCRASH_{t + 1} \;{\text{or}} \;CRASH_{t + 1} = \alpha_{0} +\mathop \sum \limits_{k = 0}^{2} \beta_{k} *\varDelta NOA_{t - k} + \mathop \sum \limits_{l = 1}^{m} \theta_{l} *Control_{l,t} + \varepsilon_{t + 1} ,$$

(2)

I include accruals of the most recent 3 years (ΔNOA _t , ΔNOA _t−1 , and ΔNOA _t−2 ) in regression model (2) to be consistent with Hutton et al. (2009), who use absolute discretionary operating accruals of the most recent 3 years to predict price crashes over the next year. This design choice also accounts for the predictability of price crashes that goes beyond 1 year. I assume a linear relation between accruals and price crashes, given the linear relationship between accruals and future mean returns documented in accruals anomaly literature.

The control variables are obtained from prior studies on predicting price crashes (Chen et al. 2001; Hutton et al. 2009; Kim et al. 2011a, b). I include book-to-market ratio (BTM _t ) as a proxy for mispricing and past annual size-adjusted stock returns (SARET _t ) as a proxy for information blockage.¹⁸ In prior studies, BTM _t negatively predicts price crashes, while SARET _t positively predicts price crashes. Share turnover (TURN _t ) is included as a proxy for differences of opinion, which positively predicts price crashes in prior research. Controls for firm risk include firm size (SIZE _t ) and book leverage (LEV _t ). However, prior studies find SIZE _t to be positively correlated with price crashes and LEV _t to be negatively correlated with price crashes. I also include idiosyncratic volatility (IVOL _t ) to control for potential mechanical correlation between return volatility and price crashes. Finally, the lagged dependent variable, VCRASH _t or CRASH _t , and return skewness (SKEW _t ) are included to control for the persistence of the dependent variable.

In a few specifications of regression model (2), I also include variables that are important for documenting the incremental predictive power of accruals. I include free cash flows of the most recent 3 years (FCF _t , FCF _t−1 , and FCF _t−2 ) to rule out the possibility that the ability of accruals to predict price crashes is due to the strong correlation between accruals and cash flows. I include other proxies for bad news hoarding from prior literature to isolate the incremental hidden bad news reflected in accruals: the long-run effective tax rate LRETR _t (Kim et al. 2011b), CFO option incentive ratio INCENTIVE _t (Kim et al. 2011a), transient institutional ownership TRA _t (Callen and Fang 2013), short interest SIR _t (Callen and Fang 2014), and sales growth SALEGR _t (Bradshaw et al. 2010).¹⁹

4.2.2 Test of hypothesis H2

To test hypothesis H2, I decompose accruals into components with different levels of reliability and compare their associations with future price crashes. Richardson et al. (2005) provide a detailed categorization of accruals based on relative reliability. I follow their extended categorization to decompose accruals (ΔNOA) into four components: current operating asset accruals (ΔCOA), non-current operating asset accruals (ΔNCOA), current operating liability accruals (Δ-COL), and non-current operating liability accruals (Δ-NCOL). Based on analysis of the nature of assets and liabilities underlying each accrual component, Richardson et al. (2005) predict that ΔCOA and ΔNCOA have low reliability, Δ-NCOL has medium reliability, and Δ-COL has high reliability. The earnings persistence of these components is largely consistent this prediction. With this decomposition of accruals, I estimate the following regression model that links the probability of price crashes in year t + 1, VCRASH _t+1 and CRASH _t+1, to accrual components of the most recent 3 years and a set of control variables:

$$\begin{aligned} VCRASH_{t + 1} \;{\text{or}}\; CRASH_{t + 1} = & \alpha_{0} + \mathop \sum \limits_{k = 0}^{2} \beta_{1,k} *\varDelta COA_{t - k} + \mathop \sum \limits_{k = 0}^{2} \beta_{2,k} *\varDelta{\text{-}}COL_{t - k} \\ & + \mathop \sum \limits_{k = 0}^{2} \beta_{3,k} *\varDelta NCOA_{t - k} + \mathop \sum \limits_{k = 0}^{2} \beta_{4,k} *\varDelta{\text{-}}NCOL_{t - k} + \mathop \sum \limits_{l = 1}^{m} \theta_{l} *Control_{l,t} + \varepsilon_{t + 1} \\ \end{aligned}$$

(3)

Hypothesis H2 predicts β _1,k and β _3,k to be the most positive (or the least negative) and β _2,k to be the least positive (or the most negative) among coefficients on accrual components.

4.2.3 Test of hypotheses H3a and H3b

To test hypotheses H3a and H3b, I construct proxies for the hypothesized determinants of the cross-sectional variation in the association between accruals and price crashes, and then I examine the interactions between these proxies and accruals in forecasting future price crashes.

