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Risk Factors in the Stock Returns for the A

Shares of China

*

Min Huang

*

, S2316234

First Supervisor: Prof. Dr. Theo Dijkstra

Second Supervisor: Dr. Lammertjan Dam

Master Thesis of Finance

Faculty of Economics and Business, University of Groningen

October 2014

                                                                                                               

*  I  would  like  to  thank  Prof.  Theo  Dijkstra  for  his  critical  comments  and  patient  guidance.  

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Abstract

In this study, we assess the explanatory power of combinations of factors for cross-sectional returns of A shares of the emerging market of China by means of the adjusted R-square for the corresponding regressions. The factors included are the overall market factor, the Fama and French factors, and an earnings management factor. Our main finding is that the overall market and size factors are of vital importance in capturing the variance in returns, and that the Fama and French three-factor model gives the best performance. The earnings management factor by itself appears to be slightly better than the book-to-market factor, however, replacing the latter by the former in the three-factor model does not lead to improvement.

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List of Contents  

1.  Introduction  ...  3   2.  Literature  Review  ...  4   3.  Methodology  ...  5   3.1. Stock-market factors  ...  5   3.2. Return analysis  ...  8   4.  Data  ...  10   4.1. Data selection  ...  10   4.2. Summary statistics  ...  11  

4.2.1. The 25 stock portfolios formed on size and BE/ME  ...  13  

4.2.2. The 30 stock portfolios formed on size and NI/CFO  ...  16  

5.  Results  ...  19  

5.1. The Fama and French three-factor model  ...  19  

5.2. The three-factor model with NI/CFO factor  ...  25  

6.  Discussion  and  conclusion  ...  29  

7.  References  ...  31  

List of Tables  

Table  1.  Descriptive  statistics  for  the  sample  stocks  ...  12  

Table  2.  Descriptive  statistics  for  25  stock  portfolios  formed  on  size  and  book-­‐to-­‐market  equity    ...  14  

Table  3.  Summary  statistics  for  the  monthly  dependent  and  explanatory  returns  in  the   regression  of  table  5  to  9  ...  15  

Table  4.  Descriptive  statistics  for  30  stock  portfolios  formed  on  size  and  earnings  quality  ...  18  

Table  5.  Regression  of  excess  stock  returns  on  the  excess  market  returns  (RM-­‐RF)  ...  21  

Table  6.  Regression  of  excess  stock  returns  on  the  excess  market  returns  (RM-­‐RF)  and  the   mimicking  returns  for  book-­‐to-­‐market  equity  (HML)  factor;  Regression  of  excess  stock   returns  on  the  excess  market  returns  (RM-­‐RF)  and  the  returns  for  size  (SMB)  factor  ...  22  

Table  7.  Regression  of  excess  stock  returns  on  the  excess  market  returns  (RM-­‐RF)  and  the   mimicking  returns  for  the  size  (SMB)  and  book-­‐to-­‐market  equity  (HML)  factors  ...  23  

Table  8.  Regression  of  excess  stock  returns  on  the  excess  market  returns  (RM-­‐RF)  and  the   mimicking  returns  for  earnings  quality  (LMS)  factor;  Regression  of  excess  stock  returns  on   the  excess  market  returns  (RM-­‐RF)  and  returns  for  the  size  (SMB)  factor  ...  27  

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1. Introduction

The predictability of future stock returns and what determinants explain equity returns are two of the most important research topics on Capital Market. As cornerstones, the publications of Sharpe (1964)’s Capital Asset Pricing Model (CAPM) and the Efficient Market Hypothesis (EMH) introduced by Fama (1965, 1970) have shaped the way people think about equity returns and risks. What’s more, their works have shed light on investigations based on firm characteristics, which are related to equity returns, and bring inspiration in many ways. Basu (1977) suggested that price-earnings (P/E) ratios are related to risk adjusted returns and considered his findings are evidence of market inefficiency. However, Ball (1978) proposed a different theory and believed that the anomalies might be attributed to a misspecification of the pricing model rather than the market inefficiency. Reinganum (1981) believed that the P/E-ratio effect is just a proxy of the size effect, whereas Banz (1981) introduced the size effect, another important empirical conflict of the Sharpe (1964) model. Banz found that on average the smaller firms have higher risk adjusted returns than larger firms. And Rosenberg et al. (1985) pointed out that a firm’s book-to-market equity (BE/ME) ratio is related to its returns.

