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Firms' profit instability and the cross-section of stock returns: Evidence from China
Journal Pre-proof Firms’ Profit Instability and the Cross-Section of Stock Returns: Evidence from China Libo Yin (Conceptualization) (Methodology) (Formal analysis) (Investigation) (Visualization) (Writing - review and editing) (Project administration) (Funding acquisition), Ya Wei (Software) (Validation) (Data curation) (Writing - original draft), Liyan Han (Resources) (Supervision)
PII:
S0275-5319(19)30825-6
DOI:
https://doi.org/10.1016/j.ribaf.2020.101203
Reference:
RIBAF 101203
To appear in:
Research in International Business and Finance
Received Date:
17 July 2019
Revised Date:
12 February 2020
Accepted Date:
15 February 2020
Please cite this article as: Yin L, Wei Y, Han L, Firms’ Profit Instability and the Cross-Section of Stock Returns: Evidence from China, Research in International Business and Finance (2020), doi: https://doi.org/10.1016/j.ribaf.2020.101203
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Firms' Profit Instability and the Cross-Section of Stock Returns: Evidence from China
Author information: Libo Yina, * a School
of Finance, Central University of Finance and Economics, Beijing, China
Ya Weia School of Finance, Central University of Finance and Economics, Beijing, China
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a
Liyan Hanb b
School of Economics and Management, Beihang Univeristy, Beijing, China
* Corresponding author.
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Professor.
Address: 39 South College Road, Haidian District, Beijing, 100081, China
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Email: [email protected] or [email protected] (Libo Yin)
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Graphical abstract
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Firm’s profit instability
Cross-sectional stock returns
Negatively predictive power
Explanation for this predictive power
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Yes Irrational: Mispricing explanation
Better recent past performance
The negative relationship is more significant among stocks with particular charateristics
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More lottery-like payoffs
Higher arbitrage risk
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Rational: Risk based explanation
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Abstract: This study utilizes samples from the Chinese A-share market to examine the relation between a firm’s profit instability and cross-sectional stock returns. The empirical evidence indicates that firms with high profit instability have substantially lower future stock returns than
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those with low profit instability. The predictive information contained in profit instability is not subsumed by the level of profitability or the volatility of cash flow and is robust after controlling
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for well-known firm characteristics and risks. In addition, the long-term predictive performance of the firm’s profit instability is permanent over at least five years. Moreover, the profit instability
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effect is stronger among firms with better recent past performance, more lottery-like payoffs, and higher arbitrage risk. This finding suggests that the immaturity of investors and high constraints on arbitrage are the main sources of the profit instability effect in the Chinese market, which is consistent with the implications of behavioral mispricing explanations. Our investigation enriches the study on profitability anomalies by uncovering profit instability as an incremental signal in predicting stock returns. Furthermore, this study provides a novel view to better understand the mechanisms of the anomalies related with firms' profitability in undeveloped stock markets of 2
emerging economies, thereby benefiting investors from all over the world to seek more efficient investment strategies.
JEL Classification: G12; G14
Keywords: Profit instability; Predictive power; Expected returns; Chinese stock market; Mispricing
1. Introduction Emerging literature has decidedly established that the level of a firm’s profitability determines
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future stock returns (Cohen, Gompers, and Vuolteenaho, 2002; Fama and French, 2006, 2008;
Griffin and Lemmon, 2002; Haugen and Baker, 1996; Novy-Marx, 2013). Fama and French (2015, 2018) and Hou, Xue, and Zhang (2015, 2017) included profitability as a factor in new multifactor
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asset pricing models to explore numerous well-documented anomalies. Barillas and Shanken (2018) provided further evidence that the recent models by Hou, Xue, and Zhang (2015, 2017) and Fama
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and French (2015, 2018) are dominated by value and profitability factors.
However, some problems remain unresolved. On one hand, the strength of the documented
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effect varies across studies (e.g., Fama and French, 2006, 2008 v.s. Novy-Marx, 2013). Fama and French (2015, 2018) claimed that their five-factor asset pricing model, designed to capture patterns
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in returns due to risks associated with profitability, is invalid and that the performance of this model is sensitive to the choice of the profitability factor. On the other hand, the explanation concerning the profitability premium from a theoretical perspective generates mixed views. From the rational
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expectations perspective, Q theory with investment friction provides a potentially rational explanation for the profitability effect (Li, Livdan and Zhang, 2009; Hou et al., 2015, 2017; Jiang
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et al., 2018). By contrast, Wang and Yu (2013), Lam, Wang, and Wei (2016), and others proposed explanations based on behavioral mispricing. They argued that investor behavior cannot fully reflect the information embedded in a firm’s profitability due to behavioral biases. These mixed views call for further investigation regarding the nature and extent of the anomalies surrounding firm profitability, which motivates the work in this study. This study contributes to the literature by indicating that a firm’s current level of profitability
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cannot give a full picture of the firm’s prospects for future stock returns. Specifically, the level of profitability reflects a firm’s current efficiency and advantages in the context of the existing competitive environment that allow it to produce a return on an investment based on its resources. However, the overall competitive environment of the product markets in which a firm operates is not static. With the passing time, firm performance changes due to alterations in the firm’s own competitive strength as does the overall competitive environment. Unlike consistently strong earnings, strong earnings in one quarter do not necessarily suggest a strong firm profitability, which could be used to predict future stock returns (Loh and Warachka,
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2012). According to Campbell, Giglio, Polk and Turley (2018), if firm profits suffer from cash flow shocks, they are likely to be permanent. This means that rational investors have no reason to expect the stock price to rebound to previous levels. However, if profit declines are due to discount rate
shocks or variance shocks, they are likely to be temporary. Accordingly, rational investors can
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expect the stock price to rebound to previous levels. Therefore, multiquarter variations in the path of profitability, which reveals the struggles that a firm has encountered in arriving at its current level
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of profitability, may highlight the prospects for future stock returns. The following example
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illustrates our point.
For instance, Luzhou Laojiao and Wu Liang Ye, two well-known firms in the Chinese stock market, have already become the largest emerging stock market in the world. Although they had
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similar levels of profitability from 2009 to 2017, as presented in Figure 1, the upward trend in the price of Wu Liang Ye is obviously more pronounced than that of Luzhou Laojiao in the five most
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recent years. In Figure 1, during the same period, the fluctuation in profitability, measured by ROA, of Wu Liang Ye is significantly smaller than that of Luzhou Laojiao. Accordingly, we hypothesize
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that firms with a higher stability in profitability will outperform those with a lower stability in profitability after accounting for the overall level of profitability. [Insert Figure 1 Here]
Our investigation focuses on the Chinese mainland stock market to test this hypothesis. Exploring the pricing mechanism of the Chinese stock market is crucial for investors worldwide as the market develops (Carpenter and Whitelaw, 2017; Carpenter, Lu and Whitelaw, 2018). Researchers have examined the price premium of A shares and the firm-specific information content 4
of prices. These researchers have thus provided new evidence on informational and behavioral effects on prices and have analyzed unique cross-sectional patterns in returns. Additionally, the Chinese stock market possesses unique features such as higher retail investor rates, price-limit rules, and short-selling restrictions; however, it is relatively underdeveloped (Chang, Luo, and Ren, 2014; Gu, Kang, and Xu, 2018; Lepone, Wen, Wong, and Yang, 2019; Liu, Gu, and Lung, 2016; Nartea, Kong, and Wu, 2017; Yao, Wang, Cui, and Fang, 2019; Yao, Ma, and He, 2014; Yang et al., 2019). These features may induce a higher likelihood of mispricing and investment friction, thereby providing a powerful test for competing theories. Focusing on the Chinese stock market thus gives
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us a promising proxy for understanding global stock returns. Our analysis of the above hypothesis proceeds in three steps. First, we examine the profit instability effect in the Chinese stock market by testing whether a firm’s profit instability provides
incremental predictive information about future stock returns beyond the information contained in
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the level of profitability. Following Novy-Marx (2013) as well as Jiang, Qi, and Tang (2018), we consider return on assets (ROA) and return on equity (ROE) as the appropriate measure of a firm’s
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profitability. We estimate profit instability each month by regressing the changes in profitability
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relative to that in the previous year on a time trend. The residual variance of this regression is our measure of the firm’s profit instability for that month. A larger value of the residual variance indicates that the firm has recently experienced a higher profit instability. Following Hou et al.
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(2015), we form value-weighted profitable decile portfolios by single and double sorting measures of a firm’s past profit instability. We determine that a firm’s past profit instability provides
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significant incremental predictive information about future returns. Firms with more unstable profitability are relatively overpriced in the stock market, whereas firms with more stable
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profitability are marginally underpriced, leading to return predictability. The negative predictive power of profit instability for subsequent stock returns remains significant when we control for wellknown firm characteristics and risks in the cross-section analysis. These include firm size (Banz, 1981), book-to-market ratio (Fama and French, 1993), Beta (Frazzini and Pedersen, 2014), momentum (Jegadeesh and Titman, 1993), idiosyncratic risk (Ang et al., 2006), MAX (Bali, Cakici,
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and Whitelaw, 2011),1 and turnover (Chordia, Subrahmanyam and Anshuman, 2001). Moreover, this ‘‘profit instability effect’’ is robust when controlling for the firm’s level and volatility of profitability, and this profit instability predicts returns up to five years later. Next, we conduct empirical tests to explore the rational risk explanations and assess whether this predictive relation represents a manifestation of rational pricing based on compensation for risk or irrational mispricing. If pricing is rational, then the predictive relation between profit instability and stock returns should reflect compensation for some form of risk associated with that profit instability. Following Wang and Yu (2013) and Daniel and Titman (1997), we employ a systematic
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approach to examine whether the profit instability effect can be explained by the loadings of the mimicking factors. We determine that the evidence does not support an argument based on rational risk compensation.
Alternatively, the profit instability effect could result from irrational mispricing associated with
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a firm’s profit instability. In the third step, considering the features of Chinese stock market, we
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propose three hypotheses and conduct empirical tests to explore behavioral mispricing. The extent to which the profit instability effect reflects mispricing should be larger among firms characterized
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by a good recent past performance (Bange, 2000; Ng and Wu, 2007; Bohl and Siklos, 2008), high lottery-like payoffs (Bali, Cakici, and Whitelaw, 2011; Nartea, Kong, and Wu, 2017; Zhong and Gray, 2016), and high arbitrage risk (Stambaugh et al., 2015; Pontiff, 2006). Our empirical evidence
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supports this inference, which indicates that firms with higher profit instability are typically associated with a higher likelihood of mispricing. The results imply that the immaturity of investors
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and high constraints on arbitrage are the main sources of mispricing in our profit instability effect. Our main contributions in this study are two-fold. First, we extend the existing studies on
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profitability anomalies and suggest an alternative investment strategy in practice. Specifically, we uncover an incremental signal of a firm’s profit instability, which measures a recent dynamic pattern of a firm’s profit, to predict future stock returns. Accordingly, a monthly hedge portfolio strategy
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Using a stock’s maximum historical return to capture the stock’s lottery characteristics, Bali et al.
(2011) proposed the MAX effect, which reveals the negative relation between the maximum historical return and future cross-sectional stock returns. 6
based on going long stocks with the lowest profit instability and shorting stocks with the highest profit instability yields an average return close to 0.5–0.7% per month in the Chinese stock market historically. Second, our investigation enriches the growing asset pricing literature concerning the Chinese stock market, which has become a crucial part of the global capital markets. This will help investors to better understand the pricing mechanisms of this emerging stock market. Literature explaining the profitability premium is relatively new (Garlappi and Yan, 2011; Hou et al., 2015, 2017; Jiang et al., 2018; Lam, Wang, and Wei, 2016; Li, Livdan, and Zhang, 2009; Ma and Yan, 2015; Wang
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and Yu, 2015). Our study provides evidence that the negative relation between a firm’s profit instability and cross-sectional stock return is more likely attributed to behavioral mispricing than
rational risk-based explanations. However, this result runs contrary to the findings of Jiang, Qi, and Tang (2018), indicating the relatively low market and investment efficiency in the Chinese market,
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which has been increasing significantly.
The remainder of this paper is organized as follows. Section 2 presents our literature review.
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Section 3 discusses the data and calculation of our profit instability measures. Section 4 uses the
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portfolio test and Fama–MacBeth regression analysis to assess the predictive power of profit instability for cross-sectional stock returns. Section 5 investigates the risk-based rational pricing and
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behavioral mispricing explanations for the profit instability effect. Section 6 concludes the paper.
2. Literature review
Several recent papers have focused on the relation between a firm’s profitability and future
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cross-sectional stock returns. Using samples from the US stock markets, researchers determined that firms with higher profitability have substantially higher future stock returns than those with lower
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profitability (Cohen, Gompers, and Vuolteenaho, 2002; Fama and French, 2006, 2008; Griffin and Lemmon, 2002; Haugen and Baker, 1996; Novy-Marx, 2013). In emerging stock markets, the positive effect of firm profitability on stock returns is also pervasive. Berggrun, Cardona, and Lizarzaburu (2020) documented that this profitability premium exists in the stock markets of Latin America. Jiang, Qi, and Tang (2018) observed significant positive predictive power for future crosssectional stock returns in the Chinese stock market. In addition, investment managers such as
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Dimensional Fund Advisors and AQR have modified their trading strategies to incorporate measures similar to profitability (CFA Institute Magazine, 2014). However, from a theoretical perspective, explanations for the profitability premium present mixed views on the rationality or irrationality of the observed price effects. Q theory with investment frictions provides a potentially rational explanation for the profitability effect. The theory indicates that profitable firms generate higher expected returns than unprofitable firms holding fixed investments since profitable firms have higher marginal returns from investment. Moreover, firms subject to fewer investment frictions have lower marginal costs for their investment, thereby
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amplifying the profitability premium. One particularly puzzling observation is that firms with high profitability behave more like growth firms, whereas firms with low profitability behave like value firms. However, value firms are well known to earn higher average returns than growth firms (Fama
and French, 1992). In addition, the profitability premium has also been related to investment-
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specific technology shocks (Kogan and Papanikolaou, 2013) and credit risk (Ma and Yan, 2015). Meanwhile, researchers have presented evidence to support explanations based on irrationality.
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Wang and Yu (2013) as well as Lam, Wang, and Wei (2016) have indicated that underreaction to the
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information embedded in a firm’s profitability figures is the basis of the profitability premium. Moreover, mispricing may not be instantly traded away due to limits to arbitrage (Shleifer and Vishny, 1997). However, such profitability-related mispricing can persist for as long as 10 years
et al., 2015).
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without being corrected, which is seemingly inconsistent with irrational pricing explanations (Ball
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In recent studies, some researchers have suggested that the recent dynamics of a firm’s profits should be considered. Mohanram (2005) developed fundamental signals pertaining to the stability
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of a firm’s earnings and growth to identify stocks less likely to be overvalued due to naïve extrapolation by stock markets. Akbas, Jiang, and Koch (2017) explicitly focused on the information content of the recent trend in a firm’s profitability. Huang (2009) employed the standard deviation of cashflow scaled by book equity to measure a firm’s cashflow volatility and reveal its negative predictive power for future stock returns. The aforementioned studies have established a large framework on the relation between a firm’s profitability and stock returns. Following this literature, based on a dynamic view, we focus 8
on the recent profit instability, which is distinct from previous studies, and investigate whether this indicator could be a stand-alone determinant of future stock returns.
3. Data and variable definitions 3.1 Data Our sample includes all Chinese A-share firms with quarterly accounting data and monthly returns sourced from the China Stock Market and Accounting Research Database. Following standard sample screening procedures (Akbas et al., 2017; Jiang et al., 2018), we exclude financial
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firms as well as firms with special treatment (st) and negative book-to-market ratios, which are distressed and lack market liquidity. As the quarterly financial reports of Chinese list firms are available only after 2002 and the measure of firms’ profit instability presented later is computed
based on the data available in at least the most recent eight quarters, the sample used in our empirical
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test spans from January 2004 through June 2018. Meanwhile, this sample period also helps ensure the uniformity and quality of accounting data. This is because accounting fraud, stock price
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manipulation, and speculation in the Chinese stock market, which were prevalent in the early years before 2000, were effectively limited by increasing market transparency, accounting quality, and
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protection of minority shareholders after 2000. 3.2. Measures of firms’ profit instability
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In an analogous investigation, Huang (2009) employed the standard deviation of cashflow scaled by book equity to measure a firm’s cashflow volatility, similar to the firm’s profit instability
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measure in our study. He demonstrated its negative predictive power for future stock returns. However, the cashflow volatility measure employed by Huang (2009) cannot present a complete
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picture of the instability of a firm’s profitability. Huang’s cashflow volatility is a static indicator, which measures the volatility of the level of a firm’s profitability. A dynamic indicator should be used to measure the volatility of change in a firm’s profitability.2
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Different with the cashflow volatility proposed by Huang (2009), our indicator is a dynamic
version of indicator to measure the firm's profit instability. For example, considering a firm A, whose profitability increases from 1 to 10 at the rate of 1 over period 1 to 10, following Huang 9
As the largest emerging economy, China has experienced rapid growth and upgrading of its industrial structure. In this macroeconomic background, the profitability of Chinese firms is subject to a continuous change in a trend that can generally be anticipated by investors. It is unreasonable to transmute this expectation into measures of a firm’s profit instability that imply unexpected uncertainty or risk in a firm’s profitability. Therefore, this study proposes a dynamic indicator to measure a firm’s profit instability, which we define below. We define the profit instability of firm i as the residual variance from the rolling regressions of that firm’s profitability change relative to that in the previous year on the time trend. Specifically,
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the procedure comprises three following steps. First, following Hou et al. (2015, 2017) and Jiang et al. (2018), we compute the profitability of all firms in our sample for every quarter q. To provide a
comprehensive characterization, we employ two different measures of profitability: ROA and ROE. Second, we calculate the profitability change relative to that in the same quarter in the previous year
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to capture the dynamic of the firm’s profitability and eliminate the seasonal effects of quarterly variables. Furthermore, let R O A and R O E denote the ROA and ROE changes for firm i in quarter iq
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iq
q, respectively. Finally, in practice, an investor would be likely to extrapolate the future change in
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a firm’s ROA and ROE based on previous trends. Therefore, using the most recent publicly available R O A iq
and R O E from step two in the preceding five years, we run the iq
following regressions of R O A and R O E on a deterministic time trend for each firm i in month t,
where
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respectively.
iq
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iq
T r e n d 1, 2 ,
,1 2
R O A iq a
ROA
bi
R O E iq a
ROE
bi
ROA
T r e n d iq
ROE
ROA
T r e n d iq
ROE
(1)
, denotes the time trend variable in the regressions. We include the time
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trend due to the profit trend effect identified by Akbas et al. (2017). For example, if equation (1)
(2009)'s method, the profit instability of firm A would be in a high level. By contrast, in dynamic view, firm A's profit instability would be in the lowest level, which implies its increase of profitability is 1, which is unchanged in every period. In this context, we conjecture that a firm would exhibit absolutely different level of profit instability in static and dynamic views. 10
does not include the trend term, a firm’s profitability with an obviously positive or negative trend would also have high variance. Accordingly, it would be difficult to distinguish whether the high variance comes from profit instability or the profit trend discussed by Akbas et al. (2017). This indicates that such a trend is positively associated with cross-sectional stock returns. Finally, we define the estimation of the residual variance from the regressions presented in equation (1) as the measures of profit instability for firm i in month t, denoted as In s R O A it and In s R O E it . For firm i, the increase in
In s R O A it
and In s R O E it implies that the firm has recently experienced a higher
instability in its profit growth.
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3.3 Summary statistics
In our analysis, we control for various other firm characteristics used to predict returns in the Chinese stock market. All the firm characteristics used in our test, including the control variables,
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are defined in Table 1. [Insert Table 1 Here]
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Table 2 presents the summary statistics for firm characteristics used in our empirical test. All data are winsorized by a level of 1% and 99% to minimize the influence of outliers on our results.
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This table indicates that the averages of InsROA and InsROE are 0.09 and 0.2, respectively, and their monthly average number of observations are both 1426.
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[Insert Table 2 Here]
4. Predictive ability of firms’ profit instability for stock returns
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In this section, we employ portfolio analysis and Fama–MacBeth regression to investigate the ability of a firm’s profit instability to predict the cross-sectional stock returns in the Chinese stock
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market. We explore the long-term historical performance of this predictive power. 4.1. Portfolio analysis sorted by firms’ profit instability 4.1.1. One-way sorting We begin our portfolio analysis using a one-way sorting approach. Specifically, at the beginning of each month t+1, we sort all stocks in our sample into decile portfolios based on the most recently available InsROA and InsROE. This step ensures that our test avoids look-ahead bias. Thereafter, we assume that the portfolios are held during month t+1 and that the monthly returns of 11
these portfolios are value-weighted. The result of this one-way sorting portfolio analysis is presented in Table 3. Here, “Low” refers to the stocks in the lowest profit instability decile, “High” refers to the stocks in the highest profit instability decile, and “H–L” is the hedge portfolio that is long stocks with the highest profit instability and short stocks with the lowest profit instability. [Insert Table 3 Here] The value-weighted monthly average excess returns of portfolios sorted by InsROA and InsROE are presented in the first row of Panel A and Panel B in Table 3. The results indicate that the stocks of firms in the lowest profit instability decile significantly outperform the stocks of firms
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in the highest profit instability decile. The monthly average excess returns for InsROA (InsROE)based profit instability deciles decrease from 1.09% (0.96%) to 0.42% (0.44%) for the lowest and
highest deciles, respectively. The hedge strategy—short stocks with the highest InsROA (InsROE) and long stocks with the lowest InsROA (InsROE)—earns an average value-weighted monthly
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return of 0.67% (0.52%) with a Newey–West t-statistic of 2.1 (2.23).
Table 3 reports the risk-adjusted returns based on the capital asset pricing model (CAPM) and
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Fama–French (1993, 2015) three- and five-factor models. Similar to the excess return, we find that
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the CAPM alphas and Fama–French alphas of the profit instability portfolios decrease from the lowest to highest decile. For example, the FF3 alpha of the lowest InsROA (InsROE) decile is 0.13% (−0.05%), whereas the alpha of the highest InsROA (InsROE) decile is −0.49% (−0.58%). The alpha
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of the hedge portfolio is −0.63% (−0.64%) with a Newey–West t-statistic of −3.56 (−4.44), which is statistically significant at the 1% level. The results measured by excess returns and the risk-
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adjusted returns indicate that profit instability measured by InsROA and InsROE negatively predict future stock returns in the Chinese stock market. This effect still exists even after controlling for the
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traditional CAPM and Fama–French three- and five-risk factors.3 Jiang et al. (2018) concluded that the profitability premium in the Chinese stock market
primarily results from the long leg rather than the short leg. This fact indicates that risk compensation is more likely to be the primary source of the profitability premium than mispricing.
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Because the results are robust for the different asset pricing models, in the following analysis,
we only present the FF3 alphas, which are most widely used in academic area and in practice. 12
This is because overvaluation is more difficult to correct than undervaluation due to short selling constraints. By contrast, the result presented in Table 3 indicates that the significantly negative Fama–French alpha of the hedge portfolios mainly results from the dramatic decline in the alphas of the highest profit instability deciles. This evidence indicates that the short leg seems to play a more important role in the profit instability effect, and mispricing is more likely to be the primary source of this effect than risk compensation (Jiang et al., 2018). 4.1.2. Robustness for double sorting
Controlling for size and BM
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Wang and Yu (2013) indicated that the profitability premium is more significant and larger in magnitude among firms with small market capitalization in US stock markets. Jiang et al. (2018)
found the opposite to be true in the Chinese stock market. Meanwhile, Novy-Marx (2013) and Jiang et al. (2018) documented that the profitability strategy belongs to an overall growth strategy, which
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indicates that the profitability premium is more pronounced among growth firms. Inspired by this
literature, this subsection employs a two-way dependent sorting portfolio approach to investigate
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the performance of the profit instability effect after controlling for firms’ market capitalization (Size)
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and book-to-market ratio (BM), the most prominent characteristics used to predict future returns (Fama and French, 1992, 2008).