I use the CFO’s option incentive ratio (INCENTIVE) to measure CFO’s incentive to hide bad news. Jiang et al. (2010) and Chava and Purnanandam (2010) show that the incentive ratio for CFO stock and option holdings is positively associated with earnings management. Kim et al. (2011a) show that, when CFOs have a larger option incentive ratio, they are more likely to hide bad news; this finding is consistent with Benmelech et al.’s (2010) theoretical prediction.

Benmelech et al. (2010) also conjecture that it is more difficult for investors to distinguish between an increase in economic capital and the hoarding of bad news among firms in industries characterized by high R&D expenditures and intellectual property and firms that are rapidly growing. Following this logic, I use the dummy variable HIGHTECH, which equals one if a firm belongs to a high-tech industry, and sales growth (SALEGR) to proxy the difficulty of unravelling hidden bad news.

Stronger external monitoring should more effectively constrain managers’ opportunistic use of accruals to conceal bad news. I consider three monitoring mechanisms: dedicated and transient institutional holding (DED and TRA, respectively), analyst following (ANCOV), and auditor tenure (TENURE). Callen and Fang (2013) show that dedicated institutional ownership is negatively associated with future price crashes, while transient institutional ownership is positively associated; this suggests that dedicated institutional investors reduce bad news hoarding, and transient institutional investors encourage it.²⁰ Using multiple measures of earnings management, Yu (2008) finds that firms with a higher analyst following manage their earnings less, suggesting that analyst following may constrain bad news hoarding. Geiger and Raghunandan (2002) and Carcello and Nagy (2004) document significantly more audit reporting failures and fraudulent financial reports in earlier years of an auditor/client relationship than when auditors have served the same clients for longer tenures. Their findings suggest that longer audit tenure facilitates better understanding of clients’ business and critical issues by auditors, and consequently leaves fewer opportunities for managers to hide bad news.

Turning to default risk, I consider three alternative measures of default risk: Altman’s (1968) Z score (ALTMAN), Shumway’s (2001) bankruptcy score (SHUMWAY), and Vassalou and Xing’s (2004) default probability (DEFPROB). These variables have been shown to predict bankruptcies. Specifically, firms with a lower ALTMAN, a higher SHUMWAY, or a higher DEFPROB are more likely to go bankrupt.

With the above proxies, I estimate the following regression model that links the probability of price crashes in year t + 1, VCRASH _t+1 and CRASH _t+1, to the interactions between accruals and these proxies:

$$\begin{aligned} VCRASH_{t + 1} \;{\text{or}}\;CRASH_{t + 1} = & \alpha_{0} + \mathop \sum \limits_{k = 0}^{2} \beta_{k} *\varDelta NOA_{t - k} \\ & + \mathop \sum \limits_{k = 0}^{2} \gamma_{k} *X_{t - k} + \mathop \sum \limits_{k = 0}^{2} \delta_{k} *\varDelta NOA_{t - k} *X_{t - k} + \mathop \sum \limits_{l = 1}^{m} \theta_{l} *Control_{l,t} + \varepsilon_{t + 1} \\ \end{aligned}$$

(4)

where X is defined as INCENTIVE, HIGHTECH, SALEGR, DED, TRA, ANCOV, TENURE, ALTMAN, SHUMWAY, or DEFPROB.

Hypothesis H3a predicts δ _k to be positive for INCENTIVE _t−k , positive for HIGHTECH _t−k , positive for SALEGR _t−k , negative for DED _t−k , positive for TRA _t−k , negative for ANCOV _t−k , and negative for TENURE _t−k . Hypothesis H3b predicts δ _k to positive for ALTMAN _t−k , negative for SHUMWAY _t−k , and negative for DEFPROB _t−k .

4.2.4 Other design choices

To facilitate interpretation of the coefficients’ economic magnitudes, I rank all non-indicator independent variables in regression models (2)–(4) into deciles of 0–9 and then divide their decile ranking by 9. Unless otherwise stated, regression results reported below are based on ranked independent variables. I use pooled OLS regression to estimate models predicting VCRASH _t+1 and pooled logistic regression to estimate models predicting CRASH _t+1. The significance levels of coefficient estimates are assessed using standard errors clustered by both firm and year (Petersen 2009; Gow et al. 2010). When estimating pooled regression models (2)–(4), I also include fixed industry effects and fixed year effects, where industries are defined as Fama and French 48 industries (Fama and French 1997).

4.3 Sample selection

My main sample consists of non-financial (SIC codes 6000–6999), non-utility (SIC codes 4900–4999) firms with non-missing values for price crashes of both the current year and the next year, accruals of the most recent 3 years, firm size, book-to-market ratio, leverage, size-adjusted returns, idiosyncratic volatility, share turnover, and returns skewness. These variables are required to estimate regression model (2). I also require an average share price of at least $2.5 for the 12 months starting from the fifth month of fiscal year t (Hutton et al. 2009). The final sample includes 108,184 firm-year observations for fiscal years between 1965 and 2013.