In the year 1993, to integrate the aforementioned findings, a prominent paper by Fama and French (1993) introduced a three-factor model, which is comprised of the overall market factor and factors related to firm size (market value of equity) and book-to-market equity. Foye et al. (2013) respecify the Fama and French (1993) model on the purpose to better serve the emerging markets of new member states of the European Union (EU). They replaced the market value of equity (ME) factor related to size with the net income/cash flow from operating activities (NI/CFO) factor proxying for earnings management.   The re-specified model appeared to have better performance when compared to the performance of the Fama and French (1993) model in the Foye et al. (2013) study. Although there are still arguments on whether these findings are risk factors, products of data mining, or merely due to investor’s irrationality, a new method for the emerging markets is worth looking into, in particular, the stock market of China.

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simultaneously to identify its explanatory ability on the Chinese stock returns. The key findings show that the Fama and French three-factor model constructed from the overall market factor and mimic risk factors related to size and book-to-market equity captures strong common variation in returns of the stock market of China. In addition to the aforementioned factors, the factor related to earnings management also has explanatory ability in stock returns.

The article proceeds with Section 2 presenting literature review of previous researches and important findings that are related to this study. Information on group setting methods for this study and all functions that have been used are highlighted in Section 3. Section 4 introduces summary of statistics for different data sets in addition to the data availability and requirements. In section 5, results of all time-series regressions are illustrated. Section 6 of this paper concludes with comprehensive discussion, and all references of the paper are listed in Section 7.

2. Literature Review

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re-specified model was evaluated in explaining the stock returns of Eastern European countries that joined the EU in 2004, whereas a poorer performances of the Fama and French (1993) model was identified for the same market.

This paper will firstly apply Fama and French (1993)’s three factor model to the Chinese stock market, due to the fact that the BE/ME factor shows limitation in addressing stock returns in this study (results can be found in Section 5), an alternative NI/CFO factor to BE/ME factor is then added to the further analysis. In a previous study, Fama and French (1992) mentioned that BE/ME is a signal of earning prospect, a measure for the quality of earnings can be a reasonable alternative factor to the BE/ME, using NI/CFO as a common risk factor can be further supported by the view that stock returns are somehow related to earnings and the components of earnings. In Wilson’s 1987 study, he found evidence of correlation between stock returns and information about the cash and non-cash components of earnings. Sloan (1996) added his view that many reports show that stock prices are found to act as if investors are ‘fixated’ on earnings. He further underlined that the earnings performance attributable to the accrual component shows lower persistence than the earnings performance attributable to the cash flow component of earnings. In a recent study by Li et al. (2011), they found evidence of accruals mispricing in China, indicating that the NI/CFO factor, as a factor of cash flow ratio, can serve better as a proxy of earnings management in the Chinese stock market.

3. Methodology

3.1. Stock-market factors

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for the bottom 30% (Low), middle 40% (Medium), and top 30% (High) are set by the ranked values of BE/ME for stocks in the CSI All Share Index. In respect to the BE/ME ratio, BE and ME are measured by book common equity and market value of equity at the end of December in year t-1. Book common equity refers to the book value of shareholders’ equity of the annual financial statements in this paper. Negative-BE firms are excluded during the procedure of forming the size-BE/ME portfolios. Six size-BE/ME portfolios (S/L, S/M, S/H, B/L, B/M, B/H) are constructed from the intersections of the two sizes and the three BE/ME groups.

The small minus big (SMB) portfolio is used to reflect returns related to size and the high minus low (HML) portfolio is created to proxy returns related to BE/ME. The portfolio SMB is the monthly differences between average returns (value-weighted) on small (S) and big (B) groups, calculated as:

SMB =!/!!!/!!!/!! −!/!!!/!!!/!!   (1)

The HML portfolio is the monthly differences between average returns (value-weighted) on the high (H) and low (L) groups, calculated as:

HML =!/!!!/!! −!/!!!/!!   (2)

For both mimicking portfolios, monthly value-weighted returns are used for the calculations. Using the value-weighted component is very important according to Fama and French (1993). They pointed out that using value-weighted returns could minimize variance due to the negative correlation between the firm’s stock return and its size. Moreover, using value-weighted components makes mimicking portfolios (SMB and HML) closer to realistic investment opportunities. These monthly returns are calculated from the last trading day of July in year t to the last trading day of June in year t+1 for each year in the nine-year period. Six size-BE/ME portfolios used for computing the SMB and HML portfolios are rearranged for each year in the nine-year period.

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are possibilities of having negative values for both NI and CFO, this paper first splits all sample stocks into two groups (group P and group Zero) based on their positive and negative values of NI and CFO. Group P contains stocks that with both positive NI and positive CFO values. The rest stocks are contained in the group Zero. Stocks in group P are then ranked to make the bottom 30% (Small), middle 40% (Medium), and top 30% (Large) portfolios based on their ranked values of NI/CFO. Both net income and cash flow from operating activities are captured in financial statements at the end of December in year t-1 for each year of the nine-year period.