First, for each month t, we sort all stocks into three portfolios using the 30th and 70th
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percentiles of two separate firm characteristics, including Size and BM. For Size (BM), stocks below the 30% breakpoint are regarded as “Small” (“Growth”), stocks between the 30% and 70%
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breakpoint are regarded as “Micro” (“Neutral”), and stocks above the 70% breakpoint are regarded as “Large” (“Value”). Second, within each portfolio, considering that the short leg is the primary
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source of the profit instability effect as concluded in Table 3 and to capture the effect more efficiently, we further sort the stocks into quintile portfolios based on the firms’ profit instability. Specifically, based on the firms’ InsROA and InsROE, the portfolio with the highest instability is labeled “High” and the portfolio with the lowest instability is labeled “Low.” Thus, we obtain 15 portfolios. Then, within each group in the first step, we construct hedge portfolios, “H–L,” which are long the “High” portfolio and short the “Low” portfolio. In addition, across the three groups in the first step, we construct “Average” portfolios by averaging the subportfolios labeled “Low,” “High,” and “H–L.” 13
Table 4 and Table 5 report the value-weighted monthly average excess returns and Fama–French alphas of the two-way dependent sorting portfolios by controlling for Size and BM. [Insert Table 4 Here] In Table 4, the “Average” rows indicate that the average returns and the Fama–French alphas of the hedge portfolios are significantly negative at a high confidence level. Specifically, in Panel A (B), the average return is −0.39% (−0.42%) with a Newey–West t-statistic of −2.58 (−2.77) and the Fama–French alpha is −0.37% (−0.45%) with a Newey–West t-statistic of −2.38 (−3.04). This evidence proves that the profit instability effect still exists even after controlling for the firm’s
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market capitalization (Size). We find that the profit instability effect is less prominent among larger firms. In particular, for
the large group, the hedge portfolio’s alpha is only −0.24% (−0.29%) and is not statistically
significant. This result provides more evidence that the profit instability effect is more likely to arise
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from mispricing than risk compensation. Because large stocks are always characterized by lower
arbitrage costs, the mispricing of stocks can be eliminated more easily by arbitragers in the stock
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market (Wang and Yu, 2013; Baker and Wurgler, 2006).
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In the recent research on the Chinese stock market, Liu et al. (2018) indicated that the shell effect from the smallest 30% of stocks plays an important role in determining stock price. The results in Table 4 imply that the shell effect is not the main source of our profit instability effect. Among
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the median groups, which exclude the smallest 30% of stocks, we still find that the average return and Fama–French alpha of the hedge portfolio are statistically significant at the 1% level.
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[Insert Table 5 Here]
In Table 5, by averaging the portfolios across three BM groups, we find that the hedge portfolios’
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average returns are negative; however, the average return in Panel A is modestly insignificant in statistic. The Fama–French alphas of the hedge portfolios in both panels A and B are significantly negative. Specifically, in Panel A, the hedge portfolio’s average return is −0.34% with a Newey– West t-statistic of −1.63, which is insignificant at the 10% level. In Panel B, the average return is significantly negative at −0.42% with a Newey–West t-statistic of −1.78. The Fama–French alpha of the hedge portfolios in Panel A (B) is −0.4% (−0.58%) with a Newey–West t-statistic of −1.78 (−2.56). In summary, similar to the analysis controlling for the firm’s market capitalization (Size), 14
the results in Table 5 document that the profit instability effect exists even after controlling for the firm’s book-to-market ratio (BM). Furthermore, in Table 5, we find that the profit instability effect is more pronounced among the growth stock groups than the other two groups. In Panel A (B), the Fama–French alpha of hedge portfolio among growth stock groups is −0.67% (−1.19%) with a Newey–West t-statistic of −2.51 (−3.86), which is larger and more significant than the alphas of the other two groups. This result presents more evidence to support the application of a value strategy in the Chinese stock market. If an investor selects stocks based on a value strategy, which means holding fewer growth stocks,
effect among growth stocks.
Controlling for the level and volatility of firms’ profitability
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they can efficiently avoid the negative influence arising from the more pronounced profit instability
As an extension of firms’ profitability, we are naturally concerned with whether our profit
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instability effect could be subsumed by the profitability premium, which indicates the strong predictive power of firms’ profitability for future stock returns. As mentioned above, the volatility
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of scaled cashflow proposed by Huang (2009) is similar to our measures of profit instability so that
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the profit instability effect could also possibly be subsumed by this volatility effect (Huang, 2009). Therefore, in this subsection, we will employ the two-way dependent sorting portfolio approach to investigate the profit instability effect while controlling for the level and volatility of firms’
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profitability. The level of a firm’s profitability is measured by ROA and ROE as defined in Table 1, and the calculation of the volatility of the firm’s profitability follows the procedure proposed by
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Huang (2009) using ROA and ROE.
Following the steps described in the previous subsection, for each month t, we sort all stocks
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into three portfolios using the 30th and 70th percentiles of the level and volatility of firms’ profitability. Stocks below the 30% breakpoint are denoted as “Low,” stocks between the 30% and 70% breakpoints are denoted as “Median,” and stocks above the 70% breakpoint are denoted as “High.” Second, within each portfolio, we further sort the stocks into quintile portfolios based on the firms’ profit instability. We then obtain five portfolios in each profitability group, including the “High,” “Low,” and “H–L” portfolios, which are identical to the definitions in the previous subsection. Finally, we construct the “Average” portfolios by averaging the “Low” to “High” and 15
“H–L” subportfolios across the three profitability groups. Table 6 and Table 7 report the valueweighted monthly average excess returns and Fama–French alphas of the two-way dependent sorting portfolios by controlling for the level and volatility of firms’ profitability. [Insert Table 6 Here] In Table 6, the average returns and Fama–French alphas of average hedge portfolios in Panel A and Panel B are all significantly negative. In particular, in Panel A (B) the average return is −0.39% (−0.33%) with a Newey–West t-statistic of −1.74 (−1.79) and the Fama–French alpha is −0.39% (−0.33%) with a Newey–West t-statistic of −2.73 (−2.76). We can therefore conclude that the profit
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instability effect would not be subsumed by the level of firm profitability measured by ROA and ROE.
Based on the result in Table 6, we find that the profit instability effect is weaker among firms
with a high level of profitability. For example, in Panel A (B), the Fama–French alpha of the hedge
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portfolio among the high profitability group is −0.02% (−0.34%), which is insignificant at 10% level. By contrast, the alphas of hedge portfolios among the other two groups are larger in magnitude
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and statistically significant. Similar to the results arrived at when controlling for firms’ book-to-
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market ratio (BM), we can conclude that an investor who selects stocks with high levels of profitability could achieve higher returns by removing the negative influence of the profit instability effect. Combining this with the result documented in Table 5, we can hypothesize that selecting
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stocks with high value and a high level of profitability is an efficient strategy to improve returns on investment, which is consistent with the conclusions of Novy-Marx (2013) and Jiang et al. (2018).
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[Insert Table 7 Here]
In Table 7, after controlling for volatility of firm profitability proposed by Huang (2009), we
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still find a pronounced profit instability effect. In panels A and B, we find that the average returns and Fama–French alphas of average hedge portfolios are all significantly negative. Specifically, in Panel A (B), the average return is −0.66% (−0.32%) with a Newey–West t-statistic of −3.14 (−2.42) and the Fama–French alpha is −0.78% (−0.6%) with a Newey–West t-statistic of −3.64 (−3.9). This evidence supports the dynamic view proposed in Section 3.2. We can conclude that as a static indicator, Huang’s cashflow volatility cannot present a complete picture of the firm’s profit instability in China. By contrast, our dynamic version of firm profit instability provides incremental 16
information for predicting cross-sectional stock returns that cannot be subsumed by a static indicator. In addition, we present the empirical evidence of our one-way sorting analysis based on the volatility of firm profitability in Appendix-Table 1. In panels A and B, we find that the average returns and Fama–French alphas are smaller and more insignificant in magnitude than the results in Table 3, which present one-way sorting analysis based on the firm’s profit instability. Furthermore, in panels C and D, when the most unstable 10% of stocks are excluded from the sample, the average returns and alphas are smaller and more insignificant. Hence, we suggest that the profit volatility effect proposed by Huang (2009) is more likely determined by our profit instability effect in the
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Chinese stock market. 4.2. Predictive power at the firm level
In this section, we extend our sorting analysis using a Fama–MacBeth regression approach that
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explicitly controls for other well-known stock characteristics documented to have predictive power for stock returns. Our main regression model is constructed as follows:
6MOM
it 1
7 IV O L it 8 M A X
it
it
5 B e ta it
(2)
9 T U R N it it 1
denotes the future return for firm I in month t+1,
In s R O A it
and In s R O E are the two it
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where R E T
it
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R E T it 1 In te r c e p t 1 In s R O A it ( In s R O E it ) 2 R O A it ( R O E it ) 3 S iz e it 4 B M
measures of the profit instability for firm i in month t, and the other independent variables, which
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are most recently available, are defined in Table 1. Specifically, we begin by estimating the coefficients each month and obtain the coefficients’ time series. Thereafter, we compute the mean coefficients as well as the adjusted robust t-statistic by averaging this time series and the Newey–
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West (1987) method. The results of these estimates are all presented in Table 8, which provides eight different model specifications that include various combinations of dependent and independent
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variables.
[Insert Table 8 Here]
In Table 8, the univariate regression results of models (1) and (5) show a negative and
statistically significant relation between a firm’s profit instability, measured by InsROA and InsROE, and the cross-sectional future stock returns. The coefficients of InsROA and InsROE in models (1) and (5) are −0.0245 and −0.0018, with corresponding Newey–West t-statistics of −2.12 and −2.08.
17
In models (2) and (6), which control for the level of profitability, we still observe that the coefficients of InsROA and InsROE are negative and statistically significant. Similarly, this result can also be found in models (3) and (7), which specify Size, BM, and Beta as the additional control variables. Finally, models (4) and (8) in Table 8 present the results of estimating the coefficients in Equation (2), which incorporates all control variables in our test. In these results, we can observe that the coefficients of the InsROA as well as InsROE are −0.0245 and −0.0017 with Newey–West t-statistics of −1.67 and −1.88, respectively, indicating that both the negative coefficients are significant at the 10% level. Overall, consistent with our two-way portfolio analysis, the Fama–
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MacBeth regressions provide more reliable and robust evidence for the profit instability effect, and this effect cannot be subsumed by other well-known predictors of stock returns.
In fact, this profit instability effect is consistent with the findings of Kogan, Li, and Zhang (2018). By decomposing gross profitability into a persistent component and a transitory component,
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they indicated that the predictive power of the persistent component of gross profitability for future
stock returns is short-lived. Only the transitory component of gross profitability, constructed as the
4.3. Long-term performance
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information about future stock returns.
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deviation of the gross profitability from its persistent component, contains more relevant predictive
In the preceding analysis, we explored the predictive power of firms’ profit instability for the
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one-head-month returns. To examine the profit instability effect more comprehensively, in this section, following Jegadeesh and Titman (1993) and Wang and Yu (2013), we construct hedge
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portfolios based on a firm’s profit instability with overlapping periods to highlight the long-term performance of this effect.
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Specifically, at the beginning of each month t, we sort all stocks into decile portfolios, which
are value-weighted, based on the most recently available InsROA and InsROE. We define “Low” and “High” as the lowest and highest profit instability deciles. “H–L” refers to the hedge portfolio that is long the “High” portfolio and short the “Low” portfolio. Then, we construct the overlapping portfolio by holding the hedge portfolio for a series of six-month windows in the five years after portfolio formation. For example, when the holding period is from the first month to sixth month, at month t, the overlapping portfolio is constructed by averaging the six portfolios, which are formed 18
at month t-6 to t-1. In Figure 2, we plot the average cumulative returns and risk adjusted returns with a holding period from 1 to 60 months for this hedge portfolio in terms of the value of one dollar invested in the hedge portfolio in month t = 0. [Insert Figure 2 Here] In Figure 2, we find that both the average cumulative returns and Fama–French alphas of the hedge portfolios seem to be permanent in the long run. Specifically, the evidence indicates that this overlapping profit instability hedge portfolio continues to appreciate slowly over the five-year holding periods, while the rate of increase becomes modestly slower when the holding period
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exceeds three years. Meanwhile, the result also indicates there is no obvious reversal in our profit instability effect, and we can hypothesize that this effect is more likely due to investor underreaction to the information embodied in a firm’s profit instability.
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5. Exploring the source of profit instability effect 5.1. Risk-based explanations
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We have thus far revealed the negative predictive power of a firm’s profit instability for future stock returns. However, we have still not provided an explanation for the profit instability effect. To
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further understand the source of the profit instability effect, we will provide additional analysis to highlight whether the said effect is due to rational pricing or irrational mispricing (Fama and French,
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2006). In this subsection, we first investigate the risk-based explanation by exploring the role of systematic risk in our effect.
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In the previous research, Daniel and Titman (1997) proposed a systematic approach to examine whether risk or mispricing explains the size and value premiums by constructing a factor-mimicking
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portfolio. If the stock return associated with a firm characteristic is indeed driven by underlying
systematic risk, this risk would be reflected in the factor-mimicking portfolio based on the firm characteristic. In other words, if risk is the main driver, the loading of this mimicking factor would provide a strong predictive power for cross-sectional stock returns. If not, the predictive power of the loading would be minimal, while the corresponding firm characteristic would still exhibit a significantly predictive power. In subsequent research, Wang and Yu (2013) applied this approach to test the profitability premium.
19
Following previous researchers, we employ this systematic approach to investigate our profit instability effect. First, following Wang and Yu (2013) and Fama and French (1993, 2015), we construct our profit instability mimicking factor, which is analogous to the value and profitability factors. We independently and evenly sort all stocks in our sample into two size groups and three profit instability (measured by InsROA and InsROE) groups, obtaining six value-weighted portfolios. Then, we define the profit instability mimicking factor as the average of the two low profit instability portfolio returns minus the average of the two high profit instability portfolio returns. Second, we compute the factor loadings for each stock in our sample by regressing the individual stock excess
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return on the factors, which include traditional Fama–French three factors and our profit instability factor. Third, we use Fama–MacBeth regressions to compare the ability of our profit instability
characteristic and factor loading to predict future returns. Furthermore, we use individual stocks as
The model specification is presented in Equation (3):
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test assets to avoid the possibility that tests may be sensitive to the portfolio grouping procedure.
9
R E T it 1 In te r c e p t 1 In s R O A it ( In s R O E it )
j O th e r _ c h a r a c te r is tic it j
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j2 9
1 b e ta _ In s R O A it ( b e ta _ In s R O E it )
(3)
k O th e r _ lo a d in g s it k
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k2
where O t h e r _ c h a r a c t e r i s t i c are identical with the control variables in Equation (2). In addition, j
it
factor loadings, including profit instability factor loadings denoted as b e ta _ In s R O A
it
( b e ta _ In s R O E it )
,
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are also contained in the model. The estimated results of the mean monthly coefficients and the Newey–West (1987) adjusted t-statistics in parentheses are reported in Table 9.
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[Insert Table 9 Here]
Table 9 shows no evidence to support that stock returns are influenced by the loadings of the
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profit instability factor. Across all eight regressions, including both the univariate and multivariate regressions, none of the time-series average monthly coefficients, which have magnitudes close to zero, are significant, with the Newey–West (1987) adjusted t-statistics ranging from 0.17 to 1.32; however, their positive signs are consistent with the theoretical prediction. In contrast, similar to the results in Table 8, the coefficients of profit instability measured by InsROA and InsROE are still negative and statistically significant. Therefore, the results, which indicate that profit instability factor loadings have no predictive power for stock returns, imply that the profit instability effect is 20
unlikely to come from risk compensation. In other words, irrational mispricing is more likely to be the main source of the profit instability effect than rational pricing. This conclusion also responds to the results in Table 3 and Table 4, which suggests that the short leg plays a more important role in our profit instability effect. 5.2. Mispricing explanations 5.2.1. Hypothesis development In this subsection, combined with the features of the Chinese stock market, we will present additional empirical evidence to explore several explanations for the profit instability effect arising
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from mispricing. It is well known that high levels of speculation, irrationality, and inefficiency are still pronounced features of the Chinese stock market; however, this relatively young market has
grown to become the largest emerging market in the world. In particular, the prevalence of retail
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investors, who are “noise traders” and are presumably more prone to behavioral biases, is widely thought to be the primary reason for prevailing irrationality (Han and Li, 2017; Cheema and Nartea,
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2017; Hsu et al., 2018; Koesrindartoto, Aaron, Yusgiantoro and Dharma, 2020). Hence, irrational investment behaviors are the most plausible sources of our profit instability effect. In our analysis,
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we focus on investors’ positive feedback trading and lottery preferences, which are frequently discussed in both practice and academic research.
Positive feedback trading
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Positive feedback traders are defined as investors who discover seeming trends in past prices and trade based on the expectation that these trends will persist. The literature has documented that
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these irrational traders widely exist in practical stock markets, and positive feedback trading is more pronounced among retail investors and in the emerging markets, including the Chinese stock market
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(Bange, 2000; Ng and Wu, 2007; Bohl and Siklos, 2008). Hence, we can hypothesize that positive feedback trading is likely to be an underlying reason for the underreaction to the profit instability effect. Specifically, among stocks with better historical performance, which are more attractive to positive feedback traders, the negative information of high profit instability is more unlikely to be reflected in current prices. This is because the preference of positive feedback traders for this type of stock pulls prices to a relatively higher level. By contrast, among stocks with poor historical performance, the negative information of high profit instability is more likely to be reflected in 21
current prices. This is because the aversion of positive feedback traders to this type of stock pushes prices to a relatively lower level. Following this logic, we can conclude that the historical performance of stocks is positively associated with the overpricing of high profit instability stocks. We should also realize the asymmetry of the profit instability effect, which indicates that the short leg will be the primary source of the effect so that the change in the overpricing of high profit instability stocks will be dominant. Therefore, we present our first hypothesis: Hypothesis 1: The profit instability effect will be more prominent among stocks with a better historical performance. Lottery preference
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Based on the preference for lottery-like assets in the stock market, Bali et al. (2011) proposed the MAX effect, which reveals the negative relation between the maximum historical return and
future cross-sectional stock returns. In subsequent studies, the empirical evidence suggested that
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this MAX effect is robust and appears stronger in emerging stock markets (Egginton and Hur, 2018; Seif et al., 2018; Zhong and Gray, 2016; Nartea et al., 2017). Similar to positive feedback trading,
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lottery preference is also an underlying reason for the profit instability effect. In particular, among
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lottery-like stocks, lottery preference by investors places upward pressure on prices, thereby increasing the underreaction to the negative information embodied in high profit instability and eliminating the underreaction to the positive information embodied in low profit instability.
hypothesis:
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Furthermore, considering the asymmetry of the profit instability effect, we reach our second
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Hypothesis 2: The profit instability effect will be more prominent among lottery-like stocks. Arbitrage risk
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In addition, the literature has presented evidence that arbitrage risk seems to play an important role in stock mispricing (Stambaugh et al., 2015; Pontiff, 2006). In particular, Akbas et al. (2017) and Wang and Yu (2013) documented that both the profit trend effect and the profitability premium are stronger among stocks with high arbitrage risk. Thus, for our profit instability effect, it is necessary to examine whether arbitrage risk could provide an alternative explanation. In general, because high arbitrage risk always implies more limits on arbitrage trading, mispricing would be more difficult to correct. Hence, this logic could also be applied to the profit instability effect, and 22
we thus propose our third hypothesis: Hypothesis 3: The profit instability effect will be more prominent among stocks with high arbitrage risk. 5.2.2. Empirical test In our empirical tests, we employ the two-way dependent sorting portfolio approach as well as Fama–MacBeth regressions to examine the three hypotheses proposed above using the history cumulative return (MOM), maximum history daily return (MAX), and idiosyncratic volatility (IVOL) as proxies for past performance (Akbas et al., 2017; Cheema and Nartea, 2017), lottery lottery-like
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characteristics (Bali et al., 2011; Egginton and Hur, 2018; Nartea et al., 2017), and arbitrage risk of stocks (Gu et al., 2018; Jiang et al., 2018; Akbas et al., 2017; Stambaugh et al.. 2015; Wang and Yu, 2013), respectively.
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In this two-way portfolio analysis, we specify MOM, MAX, and IVOL as the control variables. First, at the beginning of each month t, we sort all stocks into two portfolios using the median of the
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control variables above. Stocks below the 50% breakpoint are denoted as “Low,” and stocks above the 50% breakpoint are denoted as “High.” Second, within each portfolio, we sort the stocks into
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decile portfolios according to a firm’s profit instability (measured by InsROA and InsROE). We construct five different hedge portfolios that are long the portfolios with the highest profit instability and short the first five portfolios with the lowest profit instability. Third, we compute the difference
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in the Fama–French alphas of the five hedge portfolios between the high and low subgroups to capture the changes in our profit instability effect across the different types of stocks characterized
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by the control variables. Then, we average the five hedge portfolios within high and low subgroups and calculate their Fama–French alphas as well as their difference in the average portfolios’ alphas
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between the two subgroups. Finally, the alphas of profit instability portfolios in different subgroups are plotted in Figure 3, and the results of Fama–French alphas are presented in Table 10. [Insert Figure 3 Here]
Figure 3 plots the changing trajectory of Fama–French alphas of portfolios in the different subgroups. From this evidence, we find a descending trend of the alphas from low to high profit instability portfolios across stock groups characterized by high historical cumulative return (MOM), maximum historical daily return (MAX), and idiosyncratic volatility (IVOL). For example, when 23
controlling for MOM, in the high MOM group, we can observe a prominent decline of the Fama– French alphas after the eighth profit instability portfolio, whereas in the low MOM group, the Fama– French alphas fluctuate in a small range. When controlling for MAX and IVOL, we find similar results, which supports the arguments in Hypothesis 1 and Hypothesis 3. [Insert Table 10 Here] Table 10 reports the Fama–French alphas of the two-way sorting portfolios while controlling for the three variables above. In this table, we find that the empirical evidence is consistent with our hypotheses. Specifically, among the high MOM, MAX, and IVOL groups, which indicate the stock
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groups with better historical performance, lottery characteristics, and high arbitrage risk, the Fama– French alphas of the hedge portfolios based on profit instability are significantly negative, whereas
among the corresponding low groups, only a few alphas are significantly negative and the alphas are also smaller in magnitude. Furthermore, most of the differences in the alphas between the hedge
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portfolios among the high and low groups are negative and statistically significant. The differences in the average hedge portfolios are significantly negative. Overall, we can conclude that the results
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in Table 10 also support the above hypotheses.