Table 1 presents the descriptive statistics and correlations for my key variables. The sample mean of VCRASH _t+1 is 2.485, suggesting that the magnitude of the worst weekly return is 2.485 times the standard deviation below the mean for that firm-year. The sample mean of CRASH _t+1 is 15.9 %, which is significantly higher than the 5.1 % frequency of crashes generated by a normal distribution.²¹ The mean value decreases from 8.2 % for ΔNOA _t−2 to 6.5 % for ΔNOA _t , suggesting a slowing expansion in net operating assets for the average firm in my sample. The distributions of other variables are similar to those obtained in prior studies (Kim et al. 2011a, b). Panel B of Table 1 reports pair-wise correlations for the key variables. Consistent with the hoarding of bad news, ΔNOA _t is significantly positively correlated with both VCRASH _t+1 and CRASH _t+1, and ΔNOA _t−1 is significantly positively correlated with VCRASH _t+1. The correlations between price crash measures and other control variables are generally consistent with the findings in prior studies. For example, both SARET _t and TURN _t are positively correlated with price crashes (Chen et al. 2001; Hutton et al. 2009).

Table 1 Descriptive statistics and correlations

5 Empirical results

5.1 Examination of H1

Figure 1(1) and (2) depict strong positive correlations between accruals and measures of price crashes over the next year, consistent with the bad news hoarding explanation. Figure 1(1) presents the portfolio mean of VCRASH _t+1 by deciles of accruals for the past 3 years. For the lowest decile of ΔNOA _t , the magnitude of worst weekly return is 2.41 times the firm-specific standard deviation below the mean. This magnitude increases monotonically as the level of ΔNOA _t increases and reaches 2.51 times the standard deviation for the highest decile. The increase of VCRASH _t+1 across increasing levels of accruals with a slower pace is also observed for ΔNOA _t−1 and ΔNOA _t−2 . Figure 1(2) presents similar monotonic increases in CRASH _t+1 across increasing accruals portfolios. For example, 12.88 % of firms in the lowest decile of ΔNOA _t experience price crashes over the next year, and this probability increases to 17.27 % for the highest decile. Such an increase in price crash likelihood is economically meaningful.

Fig. 1

Likelihood of weekly price crashes over the next year, by deciles of accruals. The following figures plot the time-series average of the annual mean value of VCRASH _t+1 and CRASH _t+1 by deciles of accruals of the most recent 3 years (ΔNOA _t , ΔNOA _t−1 , and ΔNOA _t−2 ). VCRASH _t+1 represents the number of standard deviations by which the worst firm-specific weekly return over the next year falls below its mean, and CRASH _t+1 represents the incidence of weekly returns that are more than 3.09 times the standard deviation below its mean over the next year. The sample is ranked into 10 deciles of accruals each year, with decile D1 (D10) representing the lowest (highest) accruals decile. The annual mean value of VCRASH _t+1 (CRASH _t+1) is obtained by taking the average of VCRASH _t+1 (CRASH _t+1) for each decile of accruals. The sample includes 108,184 firm-year observations for fiscal years between 1965 and 2013. Variables are defined in the “Appendix”

Table 2 reports results from the estimation of regression model (2). In Panel A, I estimate OLS regressions predicting VCRASH _t+1. In almost all regression specifications (models M1–M7), accruals of the past 3 years (ΔNOA _t , ΔNOA _t−1 , and ΔNOA _t−2 ) are significantly positively associated with VCRASH _t+1 after controlling for other price crash predictors used in prior studies. The sum of coefficients on ΔNOA _t , ΔNOA _t−1 , and ΔNOA _t−2 is approximately 0.12 in these regressions, suggesting that the magnitude of worst weekly return increases by 0.12 times the standard deviation when accruals of the past 3 years all increase from the lowest to the highest decile. Moreover, the coefficient and associated t-statistic on accruals are among the largest in magnitude in these regressions.²² Model M1 of Panel A also indicates an attenuation of the association between accruals and VCRASH _t+1 as the temporal distance between the two increases. The coefficient on accruals decreases from 0.077 (with a t-statistic of 8.63) for ΔNOA _t to 0.017 (with a t-statistic of 2.00) for ΔNOA _t−2 , suggesting that accruals in the most recent year best predict future price crashes. This finding also implies that the hidden bad news reflected in accruals is released at a decreasing speed over the next 3 years. In Panel B, I estimate logistic regressions predicting CRASH _t+1. In almost all regression specifications, accruals of the past 3 years are significantly positively associated with CRASH _t+1.

Table 2 The impact of accruals on price crashes over the next year

The coefficients on control variables in model M1 of Table 2 are, for the most part, consistent with those in prior literature. As CRASH _t+1 is a more widely used crash risk measure, I focus on the results in Panel B. BTM _t is negatively correlated with CRASH _t+1, and SARET _t and TURN _t are positively correlated with CRASH _t+1. These results resemble the findings of Hutton et al. (2009) and Kim et al. (2011a, b). Unlike them, however, I do not observe a significant coefficient on SIZE _t or LEV _t in model M1. I also find IVOL _t to be uncorrelated with CRASH _t+1, which is consistent with the finding by Callen and Fang (2013) but differs from the positive correlation documented by Kim et al. (2011a, b).