Monthly differences between average returns (value-weighted) on the large (L) and small (S) groups form the large minus small (LMS) portfolio. As mentioned before, NI/CFO factor is used as an alternative to BE/ME factor in the study. Therefore, the eight size-NI/CFO portfolios (S/0, S/S, S/M, S/L, B/0, B/S, B/M, B/L) are constructed from the intersections of the two sizes and the four NI/CFO groups. Mimicking factors of the eight size-NI/CFO portfolios can be calculated by the equations as follows:

SMB =!/!!!/!!!/!!!/!! −!/!!!/!!!/!!!/!!   (3)

LMS =!/!!!/!! −!/!!!/!!   (4)

The monthly returns are calculated from the last trading day of July in year t to the last trading day of June in year t+1 for each year in the nine-year period. Eight size-NI/CFO portfolios used for computing the SMB and LMS portfolios are rearranged for each year in the nine-year period. Monthly value-weighted returns are used for the calculations.

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3.2. Return analysis

For a more detailed analysis, returns of stocks in the CSI All Share Index are then split to make the 25 stock portfolios and the 30 stock portfolios, respectively. The 25 stock portfolios are built much like the six size-BE/ME portfolios as mentioned before, while the 30 stock portfolios are formed similar to the way of the eight size-NI/CFO portfolios. The 25 stock portfolios are formed from the intersections of the size quintiles and the BE/ME quintiles. The 30 stock portfolios are constructed from the intersections of the size quintiles and the six NI/CFO groups (group Zero and the ranked NI/CFO quintiles of group P). For the size sorts, ME is measured at the end of June in year t, while it is measured at the end of December in year t-1 for the book-to-market equity sorts. BE, NI and CFO are all measured at the end of December in year t-1 for each year during the study periods. Monthly returns are calculated from the last trading day of July in year t to the last trading day of June in year t+1 for each year from 2005 to 2014. 25 stock portfolios and 30 stock portfolios are rearranged for each year in the nine-year period. Monthly value-weighted returns are used for the calculations.

In the time-series regressions, the explanatory variables include excess returns on the market portfolio and mimicking portfolios for size, book-to-market equity, and earnings management factors. Excess returns used as the dependent variables in the time-series regressions are the excess stock returns from the 25 stock portfolios or the 30 stock portfolios.

Following the portfolio ranking procedure, two sets of functions are built in order to test which variable actually contributes to the model. All sets are containing the following equations:

R(t) − RF(t) = α + β RM t − RF t + e t (5)

R t − RF(t) = α + β RM t − RF t + sSMB(t) + e t (6)

The third regression is presented respectively as follows:

R(t) − RF(t) = α + β RM t − RF t + hHML(t) + e t (7)

R t − RF(t) = α + β RM t − RF t + lLMS(t) + e t (8)

Finally, the study applies the three-factor models below:

R t − RF(t) = α + β RM t − RF t + hHML(t) + sSMB(t) + e t (9)

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R t − RF t = α + β RM t − RF t + lLMS t + sSMB t + e t (10) Firstly, Eq. (5) is examined using the excess market return (RM-RF) to explain stock returns. Secondly, in order to illustrate the impact of firm size on stock returns, the results of Eq. (6), which is containing both the overall market factor RM-RF and size factor SMB as explanatory variables, are used to compare with the results of Eq. (5). Thirdly, the SMB factor is replaced by HML factor and LMS factor respectively, as are shown in Eq. (7) and Eq. (8). These two functions are used to help explain the influence of BE/ME factor and earnings management factor separately. Finally, two three-factor models, Eq. (9) and (10), are used to test the overall explanatory ability on stock returns.

In this paper, the adjusted R2 is used as a main indicator for evaluation of the regression models. Although there are debates about using the adjusted R2 when evaluating a regression model, this statistic does have some positive aspect as a model-selection criterion. Following the illustration of Giles (August 3, 2013), selecting alternative regression model specifications by maximizing the adjusted R2 suggests that models are essentially chosen by means of the smallest residual variance

estimate. For the true model, the expected value of its residual variance is the smallest, compared to all other models that do not contain the correct independent variables. In other words, choosing the regression model with the smaller estimator of the error variance, or larger adjusted R2, is a way of selecting the true model, on average. Therefore, the criterion of maximizing the adjusted R2 can be described as an unbiased model-selection criterion. The property of unbiasedness is of importance in appraising the regression model, because it makes the selection of the true model more intuitive and the results of estimating a model simpler to be explained.

