## 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.

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## Notes

- 1.
Consistent with prior price crash studies (Hutton et al. 2009), I define price crashes based on the distribution of firm-specific weekly

*log*returns, to remove the well-known right skewness in raw returns. - 2.
Accruals literature finds that high (low) accruals are associated with future bad (good) returns and more (fewer) SEC enforcement actions for alleged earnings manipulation. This suggests that high (low) accruals firms hide more (less) bad news than investors expect and those expectations are corrected in future periods.

- 3.
- 4.
Untabulated results show that

*total*accruals are negatively associated with future price jumps, representing extreme positive observations in firm-specific returns distributions. This negative association rules out alternative risk-based explanations that predict both more price crashes and more price jumps for high accruals firms. - 5.
Current and non-current operating asset accruals are defined as the change in non-cash current assets and non-current operating assets, respectively. Current and non-current operating liability accruals are defined as the

*negative*of the change in non-debt current liabilities and non-current operating liabilities, respectively. - 6.
Operating asset accruals are defined as the sum of current and non-current operating asset accruals.

- 7.
Recall that I define current operating liability accruals as the

*negative*of change in non-debt current operating liabilities. A low level of current operating liability accruals corresponds to a high level of increase in current operating liabilities. - 8.
I first show that the cash-flows-based discretionary operating accruals examined by Hutton et al. (2009) are subsumed by balance-sheet-based discretionary operating accruals in predicting subsequent price crashes. I define balance-sheet-based discretionary operating accruals as the residual portion of operating accruals estimated from the Jones model (1991), where operating accruals equal change in non-cash current operating assets minus change in non-debt current operating liabilities minus depreciation and amortization. I then demonstrate that, when discretionary operating accruals are positive, the positive association between those accruals and price crashes is driven by discretionary current operating asset accruals. In contrast, when discretionary operating accruals are negative, the negative association is driven by discretionary current operating liability accruals.

- 9.
The lower persistence of accruals may also be explained by firm growth (Fairfield et al. 2003). Differentiating these two explanations is beyond the scope of this study.

- 10.
Managers have a higher discount rate than shareholders because managers are less diversified, have a shorter horizon due to possible early departure from the firm or death, or both (Benmelech et al. 2010). The value of managers’ option and stock portfolios depends on stock price performance. A manager’s bonus is often a function of accounting earnings.

- 11.
Campbell et al. (2008) define failures broadly to include bankruptcies, financially driven delistings, and D (“default”) ratings issued by a leading credit rating agency.

- 12.
In the differences-of-opinion model (Hong and Stein 2003), a group of investors (e.g., mutual funds) cannot short-sell stocks. Because of short-sale constraints, bearish investors do not initially participate in the market, and their negative information is not revealed in the prices. However, if other previously bullish investors exit the market, these originally bearish investors may become the marginal buyers. Thus accumulated hidden bad news surfaces and results in a price crash. In the information blockage model (Cao et al. 2002), an upward price trend triggers trading on the part of favorably informed investors. In contrast, adversely informed traders become less confident that they have received correct signals and may delay trading until the price drops. Thus, if the true state of the economy is actually low, there is a large correction upon the eventual entry of the sidelined investors with adverse signals. This information blockage leads to negative returns skewness following price run-ups and positive skewness following price rundowns.

- 13.
Hutton et al. (2009) show that the mean returns for crash weeks are −22.74 %, that the average standard deviation of firm-specific weekly return is 5.8 %, and that 17 % of firms have price crash weeks in their sample.

- 14.
I do not attempt to differentiate between the over-estimation of accruals and over-investment as the source of bad news reflected in accruals because both predict more price crashes for high accruals firms.

- 15.
- 16.
The four-month lag allows me to avoid the look-ahead bias by ensuring that the financial data are available to investors when forecasting the probability of future weekly price crashes.

- 17.
At least 26 weeks are required to estimate the regression model (1) for each firm-year. This requirement may create a forward-looking bias.

- 18.
Results remain quantitatively similar if I use returns of past three years instead of returns of the previous year in the regressions.