Model M2 of Table 2 compares accruals and free cash flows (FCF) in predicting price crashes over the next year. Desai et al. (2004) show that the ability of accruals to predict the next year’s size-adjusted buy-and-hold returns is subsumed by cash flows. Their finding implies that the positive association between accruals and price crashes may be a simple manifestation of a negative association between cash flows and price crashes. In contrast, I find free cash flows to be uncorrelated with price crashes after controlling for accruals. Models M3–M7 present the associations between other proxies for bad news hoarding used in prior studies and price crashes. I confirm previous findings that TRA _t , SIR _t , and SALEGR _t are positively associated with price crashes; however, in my sample, I do not find LRETR _t or INCENTIVE _t to be significantly associated with crashes.

In summary, Fig. 1 and Table 2 document a robust positive association between total accruals and subsequent price crashes, which is consistent with the bad news hoarding explanation but inconsistent with the default risk explanation.

5.2 Examination of H2

Table 3 presents univariate statistics and pair-wise correlations for accrual components used to test hypothesis H2. Panel A of Table 3 shows that ΔCOA _t and ΔNCOA _t have positive means and Δ-COL _t and Δ-NCOL _t have negative means, suggesting that the average firm is growing in both operating assets and operating liabilities. Both the means and standard deviations of these accrual components in my sample are comparable to those reported by Richardson et al. (2005). Panel B reports the pair-wise correlations for the accrual decomposition. These correlations reveal several regularities. First, ΔCOA _t and ΔNCOA _t are strongly positively correlated with Δ-COL _t and Δ-NCOL _t , implying that operating liabilities provide one source of funding for operating assets growth. This also highlights the importance of including all four components simultaneously in the regression when examining their abilities to predict price crashes. Second, ΔCOA _t and ΔNCOA _t have comparable correlations with ΔOA _t , suggesting that both current and non-current operating assets contribute to the variation in total operating asset accruals. In contrast, Δ-COL _t is more correlated with Δ-OL _t than Δ-NCOL _t , suggesting that current operating liabilities explain more of the variation in total operating liability accruals. Third, ΔCOA _t is much more correlated with ΔWC _t than Δ-COL _t , implying that most of the variation in ΔWC _t is attributable to ΔCOA _t . Similarly, most of the variation in ΔNCO _t is attributable to ΔNCOA _t .

Table 3 Descriptive statistics and correlations of accrual components

Figure 2 presents the portfolio mean of VCRASH _t+1 or CRASH _t+1 by deciles of each accrual component for the past 3 years. These figures reveal a wide range of variation across accrual components in their associations with price crashes. The likelihood of a price crash increases monotonically across increasing portfolios of ΔCOA and ΔNCOA, does not change much with Δ-NCOL, and decreases monotonically as the level of Δ-COL increases. The negative association between Δ-COL and price crashes is consistent with the default risk explanation but may also be driven by the positive association between ΔCOA and price crashes, given the strong negative correlation between ΔCOA and Δ-COL.

Fig. 2

Likelihood of weekly price crashes over the next year, by deciles of accrual components. The following figures plot the time-series average of annual mean value of VCRASH _t+1 and CRASH _t+1 by deciles of each accrual component of the most recent 3 years. VCRASH _t+1 represents the number of standard deviations by which the worst firm-specific weekly return over the next year falls below its mean, and CRASH _t+1 represents the incidence of weekly returns that are more than 3.09 times the standard deviation below its mean over the next year. The four accrual components are current operating asset accruals (ΔCOA), current operating liability accruals (Δ-COL), non-current operating asset accruals (ΔNCOA), and non-current operating liability accruals (Δ-NCOL). The sample is ranked into 10 deciles of each accrual component each year, with decile D1 (D10) representing the lowest (highest) decile. The annual mean value of VCRASH _t+1 (CRASH _t+1) is obtained by taking the average of VCRASH _t+1 (CRASH _t+1) for each decile of accrual component. The sample includes 108,184 firm-year observations for fiscal years between 1965 and 2013. Variables are defined in the “Appendix”

Panel A of Table 4 presents results for the estimation of model (3), which includes all four accrual components simultaneously and assumes linear relations between these components and price crashes. The coefficients on ΔCOA of the most recent 3 years (ΔCOA _t , ΔCOA _t−1 , and ΔCOA _t−2 ) are significantly positive in models predicting VCRASH _t+1 and CRASH _t+1 and consistent with the prediction of bad news hoarding. These coefficients are higher than those on the other three accrual components of the same year. Also consistent with the bad news hoarding explanation is the significantly positive coefficient on the current year’s ΔNCOA (ΔNCOA _t ). However, ΔNCOA of earlier years (ΔNCOA _t−1 and ΔCOA _t−2 ) do not appear to predict future price crashes. Turning to liability accruals, none of Δ-NCOL _t , Δ-NCOL _t−1 , and Δ-NCOL _t−2 is significantly related to price crashes. Interestingly, coefficients on Δ-COL of the most recent 3 years (Δ-COL _t , Δ-COL _t−1 , and Δ-COL _t−2 ) are generally significantly negative. These negative associations are consistent with the default risk explanation that firms with large increases of current operating liabilities have higher default risk and subsequently experience more crashes.