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model can be selected, on average, by maximizing the adjusted R2. Moreover, Kloek (1975) also showed that the probability of adopting the wrong model by using the unbiased model-selection criterion mentioned above will converge to zero as the sample size increases. The sample size of this study is sizable and continuously increasing with time, thus, it is reasonable to believe that the probability of choosing a wrong model is within an acceptable level.

Last but not least, as was demonstrated in the work of Giles (July 3, 2013), the adjusted R2 can increase, decrease or stay the same depending on the F-statistic related to the adding of independent variables to the regression model. This result holds as the OLS is applied, thus the model-selection criterion of maximizing the adjusted R2 gains its competitiveness for the loose requirement. Further more, unlike the simple R2 that never decreases when additional independent variable is added to the regression model, the adjusted R2 can, to some extend, penalize the model complexity.

4. Data

4.1. Data selection

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Some constituents of the CSI All Share Index are excluded from the data set. Characteristics for removed stocks are presented as follows:

l Lack of stock price. Firms are not included until they have appeared on CSMAR database for at least 24 months prior to July of year t. Year t is the year that the portfolios are constructed. l Missing fundamental data. Data of book value of equity, market value of equity, net income

and cash flow from operating activities at the end of December in year t-1, and market value of equity at the end of June in year t are used to form the portfolios for year t. Firms without one of these fundamental data are excluded.

l Negative-BE firms. Firms have negative book value of shareholders’ equity on the annual financial statements are not included.

4.2. Summary statistics

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Annual average July 2005-June 2006 July 2006-June 2007 July 2007-June 2008 July 2008-June 2009 July 2009-June 2010 July 2010-June 2011 July 2011-June 2012 July 2012-June 2013 July 2013-June 2014 Number of stocks 1378 1072 1124 1155 1164 1290 1407 1420 1720 2052 Average monthly return 2.59 5.41 9.22 -0.41 4.01 1.18 2.89 -1.75 0.03 2.72 Standard deviation 15.00 14.59 20.46 19.13 18.83 14.16 11.95 11.51 12.73 11.67 Table 1

Descriptive statistics for the sample stocks: 2005-2014, nine years. (returns and standard deviations are shown in percent)

The sample stocks are taken from the CSI All Share Index. Stocks without price of 24 months prior to the start of July year t are excluded. Year t is the year that the portfolios are formed. Stocks of firms that miss fundamental data, including book value of equity, market value of equity, net income, and cash flow from operating activities at the end of December in year t-1, and market value of equity at the end of June in year t are also excluded. In addition, stocks of firms that have negative book value of shareholders’ equity (represents for book value of equity) on the annual financial statements are not included.

Monthly returns from July year t to June year t+1 are calculated based on the close prices of the last trading day of each month from the CSMAR database. These returns are used to calculate average monthly returns and standard deviations of the monthly returns. Average monthly returns are the arithmetic average rate of return.

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4.2.1. The 25 stock portfolios formed on size and BE/ME

Descriptive statistics for 25 stock portfolios formed on size and BE/ME for the whole period from July 2005 to June 2014 are shown in Table 2. Because breakpoints are based on the number quintiles of the ranking observations, the number of stocks in each quintile is almost the same. However, the value of each portfolio in the smallest size quintile is less than 0.66% of the total value of the 25 portfolios. In contrast, the five portfolios in the largest size quintile together account for approximate 73% of the total value. The portfolio of stocks in both the largest size and highest BE/ME quintiles alone makes up to more than 23% of the combined value of the 25 portfolios. Table 3 summarizes the dependent and independent variables in the time-series regressions.Data that are related to the 25 stock portfolios formed on size and BE/ME are listed in Panel A of Table 3. The average excess returns on the explanatory portfolios are the average risk premiums for the common risk factors in returns. The 25 stock portfolios comprised of size and book-to-market equity contain a wide range of monthly average excess returns, from 1.14% to 3.38%. In addition, in every BE/ME quintile but the lowest, both the excess returns and their t-value decrease from smaller- to bigger-size portfolios, and the differences between the average returns for the smallest- and biggest-size portfolios range from 1.36% to 2.23% per month. This pattern confirms the finding of Fama and French (1993) that there is a negative relation between size and average return. Nevertheless, the strong positive relation between average return and BE/ME found by Fama and French (1993, 1998) is not shown in the data of Panel A of Table 3.