- 19.
Results remain quantitatively similar if I use the number of consecutive annual revenue increases over the previous three fiscal years (Bradshaw et al. 2010), instead of revenue growth over the previous year in the regressions.

- 20.
- 21.
Given my definition of a price crash, if firm-specific weekly returns were normally distributed, one would expect to observe 0.1 % of the sample firms crashing in any week. The probability of observing at least a price crash over the course of a year would then be 5.1 % = 1−(1 − 0.001)

^{52}. - 22.
The magnitude of the regression coefficient is comparable across independent variables because all non-indicator independent variables are ranked into deciles and then scaled between 0 and 1.

- 23.
The

*t*-statistic for the coefficient 0.137 (= 0.156 − 0.019) on*ΔCOA*_{ t }when it is above the median is 6.08,*t*-statistic for the coefficient 0.016 (= 0.019 − 0.003) on*ΔCOA*_{ t−1 }when it is above the median is 0.64, and*t*-statistic for the coefficient 0.042 (= 0.058 − 0.016) on*ΔCOA*_{ t-2 }when it is above the median is 1.95. - 24.
The

*t*-statistic for the coefficient 0.019 (= 0.052 − 0.033) on*Δ-COL*_{ t }when it is above the median is 0.80,*t*-statistic for the coefficient 0.025 (= 0.124 − 0.099) on*Δ-COL*_{ t−1 }when it is above the median is 1.32, and*t*-statistic for the coefficient −0.007 (= 0.019 − 0.026) on*Δ-COL*_{ t-2 }when it is above the median is −0.35. - 25.
Results from the estimation of regression model (4), which is based on

*ΔNOA*, lead to the same conclusions. These results are reported in Table A1 of the online appendix (https://business.illinois.edu/profile/wei-zhu/publications). - 26.
Coefficient estimates for

*ΔOA * DED*and*ΔOA * QIX*are not tabulated in Table 5 for simplicity. These results are available upon request. - 27.
Results from the estimation of regression model (4), which is based on

*ΔNOA*, are reported in Table A2 of the online appendix (https://business.illinois.edu/profile/wei-zhu/publications). The coefficient before the interaction between*ΔNOA*and the proxy for default risk is largely insignificant. The only exceptions are the positive coefficient before*ΔNOA*_{ t }** ALTMAN*_{ t }in predicting*VCRASH*_{ t+1 }and the positive coefficient before*ΔNOA*_{ t−2 }** DEFPROB*_{ t−2 }in predicting*CRASH*_{ t+1 }. While the former finding is consistent with*H3b*, the latter is not. - 28.
Recall from Table 2 that

*SALEGR*_{ t }is positively associated with*VCRASH*_{ t+1 }. Untabulated results show that*SALEGR*_{ t }(*NDΔ-COL*_{ t }) is weakly positively (negatively) associated with*VCRASH*_{ t+1 }even among firms with the highest level of default risk (i.e., the lowest decile of*ALTMAN*_{ t }or the highest decile of*SHUMWAY*_{ t }). - 29.
To better understand the causes of price crashes following low current operating liability accruals, I randomly sample 40 firm-years that have low total accruals (

*ΔNOA*_{ t−1 }in the lowest quintile) due to large increases of current operating liabilities (*Δ-COL*_{ t−1 }in the lowest quintile) and subsequent price crashes (*CRASH*_{ t+1 }= 1) for the 1996–2013 sample period. I sample observations with low*Δ-COL*in year t − 1 because*Δ-COL*_{ t−1 }is slightly more negatively associated with price crashes than*Δ-COL*_{ t }, as shown in Table 4. I identify the events that cause these price crashes by searching company-related news on Bloomberg over the price crash weeks. As reported in Table A3 of the online appendix (https://business.illinois.edu/profile/wei-zhu/publications), only three price crashes in my sample were caused by news about company financial distress, suggesting that default risk is unlikely to explain the negative association between*Δ-COL*and future price crashes. The two most common reasons for crashes in my sample are a disappointing earnings announcement (17 cases) and the announcement of R&D failure like a disappointing clinical trial for a new drug (8 cases). This finding suggests that firms with lower*Δ-COL*may experience more extreme negative shocks to future earnings or have higher failure rates in R&D projects, leading to the negative association between*Δ-COL*and price crashes. I leave the examination of these alternative explanations to future research. I thank Richard Sloan for suggesting this analysis. - 30.
The