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Meanwhile, we employ the Fama–MacBeth regressions to test the arguments of the three hypotheses by adding the interaction term into the original model, obtaining Equation (4) as follows: R E T it 1 I n t e r c e p t 1 I it | I n s R O A it ( I n s R O E it ) 2 I it | I n s R O A it ( I n s R O E it ) H
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+ 2 R O Ait ( R O E it ) 3 S i z e it 4 B M 6 I it
MOM
7 I it
IV O L
8 I it
L
it
,
5 B e t a it
9T U R N
M AX
it
(4)
it 1
where all variables are identical with the variables in Equation (2), except for I and I , which H
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it
L
it
indicate the dummy variable formed by the median of the MOMit, MAXit, or IVOLit. Specifically, if
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MOMit , MAXit, or IVOLit is larger than its median, I is one and I is zero; if not, I is zero and I H
L
it
H
it
it
L it
is one. The estimated results of Equation (4) are presented in Table 11. [Insert Table 11 Here]
If the hypotheses are true, we would expect to observe significantly negative coefficients of H
I it | I n s R O A it ( I n s R O E it )
in Equation (5) and significant coefficients of
models (1) to (6), we find that all of the six coefficients of significant. Meanwhile, the six coefficients of
L
H
I it | I n s R O A it ( I n s R O E it )
I it | I n s R O A it ( I n s R O E it )
24
L
I it | I n s R O A it ( I n s R O E it )
. In
are positive and
are all insignificant and
small in magnitude. Similar to the two-way portfolio analysis, this result is consistent with our expectations derived from the three advanced hypotheses. In summary, based on the evidence in Figure 3, Table 10, and Table 11, we can conclude that positive feedback trading, lottery preferences, and arbitrage risk can indeed provide explanations for the underreaction in our profit instability effect. In previous studies, researchers have documented several models to provide theoretical explanations for underreaction in the stock market. For example, Hong and Stein (1999) constructed an information diffusion model, which indicated that underreaction is mainly due to the gradual diffusion of private information across a news
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watching population. Coibion and Gorodnichenko (2012, 2015) and Bouchaud, Krueger, Landier, and Thesmar (2018) indicated that it can be optimal for investors to revise their expectations sporadically. As a result, expectations are sticky and can underreact to fundamental information,
implying the prevalence of underreaction. In fact, our conclusion that positive feedback trading,
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important extension and application of these models.
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lottery preferences, and arbitrage risk are the main reasons for the profit instability effect is an
6. Conclusion
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This study indicates that the instability in a firm’s profitability exhibits negatively and significantly predictive power for its future stock returns in the Chinese stock market. The results
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indicated that firms with high profit instability generated substantially lower future stock returns than those with low profit instability. A hedge portfolio that is long stocks with the lowest profit instability and short stocks with the highest profit instability yields a return of roughly 0.6% per
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month. This return mainly comes from the short leg. In addition, the empirical evidence documents that the predictive power of a firm’s profit
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instability is robust even when controlling for various well-known factors that affect future stock returns, including the volatility of profitability proposed by Huang(2009), which is similar to our measure of profit instability. The results of the two-way sorting portfolio indicated that the predictive power is weaker in stocks with high value and high levels of profitability. Further investigation of long-term performance indicates that the predictive power of a firm’s profit instability will be permanent over at least five years.
25
By employing the approach proposed by Daniel and Titman (1997), we find that irrational mispricing rather than rational risk compensation is more likely to be the reason undergirding the profit instability effect. In further analysis, we explore the alternative explanations for the source of this effect. We find that positive feedback trading, lottery preferences, and arbitrage risk are responsible for the profit instability effect, which is more pronounced among firms characterized by better recent past performance, more lottery-like payoffs, and higher arbitrage risk. This evidence implies that both the immaturity of investors in the Chinese market and high constraints on arbitrage
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are the main sources of the mispricing observed in our profit instability effect.
CRediT author statement
Libo Yin: Conceptualization, Methodology, Formal analysis, Investigation, Visualization, Writing-
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Reviewing and Editing, Project administration, Funding acquisition
Ya Wei: Software, Validation, Data curation, Writing- Original draft preparation
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Acknowledgements
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Liyan Han: Resources, Supervision
This research is financially supported by the National Natural Science Foundation of China under grant Nos. 71871234 and 71671193, and Program for Innovation Research in Central
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University of Finance and Economics, and the "Young talents" Support Program in Central
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University of Finance and Economics (QYP1901).
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Table 1 Variables description and construction. Variable name Panel A: Explanatory variable
Description and construction
30
InsROA
Profit instability based on ROA, which is the residual variance from rolling regressions of the profitability changes relative to the previous year on the time trend. Profit instability based on ROE, which is the residual variance from rolling regressions of the profitability changes relative to the previous year on the time trend.
InsROE
Jo
ur
na
lP
re
-p
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Panel B: Control variable ROA Return on assets, which is the quarterly net income divided by the average of the current quarterly total assets and 1-quarter-lagged total assets. ROE Return on assets, which is the quarterly net income divided by the average of the current quarterly equity and 1-quarter-lagged equity. Size Market value of tradable shares, which is taken logarithmic transformation BM Book-to-market equity ratio, which is the quarterly book value of equity divided by the market value of total shares. Beta Market beta, which is defined as the coefficient from regressing daily stock returns on market returns using previous one year sample. MOM Momentum, which is the cumulative stock return from month t-1 to t-6. IVOL Idiosyncratic volatility, which is defined as the standard deviation of the residual from regressing daily stock returns on Fama-French three factors using previous three months sample. MAX Average of maximum five history daily returns in previous one month. TURN Average of daily turnover defined as daily trading volume divided by the total number of shares outstanding in previous one months.
31
Table 2 Summary statistics.
InsROA InsROE ROA ROE Size BM Beta MOM IVOL MAX TURN
Mean 0.09 0.2 0.01 0.01 14.65 0.43 1.19 0.13 0.02 0.04 0.03
Std 2.19 2.82 0.02 0.17 0.97 0.27 0.38 0.31 0.01 0.01 0.02
Min 0 0 -0.19 -6.94 12.36 0.02 -0.48 -0.54 0.01 -0.02 0
25% 0.01 0.01 0 0.01 13.99 0.26 0.96 -0.06 0.02 0.03 0.01
Median 0.01 0.03 0.01 0.02 14.55 0.38 1.2 0.07 0.02 0.03 0.02
75% 0.03 0.05 0.02 0.03 15.2 0.54 1.43 0.24 0.03 0.04 0.03
Max 84.61 98.56 0.2 0.8 19.65 2.99 2.9 3.98 0.21 0.13 0.23
Number 1426 1426 1913 1913 1851 1913 1836 1852 1856 1839 1839
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Notes: The table reports the time series averages of the cross-sectional mean, standard deviation,
minimum, 25% quantile point, median, 75% quantile point, maximum and number of
observationsof various firm characteristics, including the instability of ROA (InsROA), instability
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of ROE (InsROE), return on assets (ROA), return on equity (ROE), logarithmic market value(Size),
book-to-market equity ratio (BM), momentum (MOM), idiosyncratic volatility (IVOL), maximum
re
daily return (MAX), and turnover (TURN), which are defined in Table 1. The sample period is
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ur
na
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from2004:01 to 2018:06.
32
Table 3 One-sorting based on firms' profit instability. 2
3
4
5
6
7
8
9
H
H_L
0.93 (0.99) 0.23 (0.95) 0.05 (0.17) 0.12 (0.52)
0.87 (0.87) 0.18 (1.01) -0.02 (-0.1) 0.04 (0.19)
0.91 (0.91) 0.23 (1.04) 0.17 (0.67) 0.29 (1.3)
0.92 (0.87) 0.21 (1.16) 0.19 (1.02) 0.21 (1.13)
0.92 (0.95) 0.19 (1.49) 0.03 (0.19) 0.11 (0.6)
0.65 (0.63) -0.08 (-0.56) -0.14 (-0.82) -0.01 (-0.07)
0.71 (0.71) -0.05 (-0.29) -0.1 (-0.6) -0.07 (-0.45)
0.95 (0.86) 0.17 (0.87) 0.02 (0.1) 0.08 (0.63)
0.42 (0.4) -0.37 (-1.47) -0.63*** (-3.56) -0.56*** (-3.19)
-0.67** (-2.1) -0.7** (-2.34) -0.76*** (-2.84) -0.87*** (-3.13)
0.92 (0.96) 0.23 (1.23) 0.1 (0.48) 0.2 (0.98)
0.96 (0.96) 0.26 (1.21) 0.16 (0.72) 0.27 (1.34)
0.96 (1.04) 0.28** (1.98) 0.16 (1.12) 0.24 (1.43)
0.9 (0.88) 0.21 (1.03) 0.1 (0.41) 0.19 (0.91)
0.87 (0.84) 0.15 (1.02) 0.21 (1.12) 0.14 (0.75)
0.67 (0.64) -0.09 (-0.9) -0.15 (-1.43) -0.07 (-0.61)
0.86 (0.79) 0.08 (0.61) -0.02 (-0.14) 0.01 (0.08)
0.73 0.44 (0.66) (0.41) -0.09 -0.35 (-0.41) (-1.6) -0.27 -0.64*** (-1.4) (-4.44) -0.15 -0.48*** (-0.76) (-3.48)
-0.52** (-2.23) -0.61*** (-3.05) -0.59** (-2.17) -0.62*** (-2.75)
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L Panel A: InsROA Average_return 1.09 (1.02) CAPM_α 0.34 (1.35) FF3_α 0.13 (0.49) FF5_α 0.31 (1.25) Panel B:InsROE Average_return 0.96 (0.99) CAPM_α 0.26 (1.07) FF3_α -0.05 (-0.19) FF5_α 0.14 (0.67)
-p
Notes: This table presents the result of the one-way sorting portfolio analysis. Each month t, wesort
all stocks into decile portfolios based on the most recently available InsROA and InsROE,
re
respectively. Then we assume that the portfolios are held for during month t+1. "Low" refers to the stocks in the lowest profit instability decile, whereas "High" refers to the stocks in the highest profit
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instability decile. The "H-L" is the hedge portfolio that is long "High" portfolio and short"Low" portfolio. This table reports the value weighted monthly average excess returns (in percentage),
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CAPM alphas (CAPM α in percentage), Fama-French three factor alphas (FF3 α in percentage) and Fama-French five factor alphas (FF5 α in percentage) of the portfolios over 2004:01 to 2018:06,
ur
and their t-statisticsreported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. The data on the Chinese risk-free rate and Fama-French (1993, 2015) three and five factors
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are from the RESSET Financial Research Database. *, **, 0.05 level, and 0.01 level, respectively.
33
***
indicate significance at the 0.1 level,
Table 4 Two-way dependent sorting controlling for market capitalization (Size) . 2
3 4 High Average_return
Panel A: InsROA Small 1.92* 2.04* (1.7) (1.79) Median 1.33 1.14 (1.26) (1.11) Large 0.89 0.71 (0.91) (0.69) Average 1.38 1.3 (1.34) (1.25) Panel B: InsROE Small 2.06* 2.01* (1.8) (1.73) Median 1.28 1.19 (1.22) (1.15) Large 0.82 0.69 (0.86) (0.75) Average 1.38 1.3 (1.35) (1.28)
H-L
Low
2
3
4 FF_α
High
H-L
2.02* (1.72) 1.11 (1.04) 0.83 (0.82) 1.32 (1.24)
1.91 (1.58) 1.13 (1.04) 0.66 (0.66) 1.23 (1.15)
1.66 (1.45) 0.77 (0.71) 0.55 (0.54) 0.99 (0.94)
-0.26 (-1.57) -0.56*** (-3.9) -0.34 (-1.14) -0.39** (-2.58)
0.26 (1.59) -0.06 (-0.29) 0.18 (0.63) 0.13 (0.66)
0.4** (2.21) -0.21 (-1.14) 0.18 (0.85) 0.12 (0.76)
0.33* (1.95) -0.22 (-1.19) 0.23 (1.41) 0.11 (0.84)
0.23 (1.23) -0.22 (-1.45) 0.03 (0.19) 0.01 (0.1)
-0.04 (-0.22) -0.62*** (-3.05) -0.07 (-0.44) -0.24* (-1.77)
-0.3* (-1.88) -0.57*** (-3.92) -0.24 (-0.76) -0.37** (-2.38)
1.96* (1.67) 1.12 (1.08) 0.77 (0.76) 1.28 (1.23)
1.95* (1.69) 1.1 (1) 0.75 (0.7) 1.26 (1.17)
1.57 (1.34) 0.79 (0.72) 0.52 (0.49) 0.96 (0.88)
-0.49*** (-2.66) -0.49*** (-2.8) -0.3 (-1.24) -0.42*** (-2.77)
0.41** (2.4) -0.08 (-0.4) 0.14 (0.63) 0.15 (0.84)
0.35** (2.32) -0.15 (-0.88) 0.15 (0.95) 0.12 (0.81)
0.3* (1.77) -0.23 (-1.32) 0.23 (1.25) 0.1 (0.68)
0.24 (1.29) -0.26 (-1.56) 0.13 (1.01) 0.04 (0.3)
-0.13 (-0.69) -0.6*** (-2.97) -0.15 (-0.98) -0.29** (-2.04)
-0.54*** (-3.12) -0.51*** (-2.99) -0.29 (-1.23) -0.45*** (-3.04)
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Low
-p
Size
Notes: This table presents the result of the two-way dependent sorting portfolio analysis based on
re
the profit instability (InsROA/InsROE) and market capitalization (Size), which have been documented to predict stock returns and are most recently available. Each month t, we begin by
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sorting all stocks into three portfolios using the 30th and 70th Size percentiles. Next, within each portfolio, we sort the stocks into quintile portfolios based on the firms' profit instability. Specifically,
na
the highest 10% stocks are grouped into the highest portfolio labeled "High", and the rest of stocks are then sorted into quartile portfolios with the lowest one is labeled "Low". The "H-L" is the hedge
ur
portfolio that is long "High" portfolio and short "Low" portfolio within each Size group. In addition, we construct the "Average" portfolios by averaging the "Low" to "High" and "H-L" sub-portfolios
Jo
across the three Size groups. The table reports the value weighted monthly average excess returns (in percentage) and Fama-French three factor alphas (FF3 α in percentage) of the portfolios over 2004:01 to 2018:06, and their t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags.*, **, *** indicate significance at the 0.1 level, 0.05 level, and 0.01 level, respectively.
34
Table 5 Two-way sorting controlling for book to market ratio(BM). 2
3 4 High Average_return
Panel A: InsROA Growth 0.83 0.85 (0.86) (0.91) Neutral 0.94 0.89 (0.92) (0.88) Value 1.41 0.99 (1.22) (1.01) Average 1.06 0.91 (1.03) (0.94) Panel B: InsROE Growth 1.01 1.02 (1.1) (1.09) Neutral 1.1 0.74 (1.11) (0.76) Value 0.99 1.15 (0.92) (1.12) Average 1.03 0.97 (1.06) (1)
H-L
Low
2
3
4 FF_α
High
H-L
0.69 (0.73) 0.83 (0.74) 1.11 (1.04) 0.88 (0.85)
0.72 (0.7) 0.77 (0.74) 0.97 (0.92) 0.82 (0.8)
0.48 (0.45) 0.72 (0.63) 0.97 (0.87) 0.72 (0.67)
-0.35 (-1.28) -0.23 (-0.72) -0.44 (-1.55) -0.34 (-1.63)
0 (-0.01) -0.06 (-0.2) 0.4 (1.52) 0.11 (0.48)
0.33 (1.16) -0.06 (-0.24) -0.03 (-0.14) 0.08 (0.41)
0.04 (0.14) -0.14 (-0.56) 0.21 (0.94) 0.04 (0.23)
-0.15 (-0.88) -0.25 (-1.31) 0.06 (0.41) -0.11 (-1.02)
-0.67** (-2.55) -0.29* (-1.87) 0.07 (0.27) -0.29** (-2.35)
-0.67** (-2.51) -0.23 (-0.66) -0.32 (-0.94) -0.4* (-1.78)
0.41 (0.41) 0.87 (0.79) 1.21 (1.17) 0.83 (0.8)
0.88 (0.86) 1.01 (0.91) 1.07 (0.96) 0.98 (0.92)
0.34 (0.3) 0.5 (0.43) 1 (0.88) 0.61 (0.55)
-0.67* (-1.79) -0.6** (-2.23) 0.01 (0.02) -0.42* (-1.78)
0.29 (0.84) 0.05 (0.22) -0.02 (-0.09) 0.1 (0.48)
0.43 (1.44) -0.27 (-0.96) 0.25 (1.26) 0.14 (0.66)
-0.26 (-1.48) 0 (0.02) 0.27** (2.06) 0 (0.03)
0 (-0.02) -0.01 (-0.04) 0.22 (1.21) 0.07 (0.51)
-0.9*** (-4.94) -0.53*** (-2.93) 0.01 (0.06) -0.47*** (-3.43)
-1.19*** (-3.86) -0.58** (-2.29) 0.04 (0.12) -0.58** (-2.56)
ro of
Low
-p
BM
Notes: This table presents the result of the two-way dependent sorting portfolio analysis based on
re
the profit instability (InsROA/InsROE) and book-to-market ratio (BM), which have been
lP
documented to predict stock returns and are most recently available. Each month t, we begin by sorting all stocks into three portfolios using the 30th and 70th BM percentiles. Next, within each portfolio, we sort the stocks into quintile portfolios based on the firms' profit instability. Specifically,
na
the highest 10% stocks are grouped into the highest portfolio labeled "High", and the rest of stocks are then sorted into quartile portfolios with the lowest one is labeled "Low". The "H-L" is the hedge
ur
portfolio that is long "High" portfolio and short "Low"portfolio within each BM group. In addition, we construct the "Average" portfolios by averaging the "Low" to "High" and "H-L" sub-portfolios
Jo
across the three BM groups. The table reports the value weighted monthly average excess returns (in percentage) and Fama-French three factor alphas (FF3 α in percentage) of the portfolios over 2004:01 to 2018:06, and their t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. *, **, *** indicate significance at the 0.1 level, 0.05 level, and 0.01 level, respectively.
35
Table 6 Two-way sorting controlling for level of profitability (ROA/ROE). Low
3 4 High Average_return
H-L
Low
2
3
4
High
H-L
FF_α
0.26 (0.23) 0.88 (0.84) 1.34 (1.32) 0.82 (0.79)
0.53 (0.46) 0.58 (0.55) 1.15 (1.2) 0.75 (0.73)
0.44 (0.38) 0.54 (0.52) 0.93 (0.95) 0.64 (0.61)
0.21 (0.19) 0.74 (0.68) 1.08 (1.01) 0.68 (0.62)
-0.56** (-2.05) -0.58*** (-2.62) -0.03 (-0.1) -0.39* (-1.74)
-0.56** (-2.12) 0.34 (1.37) 0.51* (1.89) 0.09 (0.44)
-1.05*** (-3.53) -0.15 (-0.8) 0.86*** (3.77) -0.12 (-0.58)
-0.75*** (-3.42) -0.29 (-1.36) 0.5** (2.41) -0.18 (-1.18)
-0.92*** (-4.04) -0.52*** (-3.44) 0.3 (1.5) -0.38*** (-3.42)
-1.25*** (-6.33) -0.49*** (-2.68) 0.46*** (2.87) -0.43*** (-3.48)
-0.69*** (-3.09) -0.83*** (-3.54) -0.04 (-0.14) -0.52*** (-2.73)
0.56 (0.51) 0.87 (0.84) 1.43 (1.44) 0.96 (0.92)
0.45 (0.4) 0.51 (0.52) 1.07 (1.06) 0.68 (0.66)
0.37 (0.31) 0.72 (0.65) 1.02 (1) 0.7 (0.65)
0.15 (0.13) 0.5 (0.5) 1.12 (0.98) 0.59 (0.54)
-0.6*** (-2.92) -0.26 (-1.15) -0.12 (-0.3) -0.33* (-1.79)
-0.66** (-2.58) -0.32 (-1.35) 0.74*** (2.78) -0.08 (-0.38)
-0.83*** (-3.41) -0.08 (-0.35) 0.86*** (5.29) -0.01 (-0.07)
-0.87*** (-4.09) -0.49*** (-2.7) 0.57*** (2.81) -0.26* (-1.82)
-1*** (-4.68) -0.21 (-1.04) 0.4*** (2.87) -0.27** (-2.22)
-1.35*** (-6.12) -0.65*** (-3.73) 0.4* (1.94) -0.53*** (-3.65)
-0.68*** (-2.86) -0.33* (-1.73) -0.34 (-1.08) -0.45*** (-2.76)
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Panel A: InsROA Low 0.77 (0.66) Median 1.32 (1.23) High 1.11 (1.26) Average 1.07 (1.04) Panel B: InsROE Low 0.74 (0.65) Median 0.77 (0.8) High 1.24 (1.38) Average 0.92 (0.93)
2
-p
Profitability
Notes: This table presents the result of the two-way dependent sorting portfolio analysis based on
re
the profit instability (InsROA/InsROE) and level of profitability (ROA/ROE), which have been
lP
documented to predict stock returns and are most recently available. Each month t, we begin by sorting all stocks into three portfolios using the 30th and 70th ROA/ROE percentiles. Next, within each portfolio, we sort the stocks into quintile portfolios based on the firms' profit instability.
na
Specifically, the highest 10% stocks are grouped into the highest portfolio labeled "High", and the rest of stocks are then sorted into quartile portfolios with the lowest one is labeled "Low". The "H-
ur
L" is the hedge portfolio that is long "High" portfolio and short "Low" portfolio within each profitability group. In addition, we construct the "Average" portfolios by averaging the "Low" to
Jo
"High" and "H-L" sub-portfolios across the three profitability groups. The table reports the value weighted monthly average excess returns (in percentage) and Fama-Frenchthree factor alphas (FF3 α in percentage) of the portfolios over 2004:01 to 2018:06, and their t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. *, significance at the 0.1 level, 0.05 level, and 0.01 level, respectively.
36
**, ***
indicate
Table 7 Two-way sorting controlling for volatility of profitability (VolROA/VolROE).