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Size (ME)

quintiles Low 2 3 4 High Low 2 3 4 High

Small 1.14 1.21 1.22 1.23 1.27 0.16 0.33 0.44 0.57 0.82 2 1.99 2.03 2.01 2.00 2.03 0.18 0.33 0.43 0.57 0.85 3 3.06 3.08 3.10 3.06 3.06 0.19 0.33 0.44 0.57 0.87 4 5.32 5.27 5.24 5.26 5.21 0.20 0.32 0.44 0.57 0.91 Big 22.78 21.94 26.77 35.95 47.35 0.19 0.32 0.44 0.57 1.00 Small 0.65 0.59 0.61 0.65 0.38 64 56 59 61 34 2 0.69 1.00 1.04 0.97 1.09 40 58 60 56 62 3 1.11 1.44 1.49 1.63 1.63 44 55 56 61 60 4 2.65 2.41 2.57 2.19 2.53 59 54 58 49 56 Big 13.53 10.72 11.21 13.99 23.23 68 53 44 47 64

Average of annual averages of firm size (Billion ¥) Average of annual BE/ME ratios for portfolio

Average of annual percent of market value in portfolio Average of annual number of firms in portfolio Table 2

Descriptive statistics for 25 stock portfolios formed on size and book-to-market equity: 2005-2014, 9 years.

Book-to-market equity (BE/ME) quintiles

The 25 size-BE/ME stock portfolios are formed in the following way. Each year t from 2005 to 2014, BE/ME (measured at the end of December year t-1) is used to rank stocks and split them to one of the five BE/ME quintiles. The same procedure is used to make the ME (measured at the end of June year t) quintiles. The 25 size-BE/ME portfolios are formed as the intersections of the five size and the five BE/ME groups.

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Name Mean Std.

t-statistics Name Mean Std.

t-statistics RM 1.61 9.62 1.74 RM-RF SMB HML RM 1.61 9.62 1.74 RM-RF SMB LMS RM-RF 1.42 9.62 1.53 1.00 RM-RF 1.42 9.62 1.53 1.00 SMB 1.24 5.18 2.50 0.16 1.00 SMB 1.26 5.10 2.56 0.16 1.00 HML 0.00 3.03 0.02 0.13 -0.05 1.00 LMS 0.08 2.36 0.36 0.08 0.40 1.00 Size (ME) quintiles Low 2 3 4 High Size (ME) quintiles 0 Low 2 3 4 High Small 2.90 3.27 3.30 3.38 3.21 Small 3.04 3.40 3.19 3.32 3.41 3.04 2 2.57 2.92 2.56 2.72 2.68 2 2.72 2.48 2.72 2.78 3.04 2.48 3 1.85 2.25 2.32 2.38 2.28 3 1.98 2.47 2.20 2.43 2.40 2.40 4 2.05 1.90 1.85 2.08 1.97 4 1.91 1.79 1.98 1.87 2.17 2.18 Big 1.54 1.14 1.26 1.15 1.31 Big 1.58 1.29 1.38 1.31 1.33 1.21 Small 2.62 2.96 3.12 2.96 2.84 Small 2.73 3.02 3.00 2.99 3.03 2.76 2 2.34 2.69 2.41 2.40 2.44 2 2.40 2.24 2.56 2.61 2.82 2.35 3 1.75 2.13 2.14 2.14 2.10 3 1.80 2.21 2.09 2.27 2.23 2.29 4 2.09 1.89 1.77 1.91 1.81 4 1.74 1.56 1.91 1.93 2.20 2.10 Big 1.73 1.16 1.22 1.14 1.44 Big 1.58 1.32 1.51 1.40 1.48 1.24 Small 11.49 11.46 11.01 11.84 11.74 Small 11.60 11.67 11.07 11.57 11.70 11.42 2 11.42 11.30 11.03 11.78 11.39 2 11.80 11.51 11.01 11.08 11.21 10.95 3 10.99 10.94 11.29 11.55 11.28 3 11.46 11.62 10.95 11.12 11.17 10.92 4 10.21 10.45 10.90 11.32 11.36 4 11.40 11.95 10.77 10.07 10.25 10.82 Big 9.29 10.14 10.69 10.41 9.47 Big 10.42 10.17 9.54 9.75 9.33 10.14 Table 3

Summary statistics for the monthly dependent and explanatory returns in the regression of table 5 to 9: July 2005 to June 2014, 108 observations. (returns and standard deviations are shown in percent)

Panel A Panel B

Correlations Correlations

t-statistics for means

Standard deviations Dependent variables: Excess returns on 25 stock portfolios

formed on ME and BE/ME Book-to-market equity (BE/ME) quintiles

t-statistics for means

Standard deviations Means

Dependent variables: Excess returns on 30 stock portfolios formed on ME and NI/CFO