Table 4 The impact of accrual components on price crashes over the next year

Further inspection of Fig. 2 indicates potential nonlinearities in the associations between accrual components and price crashes. As a result, I modify regression model (3) by allowing the coefficients on accrual components to differ between the top and bottom five deciles. Panel B of Table 4 presents results for this modified regression model. Consistent with the observation from Fig. 2, ΔCOA and Δ-COL are associated with price crashes in a nonlinear fashion. More precisely, the positive association between ΔCOA and price crashes is only present in the top five deciles of ΔCOA (i.e., HIGH_ΔCOA = 1). None of ΔCOA _t , ΔCOA _t−1 , and ΔCOA _t−2 is significantly associated with VCRASH _t+1 when below the cross-sectional median, while ΔCOA _t and ΔCOA _t−2 are significantly positively associated with VCRASH _t+1 when above the median.²³ In contrast, the negative association between Δ-COL and price crashes is only present in the bottom five deciles of Δ-COL. For example, Δ-COL _t and Δ-COL _t−1 are significantly negatively associated with VCRASH _t+1 when below the median, while none of Δ-COL _t , Δ-COL _t−1 , and Δ-COL _t−2 is significantly associated with VCRASH _t+1 when above the median.²⁴ These nonlinearities suggest that current operating asset (liability) accruals may be associated with hidden bad news (default risk) in nonlinear fashions. Unlike these two components, Panel B of Table 4 does not provide robust nonlinearities in the associations between non-current operating asset and liability accruals and future price crashes.

Overall, the results in Table 4 provide evidence consistent with hypothesis H2 that a less reliable accrual component is more positively associated with price crashes over the next year. This finding corroborates the bad news hoarding explanation for the positive association between total accruals and price crashes documented in Table 2.

5.3 Examination of H3a and H3b

Results in the previous section suggest that hidden bad news reflected in accruals is concentrated in the current and non-current operating asset components (ΔCOA and ΔNCOA), while default risk reflected in accruals, if any, is concentrated in the current operating liability component (Δ-COL). As a result, I test the prediction of the bad news hoarding explanation in hypothesis H3a with operating asset accruals (ΔOA = ΔCOA + ΔNCOA) and the prediction of the default risk explanation in hypothesis H3b with current operating liability accruals (Δ-COL).

5.3.1 Examination of H3a

Table 5 presents results from the estimation of regression model (4) modified by replacing ΔNOA with ΔOA.²⁵ In each regression specification, I also control for the interaction between operating asset accruals (ΔOA) and firm size (SIZE), as most of the interaction variables are highly correlated with firm size (e.g., institutional holding and analyst following). Since results for the interaction terms in models predicting CRASH _t+1 are qualitatively similar to those in models predicting VCRASH _t+1, I focus on the results in Panel A.

Table 5 Cross-sectional variations of the association between operating asset accruals and price crashes over the next year

Model M1 shows that the coefficient on ΔOA _t * INCENTIVE _t is positive and statistically significant (0.238 with a t-statistic of 3.14), consistent with the prediction of hypothesis H3a that managers are more likely to use aggressive accrual estimates when the incentive to hide bad news is stronger. The coefficient on ΔOA _t * HIGHTECH _t (0.045 with a t-statistic of 2.22) in model M2 and on ΔOA _t * SALEGR _t (0.098 with a t-statistic of 5.08) in model M3 are also significantly positive, suggesting that it is easier for managers to hide bad news using aggressive accrual estimates when it is more difficult for investors to distinguish between an increase in economic capital and bad news hoarding.

Models M4–M6 examine the impact of external monitoring on the association between ΔOA and VCRASH _t+1. Regarding institutional holdings, ΔOA * TRA of the past 3 years are all significantly positively associated with VCRASH _t+1. In contrast, neither ΔOA * DED nor ΔOA * QIX is significantly associated with VCRASH _t+1 in model M4.²⁶ These findings imply that transient institutional investors encourage the use of accruals in bad news hoarding and that dedicated institutional investors fail to constrain such opportunistic use of accruals. With regard to analyst following, model M5 shows that the positive association between ΔOA and VCRASH _t+1 is stronger instead of weaker when the firms are followed by more analysts, indicated by the positive coefficients on ΔOA _t * ANCOV _t and ΔOA _t−2 * ANCOV _t−2 . One potential explanation is that, when analyst following is higher, managers are under greater pressure to meet or beat earnings targets and consequently more likely to hide bad news. Finally, consistent with my expectation, the positive association between ΔOA and VCRASH _t+1 is weaker when the auditor has a longer tenure with the firm, as indicated by the negative coefficients on ΔOA * TENURE of the past 3 years.