Panel A: InsROA Low 1.29 (1.17) Median 1.14 (1.22) High 0.95 (0.91) Average 1.13 (1.11) Panel B: InsROE Low 0.9 (0.92) Median 1.17 (1.23) High 1 (0.92) Average 1.02 (1.03)
2
3 4 High Average_return
H-L
Low
2
3
4 FF_α
High
H-L
0.95 (0.89) 0.78 (0.74) 0.74 (0.74) 0.82 (0.8)
0.82 (0.84) 1.07 (0.99) 1.01 (0.93) 0.97 (0.93)
0.81 (0.82) 0.82 (0.83) 1.04 (0.9) 0.89 (0.86)
0.7 -0.59** (0.7) (-1.99) 0.55 -0.59** (0.54) (-2.28) 0.14 -0.81** (0.13) (-2.16) 0.46 -0.66*** (0.45) (-3.14)
0.23 (0.78) 0.32 (1.5) 0.42* (1.68) 0.32 (1.65)
0 (0.02) -0.09 (-0.38) -0.07 (-0.33) -0.05 (-0.26)
-0.18 -0.16 (-0.78) (-0.71) 0.22 -0.1 (1.13) (-0.4) 0.02 -0.04 (0.11) (-0.21) 0.02 -0.1 (0.14) (-0.56)
-0.18 (-1.09) -0.29* (-1.86) -0.91*** (-4.74) -0.46*** (-4.75)
-0.4 (-1.23) -0.61** (-2.23) -1.33*** (-4.58) -0.78*** (-3.64)
0.92 (0.91) 0.87 (0.91) 0.99 (0.9) 0.93 (0.91)
0.88 (0.85) 1.06 (1.03) 0.81 (0.73) 0.92 (0.87)
0.72 (0.8) 0.78 (0.77) 0.75 (0.65) 0.75 (0.74)
0.92 (0.89) 0.59 (0.56) 0.28 (0.25) 0.6 (0.57)
-0.19 (-0.74) 0.4 (1.4) 0.51** (2.31) 0.24 (1.24)
-0.04 (-0.18) 0.07 (0.31) 0.14 (0.8) 0.05 (0.38)
-0.08 (-0.44) 0.26 (1.28) -0.2 (-0.84) -0.01 (-0.03)
0 (0.01) -0.28* (-1.86) -0.8*** (-5.68) -0.36*** (-3)
0.19 (0.78) -0.68*** (-2.7) -1.31*** (-5.49) -0.6*** (-3.9)
0.03 (0.12) -0.58** (-2.3) -0.72** (-1.99) -0.42** (-2.42)
-0.31 (-1.62) -0.1 (-0.81) -0.41* (-1.87) -0.27** (-2.29)
ro of
Low
-p
Profit volatility
Notes: This table presents the result of the two-way dependent sorting portfolio analysis based on
re
the profit instability (InsROA/InsROE) and volatility of profitability (VolROA/VolROE). Each month
lP
t, we begin by sorting all stocks into three portfolios using the 30th and 70th VolROA/VolROE percentiles. Next, within each portfolio, we sort the stocks into quartile portfolios based on the firms' profit instability. Specifically, the highest 10% stocks are grouped into the highest portfolio labeled
na
"High", and the rest of stocks are then sorted into quartile portfolios with the lowest one is labeled "Low". The "H-L" is the hedge portfolio that is long "High" portfolio and short "Low" portfolio
ur
within each profitability group. In addition, we construct the "Average" portfolios by averaging the "Low" to "High" and "H-L" sub-portfolios across the three profitability groups. The table reports
Jo
the value weighted monthly average excess returns (in percentage) and Fama-French three factor alphas (FF3 α in percentage) of the portfolios over 2004:01 to 2018:06, and their t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. *, **, significance at the 0.1 level, 0.05 level, and 0.01 level, respectively.
37
***
indicate
Table 8 Fama-MacBeth regression analysis of the predictive power of profit instability to future
stock returns. Model InsROA
(1) -0.0245** (-2.12)
(2) -0.0219** (-2.03)
(3) -0.0233*** (-2.71)
(4) -0.017* (-1.67)
InsROE 0.1548* (1.81)
ROA
0.2894*** (5.47)
(5)
(6)
(7)
(8)
-0.0018** (-2.08)
-0.002** (-2.01)
-0.002** (-2.5)
-0.0017* (-1.88)
0.084** (2.2)
0.1312*** (5.51) -0.0061*** (-3.43) 0.0077** (2.16) -0.0095 (-1.49)
0.2663*** (5.04)
0.1234*** (5.32) Size -0.0062*** -0.0077*** -0.0077*** (-3.49) (-4.02) (-3.97) BM 0.008** 0.0014 0.0009 (2.29) (0.45) (0.28) Beta -0.008 -0.0021 -0.0032 (-1.26) (-0.11) (-0.29) MOM -0.0012 -0.0013 (-0.29) (-0.28) IVOL -0.0116 -0.0329 (-0.09) (-0.35) MAX -0.1762*** -0.1733*** (-4.21) (-4.11) TURN -0.4382*** -0.4356*** (-11.21) (-11.4) Intercept 0.0162 0.0147 0.1098*** 0.1456*** 0.0158 0.0143 0.1097*** 0.1465*** (1.54) (1.34) (3.53) (4.22) (1.49) (1.31) (3.49) (4.19) Adj_R2 0.161 2.1402 7.7438 11.4879 0.0755 1.8311 7.66 11.4222 Observations 237,798 237,798 232,160 228,143 237,798 237,798 232,160 228,143 Notes: This table presents the results of Fama-MacBeth cross-sectional regression of
lP
re
-p
ro of
ROE
individualfuture stock returns in month t+1 on independent variables, which are most recently
Model 4 (8):
na
available at the endof month t. Our main specification is Equation (2), which appears below as
R E T it 1 In te r c e p t 1 In s R O A it ( In s R O E it ) 2 R O A it ( R O E it ) 3 S iz e it 4 B M it
5 B e ta it 6 M O M
9 T U R N it it 1
it
7 IV O L it (2)
ur
8M AX
it
The dependent variable is the future return for firm i in month t+1, and the lagged independent
Jo
variables are defined in Table 1. The table reports the estimation of the Fama-MacBeth mean monthly coefficients for eight different models that include different subsets of independent variables. The sample period covers 2004:01 to 2018:06, and the t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. *, **, the 0.1 level, 0.05 level, and 0.01 level, respectively.
38
***
indicate significance at
Table 9 Fama-MacBeth monthly cross-section regression of stock returns on profit instability characteristic and factor loadings. Model InsROA
(1)
(2) -0.0131** (-2.29)
(3) -0.0133** (-2.05)
(4) -0.0168*** (-2.83)
(5)
InsROE 0.2733*** (4.59)
ROA
0.2485*** (4.02)
IVOL MAX TURN beta_InsROA
0.0003 (0.67)
0.0005 (1.15)
-0.0091*** (-4.1) 0.0017 (0.49) -0.0048 (-0.7) -0.0747 (-0.9) -0.1521*** (-3.22) -0.3867*** (-8.68) 0.0001 (0.17)
lP
beta_InsROE beta_mar_ROA
-0.0017*** (-3.04)
-0.0015*** (-2.7)
-0.0018*** (-2.93)
0.125*** (4.5) -0.0079*** (-3.24) 0.0061 (1.35)
0.1204*** (4.14) -0.0097*** (-3.83) -0.0007 (-0.16) -0.007 (-0.96) -0.0531 (-0.55) -0.1468*** (-3.3) -0.3976*** (-9.03)
0.1222*** (4.6) -0.0092*** (-3.92) 0.001 (0.28) -0.0066 (-0.92) -0.082 (-0.94) -0.1424*** (-3.08) -0.3975*** (-8.81)
0.001 (1.32)
0.0007 (0.78)
ro of
MOM
(8)
-p
BM
-0.0096*** (-4.01) 0.0001 (0.02) -0.0054 (-0.79) -0.0492 (-0.53) -0.1566*** (-3.37) -0.3853*** (-8.67) 0.0004 (0.93)
re
-0.0079*** (-3.45) 0.0077* (1.74)
(7)
0.2541*** (4.55)
ROE Size
(6)
0.0007 (0.89)
0.0008 (1.27)
0.0021 (0.78)
na
beta_mar_ROE beta_smb_ROA
ur
beta_smb_ROE
0.002 (1.55) 0.002 (1.51) -0.0018** (-2.27)
beta_hml_ROA
Jo
0.0026 (0.88)
beta_hml_ROE Intercept
Adj_R2 Observations
0.0096 (0.95) 0.4446 220,142
0.1241*** (2.95) 6.0452 195,276
0.1646*** (3.64) 9.8834 190,347
0.1528*** (3.79) 11.1993 190,347
0.0142 (1.49) 0.8584 220,142
0.129*** (2.89) 6.193 195,276
0.1716*** (3.59) 10.0407 190,347
-0.0017** (-2.25) 0.1592*** (3.74) 11.37 190,347
Notes: This table presents the results of Fama-MacBeth cross-sectional regression of individual future stock returns in month t+1 on independent variables, which are most recently available at the
39
endof month t. Our main specification is Equation (3), which appears below as Model 4(8): R E T it 1 I n te r c e p t 1 I n s R O A it ( I n s R O E it )
9 k2
9 i2
j O th e r _ c h a r a c te r is tic it 1 b e ta _ I n s R O A it ( b e ta _ I n s R O E it ) j
k O th e r _ lo a d in g s it k
(3)
The dependent variable is the future return for firm i in month t+1. The lagged independent variables are defined in Table 1. The individual stock factor loadings of traditional Fama-French three factors and profit instability factor. The construction of profit instability factor is analogous to the value factor and profitability factor in Wang and Yu (2013) and Fama and French (1993,2015). We independently and evenly sort all stocks in our sample into two size groups and three profit
ro of
instability (measured by InsROA and InsROE, respectively) groups, and obtain six value weighted portfolios. Then, profit instability mimicking factor is defined as the average of the two low profit
instability portfolio returns minus the average of the two high profit instability portfolio returns. The table reports the estimation of the Fama-MacBeth mean monthly coefficients for eight different
-p
models that include different subsets of independent variables. The sample period covers 2008:01 to 2018:06, and the t-statistics reported in parentheses are adjusted by Newey-West robust standard ***
indicate significance at the 0.1 level, 0.05 level, and 0.01 level,
re
errors with 12 lags. *,**,
Jo
ur
na
lP
respectively.
40
f oo
Table 10 Fama-French alphas of two-way sorting portfolios controlling for momentum (MOM), maximum history daily return (MAX) and idiosyncratic volatility (IVOL) H-3
H-4
Average
na l
Jo ur
H-1
H-2
H-3
H-4
H-5
Average
InsROE
-0.29 (-1.47) -0.95*** (-3.77) -0.65** (-2.5)
-0.48 (-1.24) -0.81*** (-3.6) -0.33 (-1.07)
-0.19 (-0.73) -1.08*** (-3.93) -0.89** (-2.55)
-0.46* (-1.74) -0.76** (-2.58) -0.3 (-1.05)
-0.09 (-0.4) -1.09*** (-4.83) -1*** (-3.26)
-0.43** (-2.1) -0.96*** (-4.07) -0.53** (-2.06)
-0.33 (-1.47) -0.94*** (-4.38) -0.61*** (-2.66)
-0.19 (-0.69) -1.38*** (-5.25) -1.19*** (-3.41)
-0.17 (-0.78) -1.07*** (-4) -0.9*** (-2.93)
-0.42 (-1.25) -0.8** (-2.58) -0.38 (-0.99)
-0.24 (-0.99) -1.16*** (-3.39) -0.92** (-2.11)
-0.44 (-1.43) -1.19*** (-3.48) -0.74 (-1.46)
-0.52* (-1.92) -0.98*** (-4.77) -0.46 (-1.47)
-0.47** (-2.41) -1.16*** (-5.26) -0.69** (-2.14)
-0.42* (-1.86) -1.06*** (-4.33) -0.64* (-1.97)
-0.38 (-1.48) -1.18*** (-3.41) -0.8** (-2.03)
-0.09 (-0.37) -0.95*** (-2.95) -0.86** (-2.05)
0.04 (0.12) -0.91*** (-3.18) -0.95** (-2.27)
-0.21 (-0.78) -1*** (-3.9) -0.79* (-1.88)
-0.28 (-1.05) -0.65** (-2.11) -0.37 (-0.98)
-0.25 (-0.87) -0.96*** (-3.7) -0.71* (-1.79)
-0.41 (-1.48) -0.73*** (-3.34) -0.32 (-0.95)
-0.22 (-1.01) -0.85*** (-3.83) -0.63* (-1.94)
-0.27 (-0.95) -0.87*** (-2.96) -0.59*** (-2.81)
Pr
InsROA Panel A: MOM as the control variable Low -0.52 -0.07 -0.14 -0.46* (-1.57) (-0.24) (-0.68) (-1.94) *** *** *** High -1.11 -1 -0.83 -0.93*** (-2.88) (-3.55) (-4.06) (-2.85) ** ** H-L -0.59 -0.93 -0.69 -0.47 (-1.29) (-2.48) (-2.26) (-1.34) Panel B: MAX as the control variable Low -0.43 0.05 -0.06 -0.24 (-1.38) (0.16) (-0.26) (-0.82) High -1.04*** -0.89*** -0.99*** -1.05*** (-2.69) (-2.63) (-3.72) (-3.62) * ** ** DID -0.62 -0.95 -0.93 -0.81** (-1.87) (-2.29) (-2.58) (-2.15) Panel C: IVOL as the control variable Low -0.18 0.07 0.05 -0.02 (-0.51) (0.16) (0.19) (-0.07) High -1.16*** -0.87*** -0.68** -0.86** (-2.91) (-2.62) (-2) (-2.55) * * DID -0.98 -0.93 -0.73 -0.85** (-1.95) (-1.82) (-1.5) (-2)
H-5
pr
H-2
e-
H-1
Notes: This table presents the result of the two-way dependent sorting portfolio analysis based on the profit instability (InsROA/InsROE) and the control variables, including momentum(MOM), idiosyncratic volatility (IVOL) and maximum history daily return (MAX). Each month t, we begin by sorting all stocks into two portfolios
41
f
oo
using the 50th MOM MAX or IVOL percentiles. Next, within each group, we sort the stocks intodecile portfoliosbased on the firms' profit instability and then construct five hedge portfolios using the difference between "High" portfolio and first five portfolios.In addition, we construct the "DID" portfolio, which indicates the difference
pr
of hedge portfolios and "High" portfolio between the two subgroups. The table reports Fama-French three factor alphas (FF3 α in percentage) of the portfolios over 2004:01to 2018:06, and the t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. * ,**, *** indicate significance at the 0.1
Jo ur
na l
Pr
e-
level, 0.05 level, and 0.01 level, respectively.
42
Table 11 Fama-MacBeth monthly cross-section regression of stock returns on the momentum (MOM), maximum history daily return (MAX) and idiosyncratic volatility (IVOL). MOM
MAX
(1) -0.0392*** (-3.12)
I |InsROA IH|InsROE
(2)
(3) -0.0304** (-2.47)
-0.0035*** (-2.92)
IL|InsROA
-0.0016 (-0.44)
IL|InsROE
-0.0009 (-1.05)
Beta IMOM IIVOL IMAX
na
TURN Intercept
0.124*** (5.04) -0.0078*** (-3.85) 0.0008 (0.29) -0.0024 (-0.09) 0.0009 (0.6) 0.0022*** (3.02) 0.0025*** (2.83) -0.464*** (-12.86) 0.1406*** (4.03) 10.65 228,143
-0.0079*** (-3.93) 0.0013 (0.46) -0.0014 (0.08) 0.0009 (0.6) 0.0016** (2.27) 0.0027*** (3.3) -0.4643*** (-12.58) 0.1405*** (4.09) 10.60 228,143
0.1241*** (5.07) -0.0078*** (-3.86) 0.0008 (0.3) -0.0025 (-0.11) 0.0009 (0.6) 0.002*** (2.86) 0.0026*** (3.2) -0.4618*** (-13) 0.1406*** (4.04) 10.60 228,143
ur
Adj_R2 Observations
-0.0010 (-0.71) 0.2694*** (4.85)
re
BM
-0.0078*** (-3.92) 0.0012 (0.44) -0.0012 (0.13) 0.0009 (0.62) 0.0019*** (2.66) 0.0021** (2.09) -0.4647*** (-12.62) 0.1404*** (4.09) 10.66 228,143
lP
-0.0079*** (-3.94) 0.0013 (0.47) -0.0014 (0.07) 0.0000 (0.03) 0.002*** (2.71) 0.0027*** (3.34) -0.4624*** (-12.55) 0.1408*** (4.13) 10.68 228,143
Size
-0.0061 (-0.44)
0.2685*** (4.87) 0.1257*** (5.14) -0.0078*** (-3.88) 0.0008 (0.3) -0.0025 (-0.13) 0.0007 (0.48) 0.0021*** (2.95) 0.0026*** (3.15) -0.4633*** (-12.8) 0.1412*** (4.06) 10.66 228,143
(6)
-0.0026*** (-2.83)
-0.0005 (-0.56)
0.2713*** (4.89)
ROE
(5) -0.0238** (-2.46)
-0.0025** (-2.33)
0.0002 (0.14)
ROA
(4)
ro of
H
IVOL
-p
Model
Notes: This table presents the results of Fama-MacBeth cross-sectional regression of
Jo
individualstock returns in month t+1 on independent variables, which are most recently available at the end
R E T it 1 In te r c e p t 1 In s R O A it ( In s R O E it ) I it | In s R O A it ( In s R O E it ) + 2 R O A it ( R O E it ) 3 S iz e it
4BM
it
5 B e ta it 6 M O M
C
it
7 IV O L it 8 M A X
it
9 T U R N it it 1
(4)
The dependent variable is the future return for firm i in month t+1, and the lagged independent variables are defined in Table 1. In particular,
C
I it
is the dummy variable according the median
ofthe MOM, MAX or IVOL denoted as C in I . If MOM, MAX or IVOL is smaller than its median, C
it
43
C
I it
is one, if not, I is zero. The table reports the estimation of the Fama-MacBeth mean monthly C
it
coefficients for eight different models that include different subsets of independent variables. The sample period covers 2004:01 to 2018:06, and the t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. *, **, *** indicate significance at the 0.1 level,
Jo
ur
na
lP
re
-p
ro of
0.05 level, and 0.01 level, respectively.
44
400
Index of Sstock Price
350 300 250 200 150 100 50
ro of
0
LuZhouLaoJiao
WuLiangYe
0.3
-p
0.25
re
0.2 0.15 0.1 0.05 0 2010
2011
2012
2013
na
2009
lP
Profitability of the two firms
0.35
LuZhouLaoJiao
2014
2015
2016
2017
WuLiangYe
Figure 1 The index of stock prices and firm's profitability of Lu Zhou Lao Jiao and Wu Liang Ye
Jo
ur
over the period from 2013:01 to 2018:06.
45
Ins_ROA
Ins_ROE
Cumulative Return
1.25 1.2 1.15 1.1 1.05 1
Ins_ROE
1.6
-p
1.5 1.4
re
1.3 1.2 1.1
lP
Cumulative Risk-ajusted Return
Ins_ROA
ro of
0 2 4 6 8 1012141618202224262830323436384042444648505254565860 Period
1
na
0 2 4 6 8 10 1214 16 1820 22 2426 28 3032 3436 38 40 4244 4648 50 5254 56 5860 Period
Figure 2 Long-term return performance of the profit instability hedge portfolio. The value of $1
Jo
ur
invested in the hedge portfolio in Month 0.
46
oo
0.005
0.005
0 P1
P2
P3
P4
P5
P6
P7
P8
P9
0
P10
P1
P2
P3
P4
-0.01 -0.015
e-
High history return
Ins_ROA
Pr
0.01 0
P1
P2
P3
P4
P5
P6
P7
-0.02
Low idiosyncratic volatility
P8
P9
Low history return
-0.01 -0.015
P9
P10
P1
P2
P3
P4
Low maximum return
P5
P6
High history return
0.01 0
P10
-0.005
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
-0.01 -0.015
High idiosyncratic volatility
Jo ur
-0.005
P8
Ins_ROE
Low idiosyncratic volatility
Ins_ROA
0
P7
0.005
na l
-0.01
0.005
P6
-0.01
Low history return
0.01
P5
-0.005
pr
-0.005
Ins_ROE
f
Ins_ROA
High idiosyncratic volatility
Ins_ROE
0.005 0 P7
P8
P9
-0.005
P10
P1
P2
P3
P4
P5
P6
P7
P8
P9
-0.01 -0.015 High maximum return
Low maximum return
Figure 3 Fama-French alphas of profit instability portfolios in different history return, idiosyncratic volatility, and maximum return groups.
47
High maximum return
P10
Appendix
Appendix-Table 1 One-sorting based on volatility of profitability. L
2
3
4
5
6
7
Panel A: Portfolios sorted on VolROA Average_return 1 0.98 0.83 0.81 0.94 1 1.22 (0.97) (1.03) (0.87) (0.84) (0.96) (1.03) (1.13) FF_α -0.09 0.01 -0.17 -0.22 -0.07 0.09 0.41** (-0.43) (0.04) (-0.87) (-1.25) (-0.38) (0.51) (2.42)
8
9
H
H_L
1.05 0.99 0.67 -0.33 (1.03) (1) (0.64) (-1.29) 0.24 0.13 -0.4*** -0.32 (1.25) (0.68) (-3.32) (-1.47) 1.08 0.56 (1.04) (0.5) 0.13 -0.62*** (0.73) (-3.63)
-0.23 (-0.8) -0.39* (-1.95)
ro of
Panel B: Portfolios sorted on VolROE Average_return 0.78 1.04 1.04 0.87 0.85 1.25 0.9 1.05 (0.84) (1.09) (1.05) (0.9) (0.9) (1.27) (0.9) (0.96) FF_α -0.23 -0.01 -0.01 -0.17 -0.09 0.38** 0.09 0.39** (-1.12) (-0.08) (-0.07) (-0.87) (-0.5) (2.05) (0.57) (2.07)
-p
Panel C: Portfolios sorted on VolROA excluding top 10% of stocks according to firms' InsROA. Average_return 0.92 0.95 0.64 0.66 0.74 0.89 1.16 1.11 0.88 0.62 -0.3 (0.9) (0.95) (0.64) (0.68) (0.76) (0.88) (1.02) (1.1) (0.87) (0.6) (-1.3) FF_α -0.05 0.05 -0.27 -0.26 -0.17 0.04 0.4* 0.46** 0.12 -0.23 -0.18 (-0.25) (0.25) (-1.44) (-1.42) (-1) (0.22) (1.84) (2.37) (0.66) (-1.44) (-0.94)
lP
re
Panel D: Portfolios sorted on VolROE excluding top 10% of stocks according to firms' InsROE. Average_return 0.7 0.88 0.93 0.71 0.8 1.01 0.93 1.02 0.99 0.5 -0.2 (0.73) (0.9) (0.92) (0.72) (0.82) (1.04) (0.92) (0.9) (0.93) (0.45) (-0.8) FF_α -0.22 -0.09 0 -0.25 -0.1 0.24 0.21 0.46** 0.19 -0.51*** -0.29 (-1.01) (-0.59) (0) (-1.11) (-0.56) (1.19) (1.14) (2.14) (0.98) (-2.79) (-1.61)
na
Notes: In this table, Panel A and B/ Panel C and D present the results of the one-way sorting portfolio analysis including/excluding top 10% of stocks based on firms' profit instability.
ur
Specifically, each month t we sort all stocks into decile portfolios based on the most recently available VolROA and VolROE, respectively. Then we assume that the portfolios are held for during
Jo
month t+1. "Low" refers to the stocks in the lowest profit instability decile, whereas "High" refers to the stocks in the highest profit instability decile. The "H-L" is the hedge portfolio that is long "High" portfolio and short "Low" portfolio. This table reports the value weighted monthly average excess returns (in percentage) and Fama-French three factor alphas (FF3 α in percentage) over 2004:01 to 2018:06, and their t-statisticsreported in parentheses are adjusted by Newey-West robust
48
standard errors with 12 lags. *, **, *** indicate significance at the 0.1 level, 0.05 level, and 0.01 level,
Jo
ur
na
lP
re
-p
ro of
respectively.
49
PII:
S0275-5319(19)30825-6
DOI:
https://doi.org/10.1016/j.ribaf.2020.101203
Reference:
RIBAF 101203
To appear in:
Research in International Business and Finance
Received Date:
17 July 2019
Revised Date:
12 February 2020
Accepted Date:
15 February 2020
Please cite this article as: Yin L, Wei Y, Han L, Firms’ Profit Instability and the Cross-Section of Stock Returns: Evidence from China, Research in International Business and Finance (2020), doi: https://doi.org/10.1016/j.ribaf.2020.101203
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier.
Firms' Profit Instability and the Cross-Section of Stock Returns: Evidence from China
Author information: Libo Yina, * a School
of Finance, Central University of Finance and Economics, Beijing, China
Ya Weia School of Finance, Central University of Finance and Economics, Beijing, China
ro of
a
Liyan Hanb b
School of Economics and Management, Beihang Univeristy, Beijing, China
* Corresponding author.