Earnings quality (NI/CFO) quintiles

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Each year t from 2005 to 2014, BE/ME (measured at the end of December year t-1) is used to rank stocks and split them to one of the five BE/ME quintiles. The same procedure is used to make the ME (measured at the end of June year t) quintiles. However, because there might be negative values for both NI and CFO, this paper first splits all sample stocks into two groups (group P and group Zero) based on their positive and negative values of NI and CFO. Group P contains stocks that with both positive NI and positive CFO values. The rest stocks are contained in the group Zero. Stocks in the group P are then ranked to make the five NI/CFO quintiles. Both net income and cash flow from operating activities are captured in financial statements at the end of December in year t-1 for each year of the nine-year period.

The 25 size-BE/ME portfolios are formed as the intersections of the five size and the five BE/ME groups. The 30 stock portfolios are constructed from the intersections of the five size quintiles and the six NI/CFO groups (group Zero and the five ranked NI/CFO quintiles of group P).

The small minus big (SMB) portfolio is used to reflect returns related to size and the high minus low (HML) portfolio is created to proxy returns related to BE/ME. The large minus small (LMS) portfolio is related to earnings management factor (NI/CFO). The portfolio SMB for the 25 stock portfolios is the monthly difference between average returns (value-weighted) on small (S) and big (B) groups of the six size-BE/ME portfolios, while the HML portfolio is the monthly difference between average returns (value-weighted) on the high (H) and low (L) groups of the six size-BE/ME portfolios. The portfolio SMB for the 30 stock portfolios is the monthly difference between average returns (value-weighted) on small (S) and big (B) groups of the eight size-NI/CFO portfolios. Monthly difference between average returns (value-weighted) on the large (L) and small (S) groups of the eight size-NI/CFO portfolios forms the large minus small (LMS) portfolio.

Return of the market portfolio, RM, used in this paper are monthly returns of the CSI All Share Index that is calculated from the last trading day of July in year t to the last trading day of June in year t+1 for each year in the nine-year period. The risk free rate, RF, in this paper, is the monthly rates of benchmark three-month term deposit rates announced by the People's Bank of China (PBOC).

4.2.2. The 30 stock portfolios formed on size and NI/CFO

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cover 15.64% of the total market value of the 30 stock portfolios, in other words, the average percentage of the total market value for each NI/CFO quintile is 16.87%. In addition, group Zero contains 28% of the total number of firms, while in each of the NI/CFO quintile only 14% of total firms are included. The data above indicate that there are more firms with smaller size in the group Zero. The portfolio that contains the highest average market value, which accounts for 17.26% of the combined market value of the 30 stock portfolios, is located in both the biggest size and the second smallest NI/CFO quintiles (group Zero is not ranked based on the NI/CFO value). The biggest size quintile of group P covers 64.39% of the total market value for the 30 stock portfolios. In contrast, the value of each portfolio of group P in the smallest size quintile is less than 0.55% of the total value of the 30 portfolios.

Panel B of Table 3 summarizes the dependent and independent variables in the time-series regressions for the 30 stock portfolios formed on size and NI/CFO. The monthly excess returns for the 30 stock portfolios range from 1.21% to 3.41%. In every NI/CFO quintile and the group Zero, both the excess returns and their values of t-statistic decrease from smaller- to bigger-size portfolios. Moreover, the differences between the excess returns for the smallest- and biggest-size portfolios range from 1.46% to 2.11% per month. This pattern also confirms the negative relation between size and average return that has been found before in the Panel A of Table 3. However, the relation between average return and NI/CFO is not found.

The value of RM-RF for the 30 stock portfolios is the same with that in the 25 stock portfolios. There are only slight differences between SMB factors in these two sets. The monthly average SMB return is 1.26% (t=2.56) for the 30 stock portfolios. The LMS portfolio related to NI/CFO, however, has a low average premium of 0.08% (t=0.36) per month. Low t-value indicates that the reliability of LMS different from 0 is low, which limits the explanatory ability of LMS factor on average returns.