Overall, the findings in Table 5 are consistent with hypothesis H3a, supporting the bad news hoarding explanation with regard to the link between accruals and future price crashes.

5.3.2 Examination of H3b

Table 6 presents results from the estimation of regression model (4) modified by replacing ΔNOA with Δ-COL.²⁷ In each regression specification, I also control for the interaction between current operating liability accruals (Δ-COL) and firm size (SIZE), because proxies for default risk are correlated with firm size and there may be a mechanical relationship between firm size and future price crashes. Since results for the interaction terms in models predicting CRASH _t+1 are qualitatively similar to those in models predicting VCRASH _t+1, I focus on the results in Panel A. The coefficient on Δ-COL _t * ALTMAN _t (−0.093 with a t-statistic of −4.16) in model M1 is significantly negative and that on Δ-COL _t * SHUMWAY _t (0.078 with a t-statistic of 2.73) in model M2 is significantly positive, suggesting that the negative association between Δ-COL _t and price crashes is weaker among firms of higher default risk. These findings are opposite to the prediction of hypothesis H3b that the association between accruals and price crashes is more negative for more distressed firms. Also inconsistent with H3b, none of the coefficients on Δ-COL * DEFPROB of the past 3 years is significant in model M3.

Table 6 Cross-sectional variations of the association between current operating liability accruals and price crashes over the next year

To explain the above puzzling results, I decompose Δ-COL into nondiscretionary and discretionary portions (NDΔ-COL and DΔ-COL, respectively). NDΔ-COL is proportional to sales growth, but DΔ-COL is independent of it. Model M4 (M5) shows that the negative (positive) coefficient on Δ-COL _t * ALTMAN _t (Δ-COL _t * SHUMWAY _t ) in model M1 (M2) is driven by NDΔ-COL _t rather than DΔ-COL _t . The negative coefficients on NDΔ-COL * ALTMAN in model M4 and the positive coefficients on NDΔ-COL * SHUMWAY in model M5 of the past 2 years essentially reflect a weaker positive association between sales growth and VCRASH _t+1 among firms with higher default risk.²⁸ This finding is consistent with the explanation that high sales growth is less associated with hidden bad news for more financially distressed firms but difficult to reconcile with the default risk explanation. Models M4 and M5 also show that the association between DΔ-COL and VCRASH _t+1 does not vary cross-sectionally with ALTMAN or SHUMWAY.

Overall, the results in Table 6 are inconsistent with the default risk explanation for the negative association between current operating liability accruals and future price crashes. As a result, neither bad news hoarding nor default risk seems to explain the link between current operating liability accruals and price crashes.²⁹

5.4 Reexamination of the association between financial reporting opacity and price crashes

5.4.1 Accrual components from initial decomposition of accruals and price crashes

The results in previous sections show that the association between accruals and future price crashes hinges critically on the definition of accruals because accrual components differ in reliability in accrual estimation and consequently the association with hidden bad news. In this section, I examine two common definitions of accruals in literature: working capital and non-current operating accruals (ΔWC and ΔNCO) from the initial decomposition of accruals (Richardson et al. 2005). As ΔWC equals ΔCOA plus Δ-COL, I expect the nonlinear positive association between ΔCOA and price crashes and the nonlinear negative association between Δ-COL and price crashes documented in Table 4 to result in a U-shaped relation between ΔWC and price crashes. By the same logic, as ΔNCO equals ΔNCOA plus Δ-NCOL, I expect the close linear positive association between ΔNCOA and price crashes and the lack of correlation between Δ-NCOL and price crashes to result in a close linear positive association between ΔNCO and price crashes.

Panel A of Table 7 presents results consistent with the above predictions. In the multivariate model predicting VCRASH _t+1, the coefficients on ΔWC _t and ΔWC _t−1 are significantly negative and the coefficient on ΔWC _t−2 is insignificantly negative when they are below their cross-sectional medians (i.e., HIGH_ΔWC = 0). In contrast, coefficients on ΔWC _t , ΔWC _t−1 , and ΔWC _t−2 are all significantly positive when above their cross-sectional medians.³⁰ Based on the results in Table 4, it is straightforward to conclude that the negative association for below-median ΔWC is caused by the negative association between Δ-COL and VCRASH _t+1, while the positive association for above-median ΔWC is driven by the positive association between ΔCOA and VCRASH _t+1. This U-shaped relation remains in the model predicting CRASH _t+1, but the significance level for the negative association is weaker.³¹ Turning to ΔNCO of the past 3 years, they are all positively associated with price crashes over the next year without detectable nonlinearities. This is consistent with the finding in Table 4 that ΔNCOA is positively associated with future price crashes in a close-to-linear fashion.