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Professor.
Address: 39 South College Road, Haidian District, Beijing, 100081, China
re
Email: [email protected] or [email protected] (Libo Yin)
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na
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Graphical abstract
1
Firm’s profit instability
Cross-sectional stock returns
Negatively predictive power
Explanation for this predictive power
No
Yes Irrational: Mispricing explanation
Better recent past performance
The negative relationship is more significant among stocks with particular charateristics
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More lottery-like payoffs
Higher arbitrage risk
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Rational: Risk based explanation
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Abstract: This study utilizes samples from the Chinese A-share market to examine the relation between a firm’s profit instability and cross-sectional stock returns. The empirical evidence indicates that firms with high profit instability have substantially lower future stock returns than
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those with low profit instability. The predictive information contained in profit instability is not subsumed by the level of profitability or the volatility of cash flow and is robust after controlling
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for well-known firm characteristics and risks. In addition, the long-term predictive performance of the firm’s profit instability is permanent over at least five years. Moreover, the profit instability
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effect is stronger among firms with better recent past performance, more lottery-like payoffs, and higher arbitrage risk. This finding suggests that the immaturity of investors and high constraints on arbitrage are the main sources of the profit instability effect in the Chinese market, which is consistent with the implications of behavioral mispricing explanations. Our investigation enriches the study on profitability anomalies by uncovering profit instability as an incremental signal in predicting stock returns. Furthermore, this study provides a novel view to better understand the mechanisms of the anomalies related with firms' profitability in undeveloped stock markets of 2
emerging economies, thereby benefiting investors from all over the world to seek more efficient investment strategies.
JEL Classification: G12; G14
Keywords: Profit instability; Predictive power; Expected returns; Chinese stock market; Mispricing
1. Introduction Emerging literature has decidedly established that the level of a firm’s profitability determines
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future stock returns (Cohen, Gompers, and Vuolteenaho, 2002; Fama and French, 2006, 2008;
Griffin and Lemmon, 2002; Haugen and Baker, 1996; Novy-Marx, 2013). Fama and French (2015, 2018) and Hou, Xue, and Zhang (2015, 2017) included profitability as a factor in new multifactor
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asset pricing models to explore numerous well-documented anomalies. Barillas and Shanken (2018) provided further evidence that the recent models by Hou, Xue, and Zhang (2015, 2017) and Fama
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and French (2015, 2018) are dominated by value and profitability factors.
However, some problems remain unresolved. On one hand, the strength of the documented
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effect varies across studies (e.g., Fama and French, 2006, 2008 v.s. Novy-Marx, 2013). Fama and French (2015, 2018) claimed that their five-factor asset pricing model, designed to capture patterns
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in returns due to risks associated with profitability, is invalid and that the performance of this model is sensitive to the choice of the profitability factor. On the other hand, the explanation concerning the profitability premium from a theoretical perspective generates mixed views. From the rational
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expectations perspective, Q theory with investment friction provides a potentially rational explanation for the profitability effect (Li, Livdan and Zhang, 2009; Hou et al., 2015, 2017; Jiang
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et al., 2018). By contrast, Wang and Yu (2013), Lam, Wang, and Wei (2016), and others proposed explanations based on behavioral mispricing. They argued that investor behavior cannot fully reflect the information embedded in a firm’s profitability due to behavioral biases. These mixed views call for further investigation regarding the nature and extent of the anomalies surrounding firm profitability, which motivates the work in this study. This study contributes to the literature by indicating that a firm’s current level of profitability
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cannot give a full picture of the firm’s prospects for future stock returns. Specifically, the level of profitability reflects a firm’s current efficiency and advantages in the context of the existing competitive environment that allow it to produce a return on an investment based on its resources. However, the overall competitive environment of the product markets in which a firm operates is not static. With the passing time, firm performance changes due to alterations in the firm’s own competitive strength as does the overall competitive environment. Unlike consistently strong earnings, strong earnings in one quarter do not necessarily suggest a strong firm profitability, which could be used to predict future stock returns (Loh and Warachka,
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2012). According to Campbell, Giglio, Polk and Turley (2018), if firm profits suffer from cash flow shocks, they are likely to be permanent. This means that rational investors have no reason to expect the stock price to rebound to previous levels. However, if profit declines are due to discount rate
shocks or variance shocks, they are likely to be temporary. Accordingly, rational investors can
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expect the stock price to rebound to previous levels. Therefore, multiquarter variations in the path of profitability, which reveals the struggles that a firm has encountered in arriving at its current level
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of profitability, may highlight the prospects for future stock returns. The following example
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illustrates our point.
For instance, Luzhou Laojiao and Wu Liang Ye, two well-known firms in the Chinese stock market, have already become the largest emerging stock market in the world. Although they had
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similar levels of profitability from 2009 to 2017, as presented in Figure 1, the upward trend in the price of Wu Liang Ye is obviously more pronounced than that of Luzhou Laojiao in the five most
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recent years. In Figure 1, during the same period, the fluctuation in profitability, measured by ROA, of Wu Liang Ye is significantly smaller than that of Luzhou Laojiao. Accordingly, we hypothesize
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that firms with a higher stability in profitability will outperform those with a lower stability in profitability after accounting for the overall level of profitability. [Insert Figure 1 Here]
Our investigation focuses on the Chinese mainland stock market to test this hypothesis. Exploring the pricing mechanism of the Chinese stock market is crucial for investors worldwide as the market develops (Carpenter and Whitelaw, 2017; Carpenter, Lu and Whitelaw, 2018). Researchers have examined the price premium of A shares and the firm-specific information content 4
of prices. These researchers have thus provided new evidence on informational and behavioral effects on prices and have analyzed unique cross-sectional patterns in returns. Additionally, the Chinese stock market possesses unique features such as higher retail investor rates, price-limit rules, and short-selling restrictions; however, it is relatively underdeveloped (Chang, Luo, and Ren, 2014; Gu, Kang, and Xu, 2018; Lepone, Wen, Wong, and Yang, 2019; Liu, Gu, and Lung, 2016; Nartea, Kong, and Wu, 2017; Yao, Wang, Cui, and Fang, 2019; Yao, Ma, and He, 2014; Yang et al., 2019). These features may induce a higher likelihood of mispricing and investment friction, thereby providing a powerful test for competing theories. Focusing on the Chinese stock market thus gives
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us a promising proxy for understanding global stock returns. Our analysis of the above hypothesis proceeds in three steps. First, we examine the profit instability effect in the Chinese stock market by testing whether a firm’s profit instability provides
incremental predictive information about future stock returns beyond the information contained in
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the level of profitability. Following Novy-Marx (2013) as well as Jiang, Qi, and Tang (2018), we consider return on assets (ROA) and return on equity (ROE) as the appropriate measure of a firm’s
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profitability. We estimate profit instability each month by regressing the changes in profitability
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relative to that in the previous year on a time trend. The residual variance of this regression is our measure of the firm’s profit instability for that month. A larger value of the residual variance indicates that the firm has recently experienced a higher profit instability. Following Hou et al.
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(2015), we form value-weighted profitable decile portfolios by single and double sorting measures of a firm’s past profit instability. We determine that a firm’s past profit instability provides
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significant incremental predictive information about future returns. Firms with more unstable profitability are relatively overpriced in the stock market, whereas firms with more stable
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profitability are marginally underpriced, leading to return predictability. The negative predictive power of profit instability for subsequent stock returns remains significant when we control for wellknown firm characteristics and risks in the cross-section analysis. These include firm size (Banz, 1981), book-to-market ratio (Fama and French, 1993), Beta (Frazzini and Pedersen, 2014), momentum (Jegadeesh and Titman, 1993), idiosyncratic risk (Ang et al., 2006), MAX (Bali, Cakici,
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and Whitelaw, 2011),1 and turnover (Chordia, Subrahmanyam and Anshuman, 2001). Moreover, this ‘‘profit instability effect’’ is robust when controlling for the firm’s level and volatility of profitability, and this profit instability predicts returns up to five years later. Next, we conduct empirical tests to explore the rational risk explanations and assess whether this predictive relation represents a manifestation of rational pricing based on compensation for risk or irrational mispricing. If pricing is rational, then the predictive relation between profit instability and stock returns should reflect compensation for some form of risk associated with that profit instability. Following Wang and Yu (2013) and Daniel and Titman (1997), we employ a systematic
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approach to examine whether the profit instability effect can be explained by the loadings of the mimicking factors. We determine that the evidence does not support an argument based on rational risk compensation.
Alternatively, the profit instability effect could result from irrational mispricing associated with
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a firm’s profit instability. In the third step, considering the features of Chinese stock market, we
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propose three hypotheses and conduct empirical tests to explore behavioral mispricing. The extent to which the profit instability effect reflects mispricing should be larger among firms characterized
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by a good recent past performance (Bange, 2000; Ng and Wu, 2007; Bohl and Siklos, 2008), high lottery-like payoffs (Bali, Cakici, and Whitelaw, 2011; Nartea, Kong, and Wu, 2017; Zhong and Gray, 2016), and high arbitrage risk (Stambaugh et al., 2015; Pontiff, 2006). Our empirical evidence
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supports this inference, which indicates that firms with higher profit instability are typically associated with a higher likelihood of mispricing. The results imply that the immaturity of investors
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and high constraints on arbitrage are the main sources of mispricing in our profit instability effect. Our main contributions in this study are two-fold. First, we extend the existing studies on
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profitability anomalies and suggest an alternative investment strategy in practice. Specifically, we uncover an incremental signal of a firm’s profit instability, which measures a recent dynamic pattern of a firm’s profit, to predict future stock returns. Accordingly, a monthly hedge portfolio strategy
1
Using a stock’s maximum historical return to capture the stock’s lottery characteristics, Bali et al.
(2011) proposed the MAX effect, which reveals the negative relation between the maximum historical return and future cross-sectional stock returns. 6
based on going long stocks with the lowest profit instability and shorting stocks with the highest profit instability yields an average return close to 0.5–0.7% per month in the Chinese stock market historically. Second, our investigation enriches the growing asset pricing literature concerning the Chinese stock market, which has become a crucial part of the global capital markets. This will help investors to better understand the pricing mechanisms of this emerging stock market. Literature explaining the profitability premium is relatively new (Garlappi and Yan, 2011; Hou et al., 2015, 2017; Jiang et al., 2018; Lam, Wang, and Wei, 2016; Li, Livdan, and Zhang, 2009; Ma and Yan, 2015; Wang
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and Yu, 2015). Our study provides evidence that the negative relation between a firm’s profit instability and cross-sectional stock return is more likely attributed to behavioral mispricing than
rational risk-based explanations. However, this result runs contrary to the findings of Jiang, Qi, and Tang (2018), indicating the relatively low market and investment efficiency in the Chinese market,
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which has been increasing significantly.
The remainder of this paper is organized as follows. Section 2 presents our literature review.
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Section 3 discusses the data and calculation of our profit instability measures. Section 4 uses the
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portfolio test and Fama–MacBeth regression analysis to assess the predictive power of profit instability for cross-sectional stock returns. Section 5 investigates the risk-based rational pricing and
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behavioral mispricing explanations for the profit instability effect. Section 6 concludes the paper.
2. Literature review
Several recent papers have focused on the relation between a firm’s profitability and future
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cross-sectional stock returns. Using samples from the US stock markets, researchers determined that firms with higher profitability have substantially higher future stock returns than those with lower
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profitability (Cohen, Gompers, and Vuolteenaho, 2002; Fama and French, 2006, 2008; Griffin and Lemmon, 2002; Haugen and Baker, 1996; Novy-Marx, 2013). In emerging stock markets, the positive effect of firm profitability on stock returns is also pervasive. Berggrun, Cardona, and Lizarzaburu (2020) documented that this profitability premium exists in the stock markets of Latin America. Jiang, Qi, and Tang (2018) observed significant positive predictive power for future crosssectional stock returns in the Chinese stock market. In addition, investment managers such as
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Dimensional Fund Advisors and AQR have modified their trading strategies to incorporate measures similar to profitability (CFA Institute Magazine, 2014). However, from a theoretical perspective, explanations for the profitability premium present mixed views on the rationality or irrationality of the observed price effects. Q theory with investment frictions provides a potentially rational explanation for the profitability effect. The theory indicates that profitable firms generate higher expected returns than unprofitable firms holding fixed investments since profitable firms have higher marginal returns from investment. Moreover, firms subject to fewer investment frictions have lower marginal costs for their investment, thereby
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amplifying the profitability premium. One particularly puzzling observation is that firms with high profitability behave more like growth firms, whereas firms with low profitability behave like value firms. However, value firms are well known to earn higher average returns than growth firms (Fama
and French, 1992). In addition, the profitability premium has also been related to investment-
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specific technology shocks (Kogan and Papanikolaou, 2013) and credit risk (Ma and Yan, 2015). Meanwhile, researchers have presented evidence to support explanations based on irrationality.
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Wang and Yu (2013) as well as Lam, Wang, and Wei (2016) have indicated that underreaction to the
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information embedded in a firm’s profitability figures is the basis of the profitability premium. Moreover, mispricing may not be instantly traded away due to limits to arbitrage (Shleifer and Vishny, 1997). However, such profitability-related mispricing can persist for as long as 10 years
et al., 2015).
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without being corrected, which is seemingly inconsistent with irrational pricing explanations (Ball
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In recent studies, some researchers have suggested that the recent dynamics of a firm’s profits should be considered. Mohanram (2005) developed fundamental signals pertaining to the stability
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of a firm’s earnings and growth to identify stocks less likely to be overvalued due to naïve extrapolation by stock markets. Akbas, Jiang, and Koch (2017) explicitly focused on the information content of the recent trend in a firm’s profitability. Huang (2009) employed the standard deviation of cashflow scaled by book equity to measure a firm’s cashflow volatility and reveal its negative predictive power for future stock returns. The aforementioned studies have established a large framework on the relation between a firm’s profitability and stock returns. Following this literature, based on a dynamic view, we focus 8
on the recent profit instability, which is distinct from previous studies, and investigate whether this indicator could be a stand-alone determinant of future stock returns.
3. Data and variable definitions 3.1 Data Our sample includes all Chinese A-share firms with quarterly accounting data and monthly returns sourced from the China Stock Market and Accounting Research Database. Following standard sample screening procedures (Akbas et al., 2017; Jiang et al., 2018), we exclude financial
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firms as well as firms with special treatment (st) and negative book-to-market ratios, which are distressed and lack market liquidity. As the quarterly financial reports of Chinese list firms are available only after 2002 and the measure of firms’ profit instability presented later is computed
based on the data available in at least the most recent eight quarters, the sample used in our empirical
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test spans from January 2004 through June 2018. Meanwhile, this sample period also helps ensure the uniformity and quality of accounting data. This is because accounting fraud, stock price
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manipulation, and speculation in the Chinese stock market, which were prevalent in the early years before 2000, were effectively limited by increasing market transparency, accounting quality, and
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protection of minority shareholders after 2000. 3.2. Measures of firms’ profit instability
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In an analogous investigation, Huang (2009) employed the standard deviation of cashflow scaled by book equity to measure a firm’s cashflow volatility, similar to the firm’s profit instability
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measure in our study. He demonstrated its negative predictive power for future stock returns. However, the cashflow volatility measure employed by Huang (2009) cannot present a complete
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picture of the instability of a firm’s profitability. Huang’s cashflow volatility is a static indicator, which measures the volatility of the level of a firm’s profitability. A dynamic indicator should be used to measure the volatility of change in a firm’s profitability.2
2
Different with the cashflow volatility proposed by Huang (2009), our indicator is a dynamic
version of indicator to measure the firm's profit instability. For example, considering a firm A, whose profitability increases from 1 to 10 at the rate of 1 over period 1 to 10, following Huang 9
As the largest emerging economy, China has experienced rapid growth and upgrading of its industrial structure. In this macroeconomic background, the profitability of Chinese firms is subject to a continuous change in a trend that can generally be anticipated by investors. It is unreasonable to transmute this expectation into measures of a firm’s profit instability that imply unexpected uncertainty or risk in a firm’s profitability. Therefore, this study proposes a dynamic indicator to measure a firm’s profit instability, which we define below. We define the profit instability of firm i as the residual variance from the rolling regressions of that firm’s profitability change relative to that in the previous year on the time trend. Specifically,
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the procedure comprises three following steps. First, following Hou et al. (2015, 2017) and Jiang et al. (2018), we compute the profitability of all firms in our sample for every quarter q. To provide a
comprehensive characterization, we employ two different measures of profitability: ROA and ROE. Second, we calculate the profitability change relative to that in the same quarter in the previous year
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to capture the dynamic of the firm’s profitability and eliminate the seasonal effects of quarterly variables. Furthermore, let R O A and R O E denote the ROA and ROE changes for firm i in quarter iq
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iq
q, respectively. Finally, in practice, an investor would be likely to extrapolate the future change in
12 (at least 8) samples of
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a firm’s ROA and ROE based on previous trends. Therefore, using the most recent publicly available R O A iq
and R O E from step two in the preceding five years, we run the iq
following regressions of R O A and R O E on a deterministic time trend for each firm i in month t,
where
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respectively.
iq
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iq
T r e n d 1, 2 ,
,1 2
R O A iq a
ROA
bi
R O E iq a
ROE
bi
ROA
T r e n d iq
ROE
ROA
T r e n d iq
ROE
(1)
, denotes the time trend variable in the regressions. We include the time
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trend due to the profit trend effect identified by Akbas et al. (2017). For example, if equation (1)
(2009)'s method, the profit instability of firm A would be in a high level. By contrast, in dynamic view, firm A's profit instability would be in the lowest level, which implies its increase of profitability is 1, which is unchanged in every period. In this context, we conjecture that a firm would exhibit absolutely different level of profit instability in static and dynamic views. 10
does not include the trend term, a firm’s profitability with an obviously positive or negative trend would also have high variance. Accordingly, it would be difficult to distinguish whether the high variance comes from profit instability or the profit trend discussed by Akbas et al. (2017). This indicates that such a trend is positively associated with cross-sectional stock returns. Finally, we define the estimation of the residual variance from the regressions presented in equation (1) as the measures of profit instability for firm i in month t, denoted as In s R O A it and In s R O E it . For firm i, the increase in
In s R O A it
and In s R O E it implies that the firm has recently experienced a higher
instability in its profit growth.
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3.3 Summary statistics
In our analysis, we control for various other firm characteristics used to predict returns in the Chinese stock market. All the firm characteristics used in our test, including the control variables,
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are defined in Table 1. [Insert Table 1 Here]
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Table 2 presents the summary statistics for firm characteristics used in our empirical test. All data are winsorized by a level of 1% and 99% to minimize the influence of outliers on our results.
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This table indicates that the averages of InsROA and InsROE are 0.09 and 0.2, respectively, and their monthly average number of observations are both 1426.
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[Insert Table 2 Here]
4. Predictive ability of firms’ profit instability for stock returns
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In this section, we employ portfolio analysis and Fama–MacBeth regression to investigate the ability of a firm’s profit instability to predict the cross-sectional stock returns in the Chinese stock
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market. We explore the long-term historical performance of this predictive power. 4.1. Portfolio analysis sorted by firms’ profit instability 4.1.1. One-way sorting We begin our portfolio analysis using a one-way sorting approach. Specifically, at the beginning of each month t+1, we sort all stocks in our sample into decile portfolios based on the most recently available InsROA and InsROE. This step ensures that our test avoids look-ahead bias. Thereafter, we assume that the portfolios are held during month t+1 and that the monthly returns of 11
these portfolios are value-weighted. The result of this one-way sorting portfolio analysis is presented in Table 3. Here, “Low” refers to the stocks in the lowest profit instability decile, “High” refers to the stocks in the highest profit instability decile, and “H–L” is the hedge portfolio that is long stocks with the highest profit instability and short stocks with the lowest profit instability. [Insert Table 3 Here] The value-weighted monthly average excess returns of portfolios sorted by InsROA and InsROE are presented in the first row of Panel A and Panel B in Table 3. The results indicate that the stocks of firms in the lowest profit instability decile significantly outperform the stocks of firms
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in the highest profit instability decile. The monthly average excess returns for InsROA (InsROE)based profit instability deciles decrease from 1.09% (0.96%) to 0.42% (0.44%) for the lowest and
highest deciles, respectively. The hedge strategy—short stocks with the highest InsROA (InsROE) and long stocks with the lowest InsROA (InsROE)—earns an average value-weighted monthly
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return of 0.67% (0.52%) with a Newey–West t-statistic of 2.1 (2.23).
Table 3 reports the risk-adjusted returns based on the capital asset pricing model (CAPM) and
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Fama–French (1993, 2015) three- and five-factor models. Similar to the excess return, we find that
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the CAPM alphas and Fama–French alphas of the profit instability portfolios decrease from the lowest to highest decile. For example, the FF3 alpha of the lowest InsROA (InsROE) decile is 0.13% (−0.05%), whereas the alpha of the highest InsROA (InsROE) decile is −0.49% (−0.58%). The alpha
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of the hedge portfolio is −0.63% (−0.64%) with a Newey–West t-statistic of −3.56 (−4.44), which is statistically significant at the 1% level. The results measured by excess returns and the risk-
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adjusted returns indicate that profit instability measured by InsROA and InsROE negatively predict future stock returns in the Chinese stock market. This effect still exists even after controlling for the
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traditional CAPM and Fama–French three- and five-risk factors.3 Jiang et al. (2018) concluded that the profitability premium in the Chinese stock market
primarily results from the long leg rather than the short leg. This fact indicates that risk compensation is more likely to be the primary source of the profitability premium than mispricing.
3
Because the results are robust for the different asset pricing models, in the following analysis,
we only present the FF3 alphas, which are most widely used in academic area and in practice. 12
This is because overvaluation is more difficult to correct than undervaluation due to short selling constraints. By contrast, the result presented in Table 3 indicates that the significantly negative Fama–French alpha of the hedge portfolios mainly results from the dramatic decline in the alphas of the highest profit instability deciles. This evidence indicates that the short leg seems to play a more important role in the profit instability effect, and mispricing is more likely to be the primary source of this effect than risk compensation (Jiang et al., 2018). 4.1.2. Robustness for double sorting
Controlling for size and BM
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Wang and Yu (2013) indicated that the profitability premium is more significant and larger in magnitude among firms with small market capitalization in US stock markets. Jiang et al. (2018)
found the opposite to be true in the Chinese stock market. Meanwhile, Novy-Marx (2013) and Jiang et al. (2018) documented that the profitability strategy belongs to an overall growth strategy, which
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indicates that the profitability premium is more pronounced among growth firms. Inspired by this
literature, this subsection employs a two-way dependent sorting portfolio approach to investigate
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the performance of the profit instability effect after controlling for firms’ market capitalization (Size)
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and book-to-market ratio (BM), the most prominent characteristics used to predict future returns (Fama and French, 1992, 2008).