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Size (ME)

quintiles 0 Low 2 3 4 High 0 Low 2 3 4 High

Small 1.18 1.22 1.23 1.23 1.23 1.24 -3.00 0.12 0.36 0.61 0.99 8.24 2 2.01 1.99 2.02 2.05 2.01 2.03 -1.40 0.13 0.36 0.61 0.99 9.27 3 3.06 3.05 3.04 3.10 3.09 3.12 -3.24 0.14 0.37 0.61 0.97 4.46 4 5.16 5.11 5.26 5.32 5.41 5.33 -1.82 0.14 0.37 0.62 0.97 5.50 Big 22.63 49.00 61.95 32.32 22.62 20.31 -2.37 0.14 0.38 0.62 0.98 5.51 Small 1.13 0.54 0.38 0.30 0.24 0.29 109 52 36 27 24 27 2 1.49 0.87 0.74 0.59 0.50 0.61 87 49 41 34 29 36 3 1.93 1.00 1.06 1.04 1.04 1.22 75 38 40 39 39 44 4 2.82 1.41 1.92 2.04 2.17 2.01 66 30 42 46 48 44 Big 8.27 11.02 17.26 15.79 12.15 8.17 48 28 40 53 59 48

Average of annual percent of market value in portfolio Average of annual number of firms in portfolio Table 4

Descriptive statistics for 30 stock portfolios formed on size and earnings quality: 2005-2014, 9 years.

Earnings quality (NI/CFO) quintiles

Average of annual averages of firm size (Billion ¥) Average of annual NI/CFO ratios for portfolio

The 30 size-NI/CFO stock portfolios are formed in the following way. Each year t from 2005 to 2014, ME (measured at the end of June year t) is used to rank stocks and split them into one of the five ME quintiles. However, because there might be negative values for both NI and CFO, this paper first splits all sample stocks into two groups (group P and group Zero) based on their positive and negative values of NI and CFO. Group P contains stocks that with both positive NI and positive CFO values. The rest stocks are contained in the group Zero. Stocks in the group P are then ranked to make the five NI/CFO quintiles. Both net income and cash flow from operating activities are captured in financial statements at the end of December in year t-1 for each year of the nine-year period. The 30 stock portfolios are constructed from the intersections of the five size quintiles and the six NI/CFO groups (group Zero and the five ranked NI/CFO quintiles of group P).

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5. Results

5.1. The Fama and French three-factor model

The Market – Panel A of Table 5 shows that the excess return on the market portfolio, RM-RF, has explanatory ability on returns of stock market in China. Values of t-statistics of slopes on RM-RF for the 25 stock portfolios range from 17.62 to 35.23. The smallest adjusted R2 value is 0.75, which locates in both the smallest size and lowest BE/ME quintiles. In every BE/ME quintile, except for the lowest-BE/ME and largest-size quintiles, the adjusted R2 values increase from smaller- to bigger-size portfolios. However, there are still some variation remained to be explained in stock returns. Only five out of the twenty-five adjusted R2 values, which are all included in the two biggest-size quintiles, are more than 0.90. For the time-series regression with RM-RF factor as the only explanatory variable, the average value of adjusted R2 for the 25 stock portfolios is 0.84. Therefore, small-size and low-BE/ME portfolios with adjusted R2 values less than 0.84 are the best

parts for portfolios of size and BE/ME factors to show their explanatory power.

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Secondly, for the results of two-factor regression on RM-RF and SMB factors, t-values for slopes on the RM-RF factor are considerably large, ranging from 26.10 to 57.05. Both slopes and t-values for the SMB factor, in every BE/ME quintile, decrease from the small- to big-size quintiles. The t-values of slopes for SMB factor range from -6.35 to 29.02, and the negative values of coefficient s are only contained in the biggest size quintile. Moreover, the average adjusted R2 value is 0.95 for the two-factor regression model on RM-RF and SMB factors, which means that the time-series regression has a great explanatory power in explaining stock returns.

The Market, HML, and SMB – Table 7 says that the Fama and French three-factor model, which

includes the overall market factor, HML and SMB factors as explanatory variables, apparently shows strong power of capturing common variation in stock returns. The t-values of coefficient β for the market portfolios range from 26.20 to 58.21. In every size quintile but the lowest BE/ME quintile, the values of coefficient h increase monotonically from negative values for the lower-BE/ME quintiles to positive values for the higher-BE/ME quintiles. In addition, except for the negative values in the biggest size quintile, t-values of the SMB slopes are no less than 9.44. Not surprisingly, the slopes on SMB for stocks are related to size. In every BE/ME quintile, the values of coefficient s decrease monotonically from smaller- to bigger-size quintiles. The average value of adjusted R2 for the Fama and French three-factor model is 0.96, and all of the adjusted R2 values are larger than 0.92 for the 25 stock portfolios.