Table 7 The impact of accrual components on price crashes over the next year—initial decomposition of accruals

The U-shaped relation between ΔWC and price crashes and the close linear relation between ΔNCO and price crashes imply nonlinearity in the positive association between ΔNOA and price crashes documented in Table 2. To test this prediction, I modify regression model (2) by allowing the coefficient on ΔNOA to differ between the bottom and top five deciles. Panel B of Table 7 presents results for this modified regression. In the case of predicting VCRASH _t+1, the positive associations between ΔNOA of the past 2 years and VCRASH _t+1 are concentrated in their top five deciles. In the case of predicting CRASH _t+1, the positive association between ΔNOA _t−1 and CRASH _t+1 is present only when ΔNOA _t−1 is above the median. Overall, Panel B shows that the likelihood of price crashes does not differ much between low and medium ΔNOA, due to the offsetting roles of ΔWC and ΔNCO in predicting price crashes when ΔNOA is below the median.

5.4.2 Financial reporting opacity and price crashes

The U-shaped relation between ΔWC and price crashes in Table 7 resembles the U-shaped relation between discretionary operating accruals and price crashes implied by the positive association between reporting opacity and crash risk first documented by Hutton et al. (2009).³² This observation suggests that accrual decomposition could help to better understand the mechanisms underlying the U-shaped relation between discretionary operating accruals and price crashes.

I first replicate the strong positive association between reporting opacity (SUM|DACC2 _t |) defined by Hutton et al. (2009) and price crashes over the next year for the sample period from 1989 to 2013, as shown in model M1 of Panel A in Table 8. In model M2, I further include the balance-sheet-based measure of opacity (SUM|DACC _t |).³³ When both measures of opacity are included, the balance-sheet-based measure subsumes the cash-flows-based measure. This finding allows me to focus on the balance-sheet-based measure in the following analysis, which can be easily linked to accrual components constructed from the balance sheet. Model M3 confirms that the positive association between balance-sheet-based opacity and subsequent price crashes holds in my full sample period of 1965–2013. As a result, I conduct the rest of the analysis in this section over the full sample period.

Table 8 The impact of discretionary portions of accrual components on price crashes over the next year

The positive association between SUM|DACC _t | and price crashes implies a U-shaped relation between the level of discretionary operating accruals (DACC) and price crashes, as shown in model M1 of Panel B. DACC is negatively associated with price crashes when it is negative but positively associated with crashes when it is positive.³⁴ Similar to ΔWC, the significance level for the negative associations of DACC is stronger when predicting VCRASH _t+1 than when predicting CRASH _t+1. To understand the mechanism underlying this U-shaped relation, I decompose DACC into three components: discretionary current operating asset accruals (DΔCOA), discretionary current operating liability accruals (DΔ-COL), and discretionary depreciation and amortization (DDP). Model M2 of Panel B modifies model M1 by allowing these three components of DACC to have different associations with future price crashes.

The results show that the negative association between DACC and price crashes for negative DACC is driven by the negative association between DΔ-COL and crashes. For example, in the model predicting VCRASH _t+1, coefficients on DΔ-COL of the past 3 years are all significantly negative among the bottom five deciles of DACC, while neither DΔCOA nor DDP has a stable relation with VCRASH _t+1. This finding, combined with the analysis in Sect. 5.3.2, suggests that neither default risk nor bad news hoarding (the explanation provided by Hutton et al. 2009) explains the negative association between DACC and price crashes when DACC is negative. For bad news hoarding to explain said negative association, we would need to observe DΔCOA to drive this negative relation, and we also would need an argument for more hidden bad news among firms with low DΔCOA. With regard to the positive association between DACC and price crashes for positive DACC, model M2 shows that this positive association is driven by the positive association between DΔCOA and price crashes, which is consistent with the explanation of more hidden bad news among firms with high DΔCOA (Hutton et al. 2009).³⁵

Overall, the results of Table 8 show that the negative (positive) association between DACC and price crashes when DACC is negative (positive) is driven by the most (least) reliable accrual component DΔ-COL (DΔCOA).

6 Additional analysis

6.1 Accruals and price crashes in the pre-/post-SOX periods

Cohen et al. (2008) show that the passage of the Sarbanes–Oxley Act, which substantially increased the penalties for earnings manipulation, materially reduced the incidence of accounting-based earnings management. Presumably, the act also would have reduced the use of accruals in bad news hoarding. Therefore it follows that the positive association between ΔNOA and future price crashes would become weaker or even dissipate after SOX.