First, for each month t, we sort all stocks into three portfolios using the 30th and 70th
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percentiles of two separate firm characteristics, including Size and BM. For Size (BM), stocks below the 30% breakpoint are regarded as “Small” (“Growth”), stocks between the 30% and 70%
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breakpoint are regarded as “Micro” (“Neutral”), and stocks above the 70% breakpoint are regarded as “Large” (“Value”). Second, within each portfolio, considering that the short leg is the primary
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source of the profit instability effect as concluded in Table 3 and to capture the effect more efficiently, we further sort the stocks into quintile portfolios based on the firms’ profit instability. Specifically, based on the firms’ InsROA and InsROE, the portfolio with the highest instability is labeled “High” and the portfolio with the lowest instability is labeled “Low.” Thus, we obtain 15 portfolios. Then, within each group in the first step, we construct hedge portfolios, “H–L,” which are long the “High” portfolio and short the “Low” portfolio. In addition, across the three groups in the first step, we construct “Average” portfolios by averaging the subportfolios labeled “Low,” “High,” and “H–L.” 13
Table 4 and Table 5 report the value-weighted monthly average excess returns and Fama–French alphas of the two-way dependent sorting portfolios by controlling for Size and BM. [Insert Table 4 Here] In Table 4, the “Average” rows indicate that the average returns and the Fama–French alphas of the hedge portfolios are significantly negative at a high confidence level. Specifically, in Panel A (B), the average return is −0.39% (−0.42%) with a Newey–West t-statistic of −2.58 (−2.77) and the Fama–French alpha is −0.37% (−0.45%) with a Newey–West t-statistic of −2.38 (−3.04). This evidence proves that the profit instability effect still exists even after controlling for the firm’s
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market capitalization (Size). We find that the profit instability effect is less prominent among larger firms. In particular, for
the large group, the hedge portfolio’s alpha is only −0.24% (−0.29%) and is not statistically
significant. This result provides more evidence that the profit instability effect is more likely to arise
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from mispricing than risk compensation. Because large stocks are always characterized by lower
arbitrage costs, the mispricing of stocks can be eliminated more easily by arbitragers in the stock
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market (Wang and Yu, 2013; Baker and Wurgler, 2006).
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In the recent research on the Chinese stock market, Liu et al. (2018) indicated that the shell effect from the smallest 30% of stocks plays an important role in determining stock price. The results in Table 4 imply that the shell effect is not the main source of our profit instability effect. Among
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the median groups, which exclude the smallest 30% of stocks, we still find that the average return and Fama–French alpha of the hedge portfolio are statistically significant at the 1% level.
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[Insert Table 5 Here]
In Table 5, by averaging the portfolios across three BM groups, we find that the hedge portfolios’
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average returns are negative; however, the average return in Panel A is modestly insignificant in statistic. The Fama–French alphas of the hedge portfolios in both panels A and B are significantly negative. Specifically, in Panel A, the hedge portfolio’s average return is −0.34% with a Newey– West t-statistic of −1.63, which is insignificant at the 10% level. In Panel B, the average return is significantly negative at −0.42% with a Newey–West t-statistic of −1.78. The Fama–French alpha of the hedge portfolios in Panel A (B) is −0.4% (−0.58%) with a Newey–West t-statistic of −1.78 (−2.56). In summary, similar to the analysis controlling for the firm’s market capitalization (Size), 14
the results in Table 5 document that the profit instability effect exists even after controlling for the firm’s book-to-market ratio (BM). Furthermore, in Table 5, we find that the profit instability effect is more pronounced among the growth stock groups than the other two groups. In Panel A (B), the Fama–French alpha of hedge portfolio among growth stock groups is −0.67% (−1.19%) with a Newey–West t-statistic of −2.51 (−3.86), which is larger and more significant than the alphas of the other two groups. This result presents more evidence to support the application of a value strategy in the Chinese stock market. If an investor selects stocks based on a value strategy, which means holding fewer growth stocks,
effect among growth stocks.
Controlling for the level and volatility of firms’ profitability
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they can efficiently avoid the negative influence arising from the more pronounced profit instability
As an extension of firms’ profitability, we are naturally concerned with whether our profit
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instability effect could be subsumed by the profitability premium, which indicates the strong predictive power of firms’ profitability for future stock returns. As mentioned above, the volatility
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of scaled cashflow proposed by Huang (2009) is similar to our measures of profit instability so that
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the profit instability effect could also possibly be subsumed by this volatility effect (Huang, 2009). Therefore, in this subsection, we will employ the two-way dependent sorting portfolio approach to investigate the profit instability effect while controlling for the level and volatility of firms’
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profitability. The level of a firm’s profitability is measured by ROA and ROE as defined in Table 1, and the calculation of the volatility of the firm’s profitability follows the procedure proposed by
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Huang (2009) using ROA and ROE.
Following the steps described in the previous subsection, for each month t, we sort all stocks
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into three portfolios using the 30th and 70th percentiles of the level and volatility of firms’ profitability. Stocks below the 30% breakpoint are denoted as “Low,” stocks between the 30% and 70% breakpoints are denoted as “Median,” and stocks above the 70% breakpoint are denoted as “High.” Second, within each portfolio, we further sort the stocks into quintile portfolios based on the firms’ profit instability. We then obtain five portfolios in each profitability group, including the “High,” “Low,” and “H–L” portfolios, which are identical to the definitions in the previous subsection. Finally, we construct the “Average” portfolios by averaging the “Low” to “High” and 15
“H–L” subportfolios across the three profitability groups. Table 6 and Table 7 report the valueweighted monthly average excess returns and Fama–French alphas of the two-way dependent sorting portfolios by controlling for the level and volatility of firms’ profitability. [Insert Table 6 Here] In Table 6, the average returns and Fama–French alphas of average hedge portfolios in Panel A and Panel B are all significantly negative. In particular, in Panel A (B) the average return is −0.39% (−0.33%) with a Newey–West t-statistic of −1.74 (−1.79) and the Fama–French alpha is −0.39% (−0.33%) with a Newey–West t-statistic of −2.73 (−2.76). We can therefore conclude that the profit
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instability effect would not be subsumed by the level of firm profitability measured by ROA and ROE.
Based on the result in Table 6, we find that the profit instability effect is weaker among firms
with a high level of profitability. For example, in Panel A (B), the Fama–French alpha of the hedge
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portfolio among the high profitability group is −0.02% (−0.34%), which is insignificant at 10% level. By contrast, the alphas of hedge portfolios among the other two groups are larger in magnitude
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and statistically significant. Similar to the results arrived at when controlling for firms’ book-to-
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market ratio (BM), we can conclude that an investor who selects stocks with high levels of profitability could achieve higher returns by removing the negative influence of the profit instability effect. Combining this with the result documented in Table 5, we can hypothesize that selecting
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stocks with high value and a high level of profitability is an efficient strategy to improve returns on investment, which is consistent with the conclusions of Novy-Marx (2013) and Jiang et al. (2018).
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[Insert Table 7 Here]
In Table 7, after controlling for volatility of firm profitability proposed by Huang (2009), we
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still find a pronounced profit instability effect. In panels A and B, we find that the average returns and Fama–French alphas of average hedge portfolios are all significantly negative. Specifically, in Panel A (B), the average return is −0.66% (−0.32%) with a Newey–West t-statistic of −3.14 (−2.42) and the Fama–French alpha is −0.78% (−0.6%) with a Newey–West t-statistic of −3.64 (−3.9). This evidence supports the dynamic view proposed in Section 3.2. We can conclude that as a static indicator, Huang’s cashflow volatility cannot present a complete picture of the firm’s profit instability in China. By contrast, our dynamic version of firm profit instability provides incremental 16
information for predicting cross-sectional stock returns that cannot be subsumed by a static indicator. In addition, we present the empirical evidence of our one-way sorting analysis based on the volatility of firm profitability in Appendix-Table 1. In panels A and B, we find that the average returns and Fama–French alphas are smaller and more insignificant in magnitude than the results in Table 3, which present one-way sorting analysis based on the firm’s profit instability. Furthermore, in panels C and D, when the most unstable 10% of stocks are excluded from the sample, the average returns and alphas are smaller and more insignificant. Hence, we suggest that the profit volatility effect proposed by Huang (2009) is more likely determined by our profit instability effect in the
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Chinese stock market. 4.2. Predictive power at the firm level
In this section, we extend our sorting analysis using a Fama–MacBeth regression approach that
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explicitly controls for other well-known stock characteristics documented to have predictive power for stock returns. Our main regression model is constructed as follows:
6MOM
it 1
7 IV O L it 8 M A X
it
it
5 B e ta it
(2)
9 T U R N it it 1
denotes the future return for firm I in month t+1,
In s R O A it
and In s R O E are the two it
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where R E T
it
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R E T it 1 In te r c e p t 1 In s R O A it ( In s R O E it ) 2 R O A it ( R O E it ) 3 S iz e it 4 B M
measures of the profit instability for firm i in month t, and the other independent variables, which
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are most recently available, are defined in Table 1. Specifically, we begin by estimating the coefficients each month and obtain the coefficients’ time series. Thereafter, we compute the mean coefficients as well as the adjusted robust t-statistic by averaging this time series and the Newey–
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West (1987) method. The results of these estimates are all presented in Table 8, which provides eight different model specifications that include various combinations of dependent and independent
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variables.
[Insert Table 8 Here]
In Table 8, the univariate regression results of models (1) and (5) show a negative and
statistically significant relation between a firm’s profit instability, measured by InsROA and InsROE, and the cross-sectional future stock returns. The coefficients of InsROA and InsROE in models (1) and (5) are −0.0245 and −0.0018, with corresponding Newey–West t-statistics of −2.12 and −2.08.
17
In models (2) and (6), which control for the level of profitability, we still observe that the coefficients of InsROA and InsROE are negative and statistically significant. Similarly, this result can also be found in models (3) and (7), which specify Size, BM, and Beta as the additional control variables. Finally, models (4) and (8) in Table 8 present the results of estimating the coefficients in Equation (2), which incorporates all control variables in our test. In these results, we can observe that the coefficients of the InsROA as well as InsROE are −0.0245 and −0.0017 with Newey–West t-statistics of −1.67 and −1.88, respectively, indicating that both the negative coefficients are significant at the 10% level. Overall, consistent with our two-way portfolio analysis, the Fama–
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MacBeth regressions provide more reliable and robust evidence for the profit instability effect, and this effect cannot be subsumed by other well-known predictors of stock returns.
In fact, this profit instability effect is consistent with the findings of Kogan, Li, and Zhang (2018). By decomposing gross profitability into a persistent component and a transitory component,
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they indicated that the predictive power of the persistent component of gross profitability for future
stock returns is short-lived. Only the transitory component of gross profitability, constructed as the
4.3. Long-term performance
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information about future stock returns.
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deviation of the gross profitability from its persistent component, contains more relevant predictive
In the preceding analysis, we explored the predictive power of firms’ profit instability for the
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one-head-month returns. To examine the profit instability effect more comprehensively, in this section, following Jegadeesh and Titman (1993) and Wang and Yu (2013), we construct hedge
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portfolios based on a firm’s profit instability with overlapping periods to highlight the long-term performance of this effect.
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Specifically, at the beginning of each month t, we sort all stocks into decile portfolios, which
are value-weighted, based on the most recently available InsROA and InsROE. We define “Low” and “High” as the lowest and highest profit instability deciles. “H–L” refers to the hedge portfolio that is long the “High” portfolio and short the “Low” portfolio. Then, we construct the overlapping portfolio by holding the hedge portfolio for a series of six-month windows in the five years after portfolio formation. For example, when the holding period is from the first month to sixth month, at month t, the overlapping portfolio is constructed by averaging the six portfolios, which are formed 18
at month t-6 to t-1. In Figure 2, we plot the average cumulative returns and risk adjusted returns with a holding period from 1 to 60 months for this hedge portfolio in terms of the value of one dollar invested in the hedge portfolio in month t = 0. [Insert Figure 2 Here] In Figure 2, we find that both the average cumulative returns and Fama–French alphas of the hedge portfolios seem to be permanent in the long run. Specifically, the evidence indicates that this overlapping profit instability hedge portfolio continues to appreciate slowly over the five-year holding periods, while the rate of increase becomes modestly slower when the holding period
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exceeds three years. Meanwhile, the result also indicates there is no obvious reversal in our profit instability effect, and we can hypothesize that this effect is more likely due to investor underreaction to the information embodied in a firm’s profit instability.
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5. Exploring the source of profit instability effect 5.1. Risk-based explanations
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We have thus far revealed the negative predictive power of a firm’s profit instability for future stock returns. However, we have still not provided an explanation for the profit instability effect. To
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further understand the source of the profit instability effect, we will provide additional analysis to highlight whether the said effect is due to rational pricing or irrational mispricing (Fama and French,
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2006). In this subsection, we first investigate the risk-based explanation by exploring the role of systematic risk in our effect.
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In the previous research, Daniel and Titman (1997) proposed a systematic approach to examine whether risk or mispricing explains the size and value premiums by constructing a factor-mimicking
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portfolio. If the stock return associated with a firm characteristic is indeed driven by underlying
systematic risk, this risk would be reflected in the factor-mimicking portfolio based on the firm characteristic. In other words, if risk is the main driver, the loading of this mimicking factor would provide a strong predictive power for cross-sectional stock returns. If not, the predictive power of the loading would be minimal, while the corresponding firm characteristic would still exhibit a significantly predictive power. In subsequent research, Wang and Yu (2013) applied this approach to test the profitability premium.
19
Following previous researchers, we employ this systematic approach to investigate our profit instability effect. First, following Wang and Yu (2013) and Fama and French (1993, 2015), we construct our profit instability mimicking factor, which is analogous to the value and profitability factors. We independently and evenly sort all stocks in our sample into two size groups and three profit instability (measured by InsROA and InsROE) groups, obtaining six value-weighted portfolios. Then, we define the profit instability mimicking factor as the average of the two low profit instability portfolio returns minus the average of the two high profit instability portfolio returns. Second, we compute the factor loadings for each stock in our sample by regressing the individual stock excess
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return on the factors, which include traditional Fama–French three factors and our profit instability factor. Third, we use Fama–MacBeth regressions to compare the ability of our profit instability
characteristic and factor loading to predict future returns. Furthermore, we use individual stocks as
The model specification is presented in Equation (3):
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test assets to avoid the possibility that tests may be sensitive to the portfolio grouping procedure.
9
R E T it 1 In te r c e p t 1 In s R O A it ( In s R O E it )
j O th e r _ c h a r a c te r is tic it j
re
j2 9
1 b e ta _ In s R O A it ( b e ta _ In s R O E it )
(3)
k O th e r _ lo a d in g s it k
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k2
where O t h e r _ c h a r a c t e r i s t i c are identical with the control variables in Equation (2). In addition, j
it
factor loadings, including profit instability factor loadings denoted as b e ta _ In s R O A
it
( b e ta _ In s R O E it )
,
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are also contained in the model. The estimated results of the mean monthly coefficients and the Newey–West (1987) adjusted t-statistics in parentheses are reported in Table 9.
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[Insert Table 9 Here]
Table 9 shows no evidence to support that stock returns are influenced by the loadings of the
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profit instability factor. Across all eight regressions, including both the univariate and multivariate regressions, none of the time-series average monthly coefficients, which have magnitudes close to zero, are significant, with the Newey–West (1987) adjusted t-statistics ranging from 0.17 to 1.32; however, their positive signs are consistent with the theoretical prediction. In contrast, similar to the results in Table 8, the coefficients of profit instability measured by InsROA and InsROE are still negative and statistically significant. Therefore, the results, which indicate that profit instability factor loadings have no predictive power for stock returns, imply that the profit instability effect is 20
unlikely to come from risk compensation. In other words, irrational mispricing is more likely to be the main source of the profit instability effect than rational pricing. This conclusion also responds to the results in Table 3 and Table 4, which suggests that the short leg plays a more important role in our profit instability effect. 5.2. Mispricing explanations 5.2.1. Hypothesis development In this subsection, combined with the features of the Chinese stock market, we will present additional empirical evidence to explore several explanations for the profit instability effect arising
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from mispricing. It is well known that high levels of speculation, irrationality, and inefficiency are still pronounced features of the Chinese stock market; however, this relatively young market has
grown to become the largest emerging market in the world. In particular, the prevalence of retail
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investors, who are “noise traders” and are presumably more prone to behavioral biases, is widely thought to be the primary reason for prevailing irrationality (Han and Li, 2017; Cheema and Nartea,
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2017; Hsu et al., 2018; Koesrindartoto, Aaron, Yusgiantoro and Dharma, 2020). Hence, irrational investment behaviors are the most plausible sources of our profit instability effect. In our analysis,
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we focus on investors’ positive feedback trading and lottery preferences, which are frequently discussed in both practice and academic research.
Positive feedback trading
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Positive feedback traders are defined as investors who discover seeming trends in past prices and trade based on the expectation that these trends will persist. The literature has documented that
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these irrational traders widely exist in practical stock markets, and positive feedback trading is more pronounced among retail investors and in the emerging markets, including the Chinese stock market
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(Bange, 2000; Ng and Wu, 2007; Bohl and Siklos, 2008). Hence, we can hypothesize that positive feedback trading is likely to be an underlying reason for the underreaction to the profit instability effect. Specifically, among stocks with better historical performance, which are more attractive to positive feedback traders, the negative information of high profit instability is more unlikely to be reflected in current prices. This is because the preference of positive feedback traders for this type of stock pulls prices to a relatively higher level. By contrast, among stocks with poor historical performance, the negative information of high profit instability is more likely to be reflected in 21
current prices. This is because the aversion of positive feedback traders to this type of stock pushes prices to a relatively lower level. Following this logic, we can conclude that the historical performance of stocks is positively associated with the overpricing of high profit instability stocks. We should also realize the asymmetry of the profit instability effect, which indicates that the short leg will be the primary source of the effect so that the change in the overpricing of high profit instability stocks will be dominant. Therefore, we present our first hypothesis: Hypothesis 1: The profit instability effect will be more prominent among stocks with a better historical performance. Lottery preference
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Based on the preference for lottery-like assets in the stock market, Bali et al. (2011) proposed the MAX effect, which reveals the negative relation between the maximum historical return and
future cross-sectional stock returns. In subsequent studies, the empirical evidence suggested that
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this MAX effect is robust and appears stronger in emerging stock markets (Egginton and Hur, 2018; Seif et al., 2018; Zhong and Gray, 2016; Nartea et al., 2017). Similar to positive feedback trading,
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lottery preference is also an underlying reason for the profit instability effect. In particular, among
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lottery-like stocks, lottery preference by investors places upward pressure on prices, thereby increasing the underreaction to the negative information embodied in high profit instability and eliminating the underreaction to the positive information embodied in low profit instability.
hypothesis:
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Furthermore, considering the asymmetry of the profit instability effect, we reach our second
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Hypothesis 2: The profit instability effect will be more prominent among lottery-like stocks. Arbitrage risk
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In addition, the literature has presented evidence that arbitrage risk seems to play an important role in stock mispricing (Stambaugh et al., 2015; Pontiff, 2006). In particular, Akbas et al. (2017) and Wang and Yu (2013) documented that both the profit trend effect and the profitability premium are stronger among stocks with high arbitrage risk. Thus, for our profit instability effect, it is necessary to examine whether arbitrage risk could provide an alternative explanation. In general, because high arbitrage risk always implies more limits on arbitrage trading, mispricing would be more difficult to correct. Hence, this logic could also be applied to the profit instability effect, and 22
we thus propose our third hypothesis: Hypothesis 3: The profit instability effect will be more prominent among stocks with high arbitrage risk. 5.2.2. Empirical test In our empirical tests, we employ the two-way dependent sorting portfolio approach as well as Fama–MacBeth regressions to examine the three hypotheses proposed above using the history cumulative return (MOM), maximum history daily return (MAX), and idiosyncratic volatility (IVOL) as proxies for past performance (Akbas et al., 2017; Cheema and Nartea, 2017), lottery lottery-like
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characteristics (Bali et al., 2011; Egginton and Hur, 2018; Nartea et al., 2017), and arbitrage risk of stocks (Gu et al., 2018; Jiang et al., 2018; Akbas et al., 2017; Stambaugh et al.. 2015; Wang and Yu, 2013), respectively.
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In this two-way portfolio analysis, we specify MOM, MAX, and IVOL as the control variables. First, at the beginning of each month t, we sort all stocks into two portfolios using the median of the
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control variables above. Stocks below the 50% breakpoint are denoted as “Low,” and stocks above the 50% breakpoint are denoted as “High.” Second, within each portfolio, we sort the stocks into
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decile portfolios according to a firm’s profit instability (measured by InsROA and InsROE). We construct five different hedge portfolios that are long the portfolios with the highest profit instability and short the first five portfolios with the lowest profit instability. Third, we compute the difference
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in the Fama–French alphas of the five hedge portfolios between the high and low subgroups to capture the changes in our profit instability effect across the different types of stocks characterized
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by the control variables. Then, we average the five hedge portfolios within high and low subgroups and calculate their Fama–French alphas as well as their difference in the average portfolios’ alphas
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between the two subgroups. Finally, the alphas of profit instability portfolios in different subgroups are plotted in Figure 3, and the results of Fama–French alphas are presented in Table 10. [Insert Figure 3 Here]
Figure 3 plots the changing trajectory of Fama–French alphas of portfolios in the different subgroups. From this evidence, we find a descending trend of the alphas from low to high profit instability portfolios across stock groups characterized by high historical cumulative return (MOM), maximum historical daily return (MAX), and idiosyncratic volatility (IVOL). For example, when 23
controlling for MOM, in the high MOM group, we can observe a prominent decline of the Fama– French alphas after the eighth profit instability portfolio, whereas in the low MOM group, the Fama– French alphas fluctuate in a small range. When controlling for MAX and IVOL, we find similar results, which supports the arguments in Hypothesis 1 and Hypothesis 3. [Insert Table 10 Here] Table 10 reports the Fama–French alphas of the two-way sorting portfolios while controlling for the three variables above. In this table, we find that the empirical evidence is consistent with our hypotheses. Specifically, among the high MOM, MAX, and IVOL groups, which indicate the stock
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groups with better historical performance, lottery characteristics, and high arbitrage risk, the Fama– French alphas of the hedge portfolios based on profit instability are significantly negative, whereas
among the corresponding low groups, only a few alphas are significantly negative and the alphas are also smaller in magnitude. Furthermore, most of the differences in the alphas between the hedge
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portfolios among the high and low groups are negative and statistically significant. The differences in the average hedge portfolios are significantly negative. Overall, we can conclude that the results
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in Table 10 also support the above hypotheses.
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Meanwhile, we employ the Fama–MacBeth regressions to test the arguments of the three hypotheses by adding the interaction term into the original model, obtaining Equation (4) as follows: R E T it 1 I n t e r c e p t 1 I it | I n s R O A it ( I n s R O E it ) 2 I it | I n s R O A it ( I n s R O E it ) H
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+ 2 R O Ait ( R O E it ) 3 S i z e it 4 B M 6 I it
MOM
7 I it
IV O L
8 I it
L
it
,
5 B e t a it
9T U R N
M AX
it
(4)
it 1
where all variables are identical with the variables in Equation (2), except for I and I , which H
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it
L
it
indicate the dummy variable formed by the median of the MOMit, MAXit, or IVOLit. Specifically, if
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MOMit , MAXit, or IVOLit is larger than its median, I is one and I is zero; if not, I is zero and I H
L
it
H
it
it
L it
is one. The estimated results of Equation (4) are presented in Table 11. [Insert Table 11 Here]
If the hypotheses are true, we would expect to observe significantly negative coefficients of H
I it | I n s R O A it ( I n s R O E it )
in Equation (5) and significant coefficients of
models (1) to (6), we find that all of the six coefficients of significant. Meanwhile, the six coefficients of
L
H
I it | I n s R O A it ( I n s R O E it )
I it | I n s R O A it ( I n s R O E it )
24
L
I it | I n s R O A it ( I n s R O E it )
. In
are positive and
are all insignificant and
small in magnitude. Similar to the two-way portfolio analysis, this result is consistent with our expectations derived from the three advanced hypotheses. In summary, based on the evidence in Figure 3, Table 10, and Table 11, we can conclude that positive feedback trading, lottery preferences, and arbitrage risk can indeed provide explanations for the underreaction in our profit instability effect. In previous studies, researchers have documented several models to provide theoretical explanations for underreaction in the stock market. For example, Hong and Stein (1999) constructed an information diffusion model, which indicated that underreaction is mainly due to the gradual diffusion of private information across a news
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watching population. Coibion and Gorodnichenko (2012, 2015) and Bouchaud, Krueger, Landier, and Thesmar (2018) indicated that it can be optimal for investors to revise their expectations sporadically. As a result, expectations are sticky and can underreact to fundamental information,
implying the prevalence of underreaction. In fact, our conclusion that positive feedback trading,
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important extension and application of these models.