*t*-statistic for the coefficient 0.137 (= 0.190 − 0.053) on*ΔWC*_{ t }when it is above the median is 8.31,*t*-statistic for the coefficient 0.049 (= 0.101 − 0.052) on*ΔWC*_{ t−1 }when it is above the median is 2.84, and*t*-statistic for the coefficient 0.067 (= 0.100 − 0.033) on*ΔWC*_{ t−2 }when it is above the median is 2.94. - 31.
The weaker significance level for the negative association in the model predicting

*CRASH*_{ t+1 }relative to that in the model predicting*VCRASH*_{ t+1 }is likely due to the definition of*CRASH*_{ t+1 }as an indicator variable. - 32.
Hutton et al. (2009) define operating accruals as net income minus operating cash flows, and they use the modified Jones model (Dechow et al., 1995) to estimate the discretionary portion of accruals. Reporting opacity is defined as the sum of absolute discretionary operating accruals over the past three years.

- 33.
For the balance-sheet-based measure, I define operating accruals as change of net current operating assets minus depreciation and amortization, and I use the Jones model (Jones, 1991) to estimate the discretionary portion of accruals. I use the Jones model instead of the modified Jones model because the former makes it easier to decompose discretionary operating accruals into discretionary portions of accrual components.

- 34.
Because the mean value of

*DACC*is zero, the bottom five deciles of*DACC*(*HIGH_DACC*= 0) mainly include negative*DACC*. - 35.
In model M2,

*DΔCOA*_{ t },*DΔCOA*_{ t−1 }, and*DΔCOA*_{ t−2 }are all significantly positively associated with*VCRASH*_{ t+1 }and*CRASH*_{ t+1 }, while none of*DΔ-COL*_{ t },*DΔ-COL*_{ t−1 },*DΔ-COL*_{ t−2 },*DDP*_{ t },*DDP*_{ t−1 }, and*DDP*_{ t−2 }is significantly positively associated with*VCRASH*_{ t+1 }or*CRASH*_{ t+1 }when*DACC*is positive (*HIGH_DACC**=**1*). - 36.
- 37.
Ak et al. (2015) also find earnings preannouncement/updated guidance and other firm announcements as two additional important events leading to price crashes. Therefore I expect the positive association between accruals and price crashes to also exist over the non-announcement weeks.

- 38.
The probability of a weekly price crash over an earnings announcement week is calculated as follows: for each year, I collect earnings announcement weeks over the next year for all firms within the same accrual decile. I then calculate the probability of observing a weekly price crash among these firm-weeks. The probability of a weekly price crash over a non-announcement week is calculated similarly.

- 39.
As each week has only one weekly return observation, it is not feasible to define a variable that mimics

*VCRASH*_{ t+1 }on a weekly frequency.

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## Acknowledgments

I thank my dissertation chair, Jake Thomas, for his much-appreciated guidance and help and members of my dissertation committee—Kalin Kolev, Alina Lerman, and Frank Zhang—for their thoughtful comments and suggestions. I also thank Richard Sloan (editor) and two anonymous referees for their valuable input. The manuscript has benefitted from the comments of Richard Frankel, Nikunj Kapadia, Edward Li, Yue Li, Edward Riedl, Theodore Sougiannis, Shyam Sunder, Tsahi Versano, Eric Yeung, and workshop participants at Baruch College, Boston University, University of Illinois at Urbana-Champaign, Washington University in St. Louis, Yale School of Management, and the 2013 AAA annual meeting.

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## Appendix

### Appendix

See Table 11.

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### Cite this article

Zhu, W. Accruals and price crashes.
*Rev Account Stud* **21, **349–399 (2016). https://doi.org/10.1007/s11142-016-9355-1

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### Keywords

- Accruals
- Crashes
- Bad news hoarding
- Default risk

### JEL Classification

- G12
- M41