I first compare the associations between accrual components and price crashes over the next year in the pre-SOX period with those in the post-SOX period. The results reported in Table 9 Panel A show that ΔCOA and ΔNCOA of the past 3 years in general become less positively associated with VCRASH _t+1 and CRASH _t+1. In addition, Δ-COL of the past 2 years become more negatively associated with VCRASH _t+1. Overall, the weaker positive associations between these accrual components and price crashes over the next year are consistent with the prediction that SOX reduces hidden bad news reflected in accruals. The results for ΔNOA reported in Panel B lead to the same conclusion. However, the positive association between ΔNOA _t and price crashes remains statistically and economically significant in the post-SOX period, suggesting that SOX does not eliminate bad news hoarding through accruals.³⁶

Table 9 The impact of accrual components on price crashes over the next year—Pre/Post-SOX comparison

6.2 Accruals and price crashes over earnings announcement versus non-announcement weeks

This section examines the implication of the bad news hoarding explanation on the timing of price crashes. Under the bad news hoarding explanation, a price crash results from a sudden release of accumulated bad news when managers cannot continue concealing it. Ak et al. (2015) show that a sudden release of accumulated bad news is more likely to occur over an earnings announcement week than a non-announcement week. Specifically, they show that the percentage of price crashes caused by earnings announcements increases from 20 % in 2001 to 70 % in 2013. Given the concentration of price crashes over earnings announcements, I expect a stronger positive association between accruals and price crashes over earnings announcement weeks than non-announcement weeks.³⁷

Figure 3 presents results consistent with this prediction. In Fig. 3, I separately plot the probability of observing a weekly price crash (WCRASH _t+1,w  = 1) over the next year’s earnings announcement weeks (the solid line) and non-announcement weeks (the dashed line) by deciles of accruals (ΔNOA _t , ΔNOA _t−1 , or ΔNOA _t−2 ).³⁸,³⁹ Fig. 3(1) shows that the spread of this probability between the low and high deciles of ΔNOA _t is 0.630 % over earnings announcement weeks, which is statistically and economically larger than the spread of 0.060 % over non-announcement weeks. Figure 3(2) and (3) present similar but weaker differences between earnings announcement and non-announcement weeks for ΔNOA _t−1 and ΔNOA _t−2 .

Fig. 3

Likelihood of a price crash during earnings announcement weeks versus non-announcement weeks. The following figures present the time-series mean for the annual probability of observing a weekly price crash (WCRASH _t+1,w  = 1), defined as a firm-specific weekly return more than 3.09 times the standard deviation below its mean, by deciles of accruals of the most recent 3 years (ΔNOA _t , ΔNOA _t−1 , and ΔNOA _t−2 ). The solid (dashed) line plots the series calculated over earnings announcement (non-announcement) weeks, with D1 (D10) in the figures representing the lowest (highest) accruals decile. The sample includes 5204,134 firm-weeks for fiscal years between 1970 and 2013. Variables are defined in the “Appendix”

Table 10 examines the relation between ΔNOA and the probability of weekly price crashes (WCRASH _t+1,w  = 1) after controlling for other price crash predictors used in prior literature. I allow the coefficient on ΔNOA to differ between earnings announcement weeks (EAW _t+1,w  = 1) and non-announcement weeks (EAW _t+1,w  = 0) in order to examine the timing of price crashes. Consistent with the observation from Fig. 3, the positive association between ΔNOA _t and WCRASH _t+1,w is significantly stronger over earnings announcements, as indicated by the significantly positive coefficient on ΔNOA _t * EAW _t+1,w . However, the coefficient on ΔNOA _t−1 * EAW _t+1,w and that on ΔNOA _t−2 * EAW _t+1,w are insignificant. Overall, I find a stronger positive association between accruals of the current year and weekly price crashes over the next year during earnings announcement weeks than non-announcement weeks.

Table 10 The impact of accruals on price crashes over the next year—earnings announcement weeks versus non-announcement weeks

7 Conclusion

This study investigates the relationship between accruals and future price crashes. I find that high accruals predict a higher probability of future price crashes than low accruals. Moreover, in multivariate regression models of future price crashes, accruals in the most recent year are among the strongest predictors in both economic and statistical significance. This finding can be explained by managers’ use of income-increasing accrual estimates to hoard bad news. Once accumulated bad news crosses a tipping point, it is released all at once and results in a price crash. Consistent with this explanation, I find the observed relation to be strongest for current and non-current operating assets, which are the least reliable accrual components. I also find the observed relation to be stronger among firms (1) with a higher option incentive ratio for CFOs, (2) in high-tech industries, (3) with higher sales growth, (4) with a higher level of transient institutional holding, and (5) with shorter auditor tenure. Surprisingly, I find a negative association between current operating liability accruals, a relatively reliable accrual component, and price crashes over the next year. This negative association is opposite to the prediction of the bad news hoarding explanation and cannot be explained by potential default risk reflected in large increases of current operating liabilities. I leave the explanation of this puzzling result for future research.

Appendix

See Table 11.

Table 11 Variable definition