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lottery preferences, and arbitrage risk are the main reasons for the profit instability effect is an
6. Conclusion
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This study indicates that the instability in a firm’s profitability exhibits negatively and significantly predictive power for its future stock returns in the Chinese stock market. The results
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indicated that firms with high profit instability generated substantially lower future stock returns than those with low profit instability. A hedge portfolio that is long stocks with the lowest profit instability and short stocks with the highest profit instability yields a return of roughly 0.6% per
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month. This return mainly comes from the short leg. In addition, the empirical evidence documents that the predictive power of a firm’s profit
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instability is robust even when controlling for various well-known factors that affect future stock returns, including the volatility of profitability proposed by Huang(2009), which is similar to our measure of profit instability. The results of the two-way sorting portfolio indicated that the predictive power is weaker in stocks with high value and high levels of profitability. Further investigation of long-term performance indicates that the predictive power of a firm’s profit instability will be permanent over at least five years.
25
By employing the approach proposed by Daniel and Titman (1997), we find that irrational mispricing rather than rational risk compensation is more likely to be the reason undergirding the profit instability effect. In further analysis, we explore the alternative explanations for the source of this effect. We find that positive feedback trading, lottery preferences, and arbitrage risk are responsible for the profit instability effect, which is more pronounced among firms characterized by better recent past performance, more lottery-like payoffs, and higher arbitrage risk. This evidence implies that both the immaturity of investors in the Chinese market and high constraints on arbitrage
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are the main sources of the mispricing observed in our profit instability effect.
CRediT author statement
Libo Yin: Conceptualization, Methodology, Formal analysis, Investigation, Visualization, Writing-
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Reviewing and Editing, Project administration, Funding acquisition
Ya Wei: Software, Validation, Data curation, Writing- Original draft preparation
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Acknowledgements
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Liyan Han: Resources, Supervision
This research is financially supported by the National Natural Science Foundation of China under grant Nos. 71871234 and 71671193, and Program for Innovation Research in Central
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University of Finance and Economics, and the "Young talents" Support Program in Central
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University of Finance and Economics (QYP1901).
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Liu, J., Stambaugh, R, F., Yuan, Y.,2019. Size and value in China. Journal of Financial Economics 134, 48-69.. Loh, R., K., Warachka, M., 2012. Streaks in earnings surprises and the cross-section of stock returns. Management Science 58, 1305-1321. 29
Nartea, G, V., Kong, D., Wu, J., 2017. Do extreme returns matter in emerging markets? Evidence from the Chinese stock market. Journal of Banking & Finance 76, 189-197. Ng, L., Wu, F., 2007. The trading behavior of institutions and individuals in Chinese equity markets. Journal of Banking & Finance 31, 2695-2710. Novy-Marx, R., 2013. The other side of value: The gross profitability premium. Journal of Financial Economics 108, 1-28. Pontiff, J., 2006. Costly arbitrage and the myth of idiosyncratic risk. Journal of Accounting and Economics 42, 35-52.
emerging markets. Emerging Markets Review 36, 95-109.
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Seif, M., Docherty, P., Shamsuddin, A., 2018. Limits to arbitrage and the MAX anomaly in advanced
Shleifer, A., Vishny, R, W., 1997. The limits of arbitrage. Journal of Finance 52, 35-55.
Stambaugh, R.,Yu, J., Yuan, Y., 2015. Arbitrage asymmetry and the idiosyncratic volatility puzzle.
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Journal of Finance 70, 1903-1948.
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Trammel, S., 2014. Quality control: can new research help investors define a “quality” stock? CFA
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Wang, H., Yu, J., 2013. Dissecting the profitability premium. Working paper. Yao, S., Wang, C., Cui, X., Fang, Z., 2019. Idiosyncratic skewness, gambling preference, and crosssection of stock returns: Evidence from China. Pacific-Basin Finance Journal 53, 464-483.
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Yao, J., Ma, C., He, W, P., 2014. Investor herding behaviour of Chinese stock market. International Review of Economics & Finance 29, 12-29.
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Yang, Y., Gebka, B., Hudson, R., 2019. Momentum effects in China: A review of the literature and an empirical explanation of prevailing controversies. Research in international business and
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finance 47: 78-101.
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Table 1 Variables description and construction. Variable name Panel A: Explanatory variable
Description and construction
30
InsROA
Profit instability based on ROA, which is the residual variance from rolling regressions of the profitability changes relative to the previous year on the time trend. Profit instability based on ROE, which is the residual variance from rolling regressions of the profitability changes relative to the previous year on the time trend.
InsROE
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na
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re
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Panel B: Control variable ROA Return on assets, which is the quarterly net income divided by the average of the current quarterly total assets and 1-quarter-lagged total assets. ROE Return on assets, which is the quarterly net income divided by the average of the current quarterly equity and 1-quarter-lagged equity. Size Market value of tradable shares, which is taken logarithmic transformation BM Book-to-market equity ratio, which is the quarterly book value of equity divided by the market value of total shares. Beta Market beta, which is defined as the coefficient from regressing daily stock returns on market returns using previous one year sample. MOM Momentum, which is the cumulative stock return from month t-1 to t-6. IVOL Idiosyncratic volatility, which is defined as the standard deviation of the residual from regressing daily stock returns on Fama-French three factors using previous three months sample. MAX Average of maximum five history daily returns in previous one month. TURN Average of daily turnover defined as daily trading volume divided by the total number of shares outstanding in previous one months.
31
Table 2 Summary statistics.
InsROA InsROE ROA ROE Size BM Beta MOM IVOL MAX TURN
Mean 0.09 0.2 0.01 0.01 14.65 0.43 1.19 0.13 0.02 0.04 0.03
Std 2.19 2.82 0.02 0.17 0.97 0.27 0.38 0.31 0.01 0.01 0.02
Min 0 0 -0.19 -6.94 12.36 0.02 -0.48 -0.54 0.01 -0.02 0
25% 0.01 0.01 0 0.01 13.99 0.26 0.96 -0.06 0.02 0.03 0.01
Median 0.01 0.03 0.01 0.02 14.55 0.38 1.2 0.07 0.02 0.03 0.02
75% 0.03 0.05 0.02 0.03 15.2 0.54 1.43 0.24 0.03 0.04 0.03
Max 84.61 98.56 0.2 0.8 19.65 2.99 2.9 3.98 0.21 0.13 0.23
Number 1426 1426 1913 1913 1851 1913 1836 1852 1856 1839 1839
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Notes: The table reports the time series averages of the cross-sectional mean, standard deviation,
minimum, 25% quantile point, median, 75% quantile point, maximum and number of
observationsof various firm characteristics, including the instability of ROA (InsROA), instability
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of ROE (InsROE), return on assets (ROA), return on equity (ROE), logarithmic market value(Size),
book-to-market equity ratio (BM), momentum (MOM), idiosyncratic volatility (IVOL), maximum
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daily return (MAX), and turnover (TURN), which are defined in Table 1. The sample period is
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ur
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from2004:01 to 2018:06.
32
Table 3 One-sorting based on firms' profit instability. 2
3
4
5
6
7
8
9
H
H_L
0.93 (0.99) 0.23 (0.95) 0.05 (0.17) 0.12 (0.52)
0.87 (0.87) 0.18 (1.01) -0.02 (-0.1) 0.04 (0.19)
0.91 (0.91) 0.23 (1.04) 0.17 (0.67) 0.29 (1.3)
0.92 (0.87) 0.21 (1.16) 0.19 (1.02) 0.21 (1.13)
0.92 (0.95) 0.19 (1.49) 0.03 (0.19) 0.11 (0.6)
0.65 (0.63) -0.08 (-0.56) -0.14 (-0.82) -0.01 (-0.07)
0.71 (0.71) -0.05 (-0.29) -0.1 (-0.6) -0.07 (-0.45)
0.95 (0.86) 0.17 (0.87) 0.02 (0.1) 0.08 (0.63)
0.42 (0.4) -0.37 (-1.47) -0.63*** (-3.56) -0.56*** (-3.19)
-0.67** (-2.1) -0.7** (-2.34) -0.76*** (-2.84) -0.87*** (-3.13)
0.92 (0.96) 0.23 (1.23) 0.1 (0.48) 0.2 (0.98)
0.96 (0.96) 0.26 (1.21) 0.16 (0.72) 0.27 (1.34)
0.96 (1.04) 0.28** (1.98) 0.16 (1.12) 0.24 (1.43)
0.9 (0.88) 0.21 (1.03) 0.1 (0.41) 0.19 (0.91)
0.87 (0.84) 0.15 (1.02) 0.21 (1.12) 0.14 (0.75)
0.67 (0.64) -0.09 (-0.9) -0.15 (-1.43) -0.07 (-0.61)
0.86 (0.79) 0.08 (0.61) -0.02 (-0.14) 0.01 (0.08)
0.73 0.44 (0.66) (0.41) -0.09 -0.35 (-0.41) (-1.6) -0.27 -0.64*** (-1.4) (-4.44) -0.15 -0.48*** (-0.76) (-3.48)
-0.52** (-2.23) -0.61*** (-3.05) -0.59** (-2.17) -0.62*** (-2.75)
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L Panel A: InsROA Average_return 1.09 (1.02) CAPM_α 0.34 (1.35) FF3_α 0.13 (0.49) FF5_α 0.31 (1.25) Panel B:InsROE Average_return 0.96 (0.99) CAPM_α 0.26 (1.07) FF3_α -0.05 (-0.19) FF5_α 0.14 (0.67)
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Notes: This table presents the result of the one-way sorting portfolio analysis. Each month t, wesort
all stocks into decile portfolios based on the most recently available InsROA and InsROE,
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respectively. Then we assume that the portfolios are held for during month t+1. "Low" refers to the stocks in the lowest profit instability decile, whereas "High" refers to the stocks in the highest profit
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instability decile. The "H-L" is the hedge portfolio that is long "High" portfolio and short"Low" portfolio. This table reports the value weighted monthly average excess returns (in percentage),
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CAPM alphas (CAPM α in percentage), Fama-French three factor alphas (FF3 α in percentage) and Fama-French five factor alphas (FF5 α in percentage) of the portfolios over 2004:01 to 2018:06,
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and their t-statisticsreported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. The data on the Chinese risk-free rate and Fama-French (1993, 2015) three and five factors
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are from the RESSET Financial Research Database. *, **, 0.05 level, and 0.01 level, respectively.
33
***
indicate significance at the 0.1 level,
Table 4 Two-way dependent sorting controlling for market capitalization (Size) . 2
3 4 High Average_return
Panel A: InsROA Small 1.92* 2.04* (1.7) (1.79) Median 1.33 1.14 (1.26) (1.11) Large 0.89 0.71 (0.91) (0.69) Average 1.38 1.3 (1.34) (1.25) Panel B: InsROE Small 2.06* 2.01* (1.8) (1.73) Median 1.28 1.19 (1.22) (1.15) Large 0.82 0.69 (0.86) (0.75) Average 1.38 1.3 (1.35) (1.28)
H-L
Low
2
3
4 FF_α
High
H-L
2.02* (1.72) 1.11 (1.04) 0.83 (0.82) 1.32 (1.24)
1.91 (1.58) 1.13 (1.04) 0.66 (0.66) 1.23 (1.15)
1.66 (1.45) 0.77 (0.71) 0.55 (0.54) 0.99 (0.94)
-0.26 (-1.57) -0.56*** (-3.9) -0.34 (-1.14) -0.39** (-2.58)
0.26 (1.59) -0.06 (-0.29) 0.18 (0.63) 0.13 (0.66)
0.4** (2.21) -0.21 (-1.14) 0.18 (0.85) 0.12 (0.76)
0.33* (1.95) -0.22 (-1.19) 0.23 (1.41) 0.11 (0.84)
0.23 (1.23) -0.22 (-1.45) 0.03 (0.19) 0.01 (0.1)
-0.04 (-0.22) -0.62*** (-3.05) -0.07 (-0.44) -0.24* (-1.77)
-0.3* (-1.88) -0.57*** (-3.92) -0.24 (-0.76) -0.37** (-2.38)
1.96* (1.67) 1.12 (1.08) 0.77 (0.76) 1.28 (1.23)
1.95* (1.69) 1.1 (1) 0.75 (0.7) 1.26 (1.17)
1.57 (1.34) 0.79 (0.72) 0.52 (0.49) 0.96 (0.88)
-0.49*** (-2.66) -0.49*** (-2.8) -0.3 (-1.24) -0.42*** (-2.77)
0.41** (2.4) -0.08 (-0.4) 0.14 (0.63) 0.15 (0.84)
0.35** (2.32) -0.15 (-0.88) 0.15 (0.95) 0.12 (0.81)
0.3* (1.77) -0.23 (-1.32) 0.23 (1.25) 0.1 (0.68)
0.24 (1.29) -0.26 (-1.56) 0.13 (1.01) 0.04 (0.3)
-0.13 (-0.69) -0.6*** (-2.97) -0.15 (-0.98) -0.29** (-2.04)
-0.54*** (-3.12) -0.51*** (-2.99) -0.29 (-1.23) -0.45*** (-3.04)
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Low
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Size
Notes: This table presents the result of the two-way dependent sorting portfolio analysis based on
re
the profit instability (InsROA/InsROE) and market capitalization (Size), which have been documented to predict stock returns and are most recently available. Each month t, we begin by
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sorting all stocks into three portfolios using the 30th and 70th Size percentiles. Next, within each portfolio, we sort the stocks into quintile portfolios based on the firms' profit instability. Specifically,
na
the highest 10% stocks are grouped into the highest portfolio labeled "High", and the rest of stocks are then sorted into quartile portfolios with the lowest one is labeled "Low". The "H-L" is the hedge
ur
portfolio that is long "High" portfolio and short "Low" portfolio within each Size group. In addition, we construct the "Average" portfolios by averaging the "Low" to "High" and "H-L" sub-portfolios
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across the three Size groups. The table reports the value weighted monthly average excess returns (in percentage) and Fama-French three factor alphas (FF3 α in percentage) of the portfolios over 2004:01 to 2018:06, and their t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags.*, **, *** indicate significance at the 0.1 level, 0.05 level, and 0.01 level, respectively.
34
Table 5 Two-way sorting controlling for book to market ratio(BM). 2
3 4 High Average_return
Panel A: InsROA Growth 0.83 0.85 (0.86) (0.91) Neutral 0.94 0.89 (0.92) (0.88) Value 1.41 0.99 (1.22) (1.01) Average 1.06 0.91 (1.03) (0.94) Panel B: InsROE Growth 1.01 1.02 (1.1) (1.09) Neutral 1.1 0.74 (1.11) (0.76) Value 0.99 1.15 (0.92) (1.12) Average 1.03 0.97 (1.06) (1)
H-L
Low
2
3
4 FF_α
High
H-L
0.69 (0.73) 0.83 (0.74) 1.11 (1.04) 0.88 (0.85)
0.72 (0.7) 0.77 (0.74) 0.97 (0.92) 0.82 (0.8)
0.48 (0.45) 0.72 (0.63) 0.97 (0.87) 0.72 (0.67)
-0.35 (-1.28) -0.23 (-0.72) -0.44 (-1.55) -0.34 (-1.63)
0 (-0.01) -0.06 (-0.2) 0.4 (1.52) 0.11 (0.48)
0.33 (1.16) -0.06 (-0.24) -0.03 (-0.14) 0.08 (0.41)
0.04 (0.14) -0.14 (-0.56) 0.21 (0.94) 0.04 (0.23)
-0.15 (-0.88) -0.25 (-1.31) 0.06 (0.41) -0.11 (-1.02)
-0.67** (-2.55) -0.29* (-1.87) 0.07 (0.27) -0.29** (-2.35)
-0.67** (-2.51) -0.23 (-0.66) -0.32 (-0.94) -0.4* (-1.78)
0.41 (0.41) 0.87 (0.79) 1.21 (1.17) 0.83 (0.8)
0.88 (0.86) 1.01 (0.91) 1.07 (0.96) 0.98 (0.92)
0.34 (0.3) 0.5 (0.43) 1 (0.88) 0.61 (0.55)
-0.67* (-1.79) -0.6** (-2.23) 0.01 (0.02) -0.42* (-1.78)
0.29 (0.84) 0.05 (0.22) -0.02 (-0.09) 0.1 (0.48)
0.43 (1.44) -0.27 (-0.96) 0.25 (1.26) 0.14 (0.66)
-0.26 (-1.48) 0 (0.02) 0.27** (2.06) 0 (0.03)
0 (-0.02) -0.01 (-0.04) 0.22 (1.21) 0.07 (0.51)
-0.9*** (-4.94) -0.53*** (-2.93) 0.01 (0.06) -0.47*** (-3.43)
-1.19*** (-3.86) -0.58** (-2.29) 0.04 (0.12) -0.58** (-2.56)
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Low
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BM
Notes: This table presents the result of the two-way dependent sorting portfolio analysis based on
re
the profit instability (InsROA/InsROE) and book-to-market ratio (BM), which have been
lP
documented to predict stock returns and are most recently available. Each month t, we begin by sorting all stocks into three portfolios using the 30th and 70th BM percentiles. Next, within each portfolio, we sort the stocks into quintile portfolios based on the firms' profit instability. Specifically,
na
the highest 10% stocks are grouped into the highest portfolio labeled "High", and the rest of stocks are then sorted into quartile portfolios with the lowest one is labeled "Low". The "H-L" is the hedge
ur
portfolio that is long "High" portfolio and short "Low"portfolio within each BM group. In addition, we construct the "Average" portfolios by averaging the "Low" to "High" and "H-L" sub-portfolios
Jo
across the three BM groups. The table reports the value weighted monthly average excess returns (in percentage) and Fama-French three factor alphas (FF3 α in percentage) of the portfolios over 2004:01 to 2018:06, and their t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. *, **, *** indicate significance at the 0.1 level, 0.05 level, and 0.01 level, respectively.
35
Table 6 Two-way sorting controlling for level of profitability (ROA/ROE). Low
3 4 High Average_return
H-L
Low
2
3
4
High
H-L
FF_α
0.26 (0.23) 0.88 (0.84) 1.34 (1.32) 0.82 (0.79)
0.53 (0.46) 0.58 (0.55) 1.15 (1.2) 0.75 (0.73)
0.44 (0.38) 0.54 (0.52) 0.93 (0.95) 0.64 (0.61)
0.21 (0.19) 0.74 (0.68) 1.08 (1.01) 0.68 (0.62)
-0.56** (-2.05) -0.58*** (-2.62) -0.03 (-0.1) -0.39* (-1.74)
-0.56** (-2.12) 0.34 (1.37) 0.51* (1.89) 0.09 (0.44)
-1.05*** (-3.53) -0.15 (-0.8) 0.86*** (3.77) -0.12 (-0.58)
-0.75*** (-3.42) -0.29 (-1.36) 0.5** (2.41) -0.18 (-1.18)
-0.92*** (-4.04) -0.52*** (-3.44) 0.3 (1.5) -0.38*** (-3.42)
-1.25*** (-6.33) -0.49*** (-2.68) 0.46*** (2.87) -0.43*** (-3.48)
-0.69*** (-3.09) -0.83*** (-3.54) -0.04 (-0.14) -0.52*** (-2.73)
0.56 (0.51) 0.87 (0.84) 1.43 (1.44) 0.96 (0.92)
0.45 (0.4) 0.51 (0.52) 1.07 (1.06) 0.68 (0.66)
0.37 (0.31) 0.72 (0.65) 1.02 (1) 0.7 (0.65)
0.15 (0.13) 0.5 (0.5) 1.12 (0.98) 0.59 (0.54)
-0.6*** (-2.92) -0.26 (-1.15) -0.12 (-0.3) -0.33* (-1.79)
-0.66** (-2.58) -0.32 (-1.35) 0.74*** (2.78) -0.08 (-0.38)
-0.83*** (-3.41) -0.08 (-0.35) 0.86*** (5.29) -0.01 (-0.07)
-0.87*** (-4.09) -0.49*** (-2.7) 0.57*** (2.81) -0.26* (-1.82)
-1*** (-4.68) -0.21 (-1.04) 0.4*** (2.87) -0.27** (-2.22)
-1.35*** (-6.12) -0.65*** (-3.73) 0.4* (1.94) -0.53*** (-3.65)
-0.68*** (-2.86) -0.33* (-1.73) -0.34 (-1.08) -0.45*** (-2.76)
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Panel A: InsROA Low 0.77 (0.66) Median 1.32 (1.23) High 1.11 (1.26) Average 1.07 (1.04) Panel B: InsROE Low 0.74 (0.65) Median 0.77 (0.8) High 1.24 (1.38) Average 0.92 (0.93)
2
-p
Profitability
Notes: This table presents the result of the two-way dependent sorting portfolio analysis based on
re
the profit instability (InsROA/InsROE) and level of profitability (ROA/ROE), which have been
lP
documented to predict stock returns and are most recently available. Each month t, we begin by sorting all stocks into three portfolios using the 30th and 70th ROA/ROE percentiles. Next, within each portfolio, we sort the stocks into quintile portfolios based on the firms' profit instability.
na
Specifically, the highest 10% stocks are grouped into the highest portfolio labeled "High", and the rest of stocks are then sorted into quartile portfolios with the lowest one is labeled "Low". The "H-
ur
L" is the hedge portfolio that is long "High" portfolio and short "Low" portfolio within each profitability group. In addition, we construct the "Average" portfolios by averaging the "Low" to
Jo
"High" and "H-L" sub-portfolios across the three profitability groups. The table reports the value weighted monthly average excess returns (in percentage) and Fama-Frenchthree factor alphas (FF3 α in percentage) of the portfolios over 2004:01 to 2018:06, and their t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. *, significance at the 0.1 level, 0.05 level, and 0.01 level, respectively.
36
**, ***
indicate
Table 7 Two-way sorting controlling for volatility of profitability (VolROA/VolROE).
Panel A: InsROA Low 1.29 (1.17) Median 1.14 (1.22) High 0.95 (0.91) Average 1.13 (1.11) Panel B: InsROE Low 0.9 (0.92) Median 1.17 (1.23) High 1 (0.92) Average 1.02 (1.03)
2
3 4 High Average_return
H-L
Low
2
3
4 FF_α
High
H-L
0.95 (0.89) 0.78 (0.74) 0.74 (0.74) 0.82 (0.8)
0.82 (0.84) 1.07 (0.99) 1.01 (0.93) 0.97 (0.93)
0.81 (0.82) 0.82 (0.83) 1.04 (0.9) 0.89 (0.86)
0.7 -0.59** (0.7) (-1.99) 0.55 -0.59** (0.54) (-2.28) 0.14 -0.81** (0.13) (-2.16) 0.46 -0.66*** (0.45) (-3.14)
0.23 (0.78) 0.32 (1.5) 0.42* (1.68) 0.32 (1.65)
0 (0.02) -0.09 (-0.38) -0.07 (-0.33) -0.05 (-0.26)
-0.18 -0.16 (-0.78) (-0.71) 0.22 -0.1 (1.13) (-0.4) 0.02 -0.04 (0.11) (-0.21) 0.02 -0.1 (0.14) (-0.56)
-0.18 (-1.09) -0.29* (-1.86) -0.91*** (-4.74) -0.46*** (-4.75)
-0.4 (-1.23) -0.61** (-2.23) -1.33*** (-4.58) -0.78*** (-3.64)
0.92 (0.91) 0.87 (0.91) 0.99 (0.9) 0.93 (0.91)
0.88 (0.85) 1.06 (1.03) 0.81 (0.73) 0.92 (0.87)
0.72 (0.8) 0.78 (0.77) 0.75 (0.65) 0.75 (0.74)
0.92 (0.89) 0.59 (0.56) 0.28 (0.25) 0.6 (0.57)
-0.19 (-0.74) 0.4 (1.4) 0.51** (2.31) 0.24 (1.24)
-0.04 (-0.18) 0.07 (0.31) 0.14 (0.8) 0.05 (0.38)
-0.08 (-0.44) 0.26 (1.28) -0.2 (-0.84) -0.01 (-0.03)
0 (0.01) -0.28* (-1.86) -0.8*** (-5.68) -0.36*** (-3)
0.19 (0.78) -0.68*** (-2.7) -1.31*** (-5.49) -0.6*** (-3.9)
0.03 (0.12) -0.58** (-2.3) -0.72** (-1.99) -0.42** (-2.42)
-0.31 (-1.62) -0.1 (-0.81) -0.41* (-1.87) -0.27** (-2.29)
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Low
-p
Profit volatility
Notes: This table presents the result of the two-way dependent sorting portfolio analysis based on
re
the profit instability (InsROA/InsROE) and volatility of profitability (VolROA/VolROE). Each month
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t, we begin by sorting all stocks into three portfolios using the 30th and 70th VolROA/VolROE percentiles. Next, within each portfolio, we sort the stocks into quartile portfolios based on the firms' profit instability. Specifically, the highest 10% stocks are grouped into the highest portfolio labeled
na
"High", and the rest of stocks are then sorted into quartile portfolios with the lowest one is labeled "Low". The "H-L" is the hedge portfolio that is long "High" portfolio and short "Low" portfolio
ur
within each profitability group. In addition, we construct the "Average" portfolios by averaging the "Low" to "High" and "H-L" sub-portfolios across the three profitability groups. The table reports
Jo
the value weighted monthly average excess returns (in percentage) and Fama-French three factor alphas (FF3 α in percentage) of the portfolios over 2004:01 to 2018:06, and their t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. *, **, significance at the 0.1 level, 0.05 level, and 0.01 level, respectively.
37
***
indicate
Table 8 Fama-MacBeth regression analysis of the predictive power of profit instability to future
stock returns. Model InsROA
(1) -0.0245** (-2.12)
(2) -0.0219** (-2.03)
(3) -0.0233*** (-2.71)
(4) -0.017* (-1.67)
InsROE 0.1548* (1.81)
ROA
0.2894*** (5.47)
(5)
(6)
(7)
(8)
-0.0018** (-2.08)
-0.002** (-2.01)
-0.002** (-2.5)
-0.0017* (-1.88)
0.084** (2.2)
0.1312*** (5.51) -0.0061*** (-3.43) 0.0077** (2.16) -0.0095 (-1.49)
0.2663*** (5.04)
0.1234*** (5.32) Size -0.0062*** -0.0077*** -0.0077*** (-3.49) (-4.02) (-3.97) BM 0.008** 0.0014 0.0009 (2.29) (0.45) (0.28) Beta -0.008 -0.0021 -0.0032 (-1.26) (-0.11) (-0.29) MOM -0.0012 -0.0013 (-0.29) (-0.28) IVOL -0.0116 -0.0329 (-0.09) (-0.35) MAX -0.1762*** -0.1733*** (-4.21) (-4.11) TURN -0.4382*** -0.4356*** (-11.21) (-11.4) Intercept 0.0162 0.0147 0.1098*** 0.1456*** 0.0158 0.0143 0.1097*** 0.1465*** (1.54) (1.34) (3.53) (4.22) (1.49) (1.31) (3.49) (4.19) Adj_R2 0.161 2.1402 7.7438 11.4879 0.0755 1.8311 7.66 11.4222 Observations 237,798 237,798 232,160 228,143 237,798 237,798 232,160 228,143 Notes: This table presents the results of Fama-MacBeth cross-sectional regression of
lP
re
-p
ro of
ROE
individualfuture stock returns in month t+1 on independent variables, which are most recently
Model 4 (8):
na
available at the endof month t. Our main specification is Equation (2), which appears below as
R E T it 1 In te r c e p t 1 In s R O A it ( In s R O E it ) 2 R O A it ( R O E it ) 3 S iz e it 4 B M it
5 B e ta it 6 M O M
9 T U R N it it 1
it
7 IV O L it (2)
ur
8M AX
it
The dependent variable is the future return for firm i in month t+1, and the lagged independent
Jo
variables are defined in Table 1. The table reports the estimation of the Fama-MacBeth mean monthly coefficients for eight different models that include different subsets of independent variables. The sample period covers 2004:01 to 2018:06, and the t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. *, **, the 0.1 level, 0.05 level, and 0.01 level, respectively.
38
***
indicate significance at
Table 9 Fama-MacBeth monthly cross-section regression of stock returns on profit instability characteristic and factor loadings. Model InsROA
(1)
(2) -0.0131** (-2.29)
(3) -0.0133** (-2.05)
(4) -0.0168*** (-2.83)
(5)
InsROE 0.2733*** (4.59)
ROA
0.2485*** (4.02)
IVOL MAX TURN beta_InsROA
0.0003 (0.67)
0.0005 (1.15)
-0.0091*** (-4.1) 0.0017 (0.49) -0.0048 (-0.7) -0.0747 (-0.9) -0.1521*** (-3.22) -0.3867*** (-8.68) 0.0001 (0.17)
lP
beta_InsROE beta_mar_ROA
-0.0017*** (-3.04)
-0.0015*** (-2.7)
-0.0018*** (-2.93)
0.125*** (4.5) -0.0079*** (-3.24) 0.0061 (1.35)
0.1204*** (4.14) -0.0097*** (-3.83) -0.0007 (-0.16) -0.007 (-0.96) -0.0531 (-0.55) -0.1468*** (-3.3) -0.3976*** (-9.03)
0.1222*** (4.6) -0.0092*** (-3.92) 0.001 (0.28) -0.0066 (-0.92) -0.082 (-0.94) -0.1424*** (-3.08) -0.3975*** (-8.81)
0.001 (1.32)
0.0007 (0.78)
ro of
MOM
(8)
-p
BM
-0.0096*** (-4.01) 0.0001 (0.02) -0.0054 (-0.79) -0.0492 (-0.53) -0.1566*** (-3.37) -0.3853*** (-8.67) 0.0004 (0.93)
re
-0.0079*** (-3.45) 0.0077* (1.74)
(7)
0.2541*** (4.55)
ROE Size
(6)
0.0007 (0.89)
0.0008 (1.27)
0.0021 (0.78)
na
beta_mar_ROE beta_smb_ROA
ur
beta_smb_ROE
0.002 (1.55) 0.002 (1.51) -0.0018** (-2.27)
beta_hml_ROA
Jo
0.0026 (0.88)
beta_hml_ROE Intercept
Adj_R2 Observations
0.0096 (0.95) 0.4446 220,142
0.1241*** (2.95) 6.0452 195,276
0.1646*** (3.64) 9.8834 190,347
0.1528*** (3.79) 11.1993 190,347
0.0142 (1.49) 0.8584 220,142
0.129*** (2.89) 6.193 195,276
0.1716*** (3.59) 10.0407 190,347
-0.0017** (-2.25) 0.1592*** (3.74) 11.37 190,347
Notes: This table presents the results of Fama-MacBeth cross-sectional regression of individual future stock returns in month t+1 on independent variables, which are most recently available at the
39
endof month t. Our main specification is Equation (3), which appears below as Model 4(8): R E T it 1 I n te r c e p t 1 I n s R O A it ( I n s R O E it )
9 k2
9 i2
j O th e r _ c h a r a c te r is tic it 1 b e ta _ I n s R O A it ( b e ta _ I n s R O E it ) j
k O th e r _ lo a d in g s it k
(3)
The dependent variable is the future return for firm i in month t+1. The lagged independent variables are defined in Table 1. The individual stock factor loadings of traditional Fama-French three factors and profit instability factor. The construction of profit instability factor is analogous to the value factor and profitability factor in Wang and Yu (2013) and Fama and French (1993,2015). We independently and evenly sort all stocks in our sample into two size groups and three profit
ro of
instability (measured by InsROA and InsROE, respectively) groups, and obtain six value weighted portfolios. Then, profit instability mimicking factor is defined as the average of the two low profit
instability portfolio returns minus the average of the two high profit instability portfolio returns. The table reports the estimation of the Fama-MacBeth mean monthly coefficients for eight different
-p
models that include different subsets of independent variables. The sample period covers 2008:01 to 2018:06, and the t-statistics reported in parentheses are adjusted by Newey-West robust standard ***
indicate significance at the 0.1 level, 0.05 level, and 0.01 level,
re
errors with 12 lags. *,**,
Jo
ur
na
lP
respectively.
40
f oo
Table 10 Fama-French alphas of two-way sorting portfolios controlling for momentum (MOM), maximum history daily return (MAX) and idiosyncratic volatility (IVOL) H-3
H-4
Average
na l
Jo ur
H-1
H-2
H-3
H-4
H-5
Average
InsROE
-0.29 (-1.47) -0.95*** (-3.77) -0.65** (-2.5)
-0.48 (-1.24) -0.81*** (-3.6) -0.33 (-1.07)
-0.19 (-0.73) -1.08*** (-3.93) -0.89** (-2.55)
-0.46* (-1.74) -0.76** (-2.58) -0.3 (-1.05)
-0.09 (-0.4) -1.09*** (-4.83) -1*** (-3.26)
-0.43** (-2.1) -0.96*** (-4.07) -0.53** (-2.06)
-0.33 (-1.47) -0.94*** (-4.38) -0.61*** (-2.66)
-0.19 (-0.69) -1.38*** (-5.25) -1.19*** (-3.41)
-0.17 (-0.78) -1.07*** (-4) -0.9*** (-2.93)
-0.42 (-1.25) -0.8** (-2.58) -0.38 (-0.99)
-0.24 (-0.99) -1.16*** (-3.39) -0.92** (-2.11)
-0.44 (-1.43) -1.19*** (-3.48) -0.74 (-1.46)
-0.52* (-1.92) -0.98*** (-4.77) -0.46 (-1.47)
-0.47** (-2.41) -1.16*** (-5.26) -0.69** (-2.14)
-0.42* (-1.86) -1.06*** (-4.33) -0.64* (-1.97)
-0.38 (-1.48) -1.18*** (-3.41) -0.8** (-2.03)
-0.09 (-0.37) -0.95*** (-2.95) -0.86** (-2.05)
0.04 (0.12) -0.91*** (-3.18) -0.95** (-2.27)
-0.21 (-0.78) -1*** (-3.9) -0.79* (-1.88)
-0.28 (-1.05) -0.65** (-2.11) -0.37 (-0.98)
-0.25 (-0.87) -0.96*** (-3.7) -0.71* (-1.79)
-0.41 (-1.48) -0.73*** (-3.34) -0.32 (-0.95)
-0.22 (-1.01) -0.85*** (-3.83) -0.63* (-1.94)
-0.27 (-0.95) -0.87*** (-2.96) -0.59*** (-2.81)
Pr
InsROA Panel A: MOM as the control variable Low -0.52 -0.07 -0.14 -0.46* (-1.57) (-0.24) (-0.68) (-1.94) *** *** *** High -1.11 -1 -0.83 -0.93*** (-2.88) (-3.55) (-4.06) (-2.85) ** ** H-L -0.59 -0.93 -0.69 -0.47 (-1.29) (-2.48) (-2.26) (-1.34) Panel B: MAX as the control variable Low -0.43 0.05 -0.06 -0.24 (-1.38) (0.16) (-0.26) (-0.82) High -1.04*** -0.89*** -0.99*** -1.05*** (-2.69) (-2.63) (-3.72) (-3.62) * ** ** DID -0.62 -0.95 -0.93 -0.81** (-1.87) (-2.29) (-2.58) (-2.15) Panel C: IVOL as the control variable Low -0.18 0.07 0.05 -0.02 (-0.51) (0.16) (0.19) (-0.07) High -1.16*** -0.87*** -0.68** -0.86** (-2.91) (-2.62) (-2) (-2.55) * * DID -0.98 -0.93 -0.73 -0.85** (-1.95) (-1.82) (-1.5) (-2)
H-5
pr
H-2
e-
H-1
Notes: This table presents the result of the two-way dependent sorting portfolio analysis based on the profit instability (InsROA/InsROE) and the control variables, including momentum(MOM), idiosyncratic volatility (IVOL) and maximum history daily return (MAX). Each month t, we begin by sorting all stocks into two portfolios
41
f
oo
using the 50th MOM MAX or IVOL percentiles. Next, within each group, we sort the stocks intodecile portfoliosbased on the firms' profit instability and then construct five hedge portfolios using the difference between "High" portfolio and first five portfolios.In addition, we construct the "DID" portfolio, which indicates the difference
pr
of hedge portfolios and "High" portfolio between the two subgroups. The table reports Fama-French three factor alphas (FF3 α in percentage) of the portfolios over 2004:01to 2018:06, and the t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. * ,**, *** indicate significance at the 0.1
Jo ur
na l
Pr
e-
level, 0.05 level, and 0.01 level, respectively.
42
Table 11 Fama-MacBeth monthly cross-section regression of stock returns on the momentum (MOM), maximum history daily return (MAX) and idiosyncratic volatility (IVOL). MOM
MAX
(1) -0.0392*** (-3.12)
I |InsROA IH|InsROE
(2)
(3) -0.0304** (-2.47)
-0.0035*** (-2.92)
IL|InsROA
-0.0016 (-0.44)
IL|InsROE
-0.0009 (-1.05)
Beta IMOM IIVOL IMAX
na
TURN Intercept
0.124*** (5.04) -0.0078*** (-3.85) 0.0008 (0.29) -0.0024 (-0.09) 0.0009 (0.6) 0.0022*** (3.02) 0.0025*** (2.83) -0.464*** (-12.86) 0.1406*** (4.03) 10.65 228,143
-0.0079*** (-3.93) 0.0013 (0.46) -0.0014 (0.08) 0.0009 (0.6) 0.0016** (2.27) 0.0027*** (3.3) -0.4643*** (-12.58) 0.1405*** (4.09) 10.60 228,143
0.1241*** (5.07) -0.0078*** (-3.86) 0.0008 (0.3) -0.0025 (-0.11) 0.0009 (0.6) 0.002*** (2.86) 0.0026*** (3.2) -0.4618*** (-13) 0.1406*** (4.04) 10.60 228,143
ur
Adj_R2 Observations
-0.0010 (-0.71) 0.2694*** (4.85)
re
BM
-0.0078*** (-3.92) 0.0012 (0.44) -0.0012 (0.13) 0.0009 (0.62) 0.0019*** (2.66) 0.0021** (2.09) -0.4647*** (-12.62) 0.1404*** (4.09) 10.66 228,143
lP
-0.0079*** (-3.94) 0.0013 (0.47) -0.0014 (0.07) 0.0000 (0.03) 0.002*** (2.71) 0.0027*** (3.34) -0.4624*** (-12.55) 0.1408*** (4.13) 10.68 228,143
Size
-0.0061 (-0.44)
0.2685*** (4.87) 0.1257*** (5.14) -0.0078*** (-3.88) 0.0008 (0.3) -0.0025 (-0.13) 0.0007 (0.48) 0.0021*** (2.95) 0.0026*** (3.15) -0.4633*** (-12.8) 0.1412*** (4.06) 10.66 228,143
(6)
-0.0026*** (-2.83)
-0.0005 (-0.56)
0.2713*** (4.89)
ROE
(5) -0.0238** (-2.46)
-0.0025** (-2.33)
0.0002 (0.14)
ROA
(4)
ro of
H
IVOL
-p
Model
Notes: This table presents the results of Fama-MacBeth cross-sectional regression of
Jo
individualstock returns in month t+1 on independent variables, which are most recently available at the end
R E T it 1 In te r c e p t 1 In s R O A it ( In s R O E it ) I it | In s R O A it ( In s R O E it ) + 2 R O A it ( R O E it ) 3 S iz e it
4BM
it
5 B e ta it 6 M O M
C
it
7 IV O L it 8 M A X
it
9 T U R N it it 1
(4)
The dependent variable is the future return for firm i in month t+1, and the lagged independent variables are defined in Table 1. In particular,
C
I it
is the dummy variable according the median
ofthe MOM, MAX or IVOL denoted as C in I . If MOM, MAX or IVOL is smaller than its median, C
it
43
C
I it
is one, if not, I is zero. The table reports the estimation of the Fama-MacBeth mean monthly C
it
coefficients for eight different models that include different subsets of independent variables. The sample period covers 2004:01 to 2018:06, and the t-statistics reported in parentheses are adjusted by Newey-West robust standard errors with 12 lags. *, **, *** indicate significance at the 0.1 level,
Jo
ur
na
lP
re
-p
ro of
0.05 level, and 0.01 level, respectively.
44
400
Index of Sstock Price
350 300 250 200 150 100 50
ro of
0
LuZhouLaoJiao
WuLiangYe
0.3
-p
0.25
re
0.2 0.15 0.1 0.05 0 2010
2011
2012
2013
na
2009
lP
Profitability of the two firms
0.35
LuZhouLaoJiao
2014
2015
2016
2017
WuLiangYe
Figure 1 The index of stock prices and firm's profitability of Lu Zhou Lao Jiao and Wu Liang Ye
Jo
ur
over the period from 2013:01 to 2018:06.
45
Ins_ROA
Ins_ROE
Cumulative Return
1.25 1.2 1.15 1.1 1.05 1
Ins_ROE
1.6
-p
1.5 1.4
re
1.3 1.2 1.1
lP
Cumulative Risk-ajusted Return
Ins_ROA
ro of
0 2 4 6 8 1012141618202224262830323436384042444648505254565860 Period
1
na
0 2 4 6 8 10 1214 16 1820 22 2426 28 3032 3436 38 40 4244 4648 50 5254 56 5860 Period
Figure 2 Long-term return performance of the profit instability hedge portfolio. The value of $1
Jo
ur
invested in the hedge portfolio in Month 0.
46
oo
0.005
0.005
0 P1
P2
P3
P4
P5
P6
P7
P8
P9
0
P10
P1
P2
P3
P4
-0.01 -0.015
e-
High history return
Ins_ROA
Pr
0.01 0
P1
P2
P3
P4
P5
P6
P7
-0.02
Low idiosyncratic volatility
P8
P9
Low history return
-0.01 -0.015
P9
P10
P1
P2
P3
P4
Low maximum return
P5
P6
High history return
0.01 0
P10
-0.005
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
-0.01 -0.015
High idiosyncratic volatility
Jo ur
-0.005
P8
Ins_ROE
Low idiosyncratic volatility
Ins_ROA
0
P7
0.005
na l
-0.01
0.005
P6
-0.01
Low history return
0.01
P5
-0.005
pr
-0.005
Ins_ROE
f
Ins_ROA
High idiosyncratic volatility
Ins_ROE
0.005 0 P7
P8
P9
-0.005
P10
P1
P2
P3
P4
P5
P6
P7
P8
P9
-0.01 -0.015 High maximum return
Low maximum return
Figure 3 Fama-French alphas of profit instability portfolios in different history return, idiosyncratic volatility, and maximum return groups.
47
High maximum return
P10
Appendix
Appendix-Table 1 One-sorting based on volatility of profitability. L
2
3
4
5
6
7
Panel A: Portfolios sorted on VolROA Average_return 1 0.98 0.83 0.81 0.94 1 1.22 (0.97) (1.03) (0.87) (0.84) (0.96) (1.03) (1.13) FF_α -0.09 0.01 -0.17 -0.22 -0.07 0.09 0.41** (-0.43) (0.04) (-0.87) (-1.25) (-0.38) (0.51) (2.42)
8
9
H
H_L
1.05 0.99 0.67 -0.33 (1.03) (1) (0.64) (-1.29) 0.24 0.13 -0.4*** -0.32 (1.25) (0.68) (-3.32) (-1.47) 1.08 0.56 (1.04) (0.5) 0.13 -0.62*** (0.73) (-3.63)
-0.23 (-0.8) -0.39* (-1.95)
ro of
Panel B: Portfolios sorted on VolROE Average_return 0.78 1.04 1.04 0.87 0.85 1.25 0.9 1.05 (0.84) (1.09) (1.05) (0.9) (0.9) (1.27) (0.9) (0.96) FF_α -0.23 -0.01 -0.01 -0.17 -0.09 0.38** 0.09 0.39** (-1.12) (-0.08) (-0.07) (-0.87) (-0.5) (2.05) (0.57) (2.07)
-p
Panel C: Portfolios sorted on VolROA excluding top 10% of stocks according to firms' InsROA. Average_return 0.92 0.95 0.64 0.66 0.74 0.89 1.16 1.11 0.88 0.62 -0.3 (0.9) (0.95) (0.64) (0.68) (0.76) (0.88) (1.02) (1.1) (0.87) (0.6) (-1.3) FF_α -0.05 0.05 -0.27 -0.26 -0.17 0.04 0.4* 0.46** 0.12 -0.23 -0.18 (-0.25) (0.25) (-1.44) (-1.42) (-1) (0.22) (1.84) (2.37) (0.66) (-1.44) (-0.94)
lP
re
Panel D: Portfolios sorted on VolROE excluding top 10% of stocks according to firms' InsROE. Average_return 0.7 0.88 0.93 0.71 0.8 1.01 0.93 1.02 0.99 0.5 -0.2 (0.73) (0.9) (0.92) (0.72) (0.82) (1.04) (0.92) (0.9) (0.93) (0.45) (-0.8) FF_α -0.22 -0.09 0 -0.25 -0.1 0.24 0.21 0.46** 0.19 -0.51*** -0.29 (-1.01) (-0.59) (0) (-1.11) (-0.56) (1.19) (1.14) (2.14) (0.98) (-2.79) (-1.61)
na
Notes: In this table, Panel A and B/ Panel C and D present the results of the one-way sorting portfolio analysis including/excluding top 10% of stocks based on firms' profit instability.
ur
Specifically, each month t we sort all stocks into decile portfolios based on the most recently available VolROA and VolROE, respectively. Then we assume that the portfolios are held for during
Jo
month t+1. "Low" refers to the stocks in the lowest profit instability decile, whereas "High" refers to the stocks in the highest profit instability decile. The "H-L" is the hedge portfolio that is long "High" portfolio and short "Low" portfolio. This table reports the value weighted monthly average excess returns (in percentage) and Fama-French three factor alphas (FF3 α in percentage) over 2004:01 to 2018:06, and their t-statisticsreported in parentheses are adjusted by Newey-West robust
48
standard errors with 12 lags. *, **, *** indicate significance at the 0.1 level, 0.05 level, and 0.01 level,
Jo
ur
na
lP
re
-p
ro of
respectively.
49