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Size (ME)

quintiles Low 2 3 4 High

Size (ME)

quintiles 0 Low 2 3 4 High Small 1.03 1.04 1.02 1.09 1.09 Small 1.06 1.06 1.01 1.05 1.08 1.04 2 1.05 1.08 1.04 1.11 1.08 2 1.11 1.09 1.03 1.05 1.05 1.02 3 1.01 1.04 1.09 1.11 1.10 3 1.09 1.11 1.05 1.07 1.07 1.05 4 0.98 1.01 1.08 1.12 1.12 4 1.12 1.17 1.07 0.99 0.99 1.05 Big 0.91 1.01 1.00 1.04 0.90 Big 1.03 0.91 0.92 0.93 0.94 1.02 17.62 18.71 19.86 19.56 20.35 Small 19.06 18.53 18.76 18.13 20.29 18.77 19.67 23.87 22.49 22.42 22.51 2 21.84 23.26 20.88 23.12 21.90 20.58 19.28 23.81 25.30 25.14 27.08 3 23.10 24.62 24.87 25.62 24.66 25.16 24.57 26.24 33.84 32.80 31.00 4 30.94 28.01 34.46 30.83 26.18 27.26 29.31 35.23 21.87 34.92 23.61 Big 32.42 17.81 24.76 23.46 44.25 40.57 Small 0.75 0.77 0.79 0.78 0.80 Small 0.77 0.76 0.77 0.76 0.80 0.77 2 0.79 0.84 0.83 0.83 0.83 2 0.82 0.84 0.80 0.83 0.82 0.80 3 0.78 0.84 0.86 0.86 0.87 3 0.83 0.85 0.85 0.86 0.85 0.86 4 0.85 0.87 0.92 0.91 0.90 4 0.90 0.88 0.92 0.90 0.87 0.88 Big 0.89 0.92 0.82 0.92 0.84 Big 0.91 0.75 0.85 0.84 0.95 0.94 Average R2 0.84 Average R2 0.84 Table 5

Regression of excess stock returns on the excess market returns (RM-RF). RM-RF: July 2005 to June 2014. 108 months.

R(t)-RF(t)=α+β[RM(t)-RF(t)]+e(t)

Panel A Panel B

t(β) t(β)

Adjusted R2 Adjusted R2

Dependent variables: Excess returns on 25 stock portfolios formed on ME and BE/ME

Dependent variables: Excess returns on 30 stock portfolios formed on ME and NI/CFO

Book-to-market equity (BE/ME)

quintiles Earnings quality (NI/CFO) quintiles

β β

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Size (ME)

quintiles Low 2 3 4 High Low 2 3 4 High

Small 1.04 1.05 1.02 1.09 1.08 0.94 0.96 0.94 1.00 1.01 2 1.06 1.09 1.04 1.11 1.06 0.97 1.01 0.97 1.04 1.00 3 1.02 1.06 1.09 1.10 1.08 0.94 0.98 1.02 1.05 1.04 4 0.99 1.02 1.09 1.11 1.10 0.93 0.96 1.04 1.08 1.08 Big 0.94 1.02 1.01 1.01 0.87 0.93 1.03 1.04 1.06 0.93 Small 17.56 18.74 19.75 19.28 20.09 35.95 38.28 47.72 53.11 37.62 2 19.99 24.08 22.18 22.14 22.42 38.86 57.05 50.76 49.09 49.18 3 19.65 24.60 25.03 24.86 27.45 30.03 40.13 47.02 50.96 45.46 4 26.02 27.19 33.52 32.61 32.80 30.91 37.74 54.66 50.22 40.85 Big 37.59 36.96 21.68 42.10 32.04 32.30 38.99 26.29 38.28 26.10 Small -0.16 -0.21 -0.12 0.08 0.23 1.02 0.97 0.92 1.02 0.90 2 -0.32 -0.24 0.03 -0.01 0.31 0.92 0.81 0.82 0.87 0.84 3 -0.33 -0.36 -0.04 0.19 0.37 0.82 0.71 0.72 0.76 0.65 4 -0.42 -0.33 -0.05 0.18 0.47 0.51 0.57 0.50 0.52 0.49 Big -0.63 -0.29 -0.07 0.59 0.90 -0.25 -0.24 -0.47 -0.23 -0.30 Small -0.85 -1.17 -0.72 0.42 1.33 20.87 20.81 25.16 29.02 18.05 2 -1.89 -1.65 0.21 -0.04 2.09 19.77 24.58 23.07 22.24 22.16 3 -2.01 -2.63 -0.28 1.33 2.95 14.15 15.60 17.81 19.99 15.34 4 -3.43 -2.77 -0.52 1.69 4.44 9.15 11.97 14.24 13.10 9.94 Big -7.93 -3.30 -0.49 7.68 10.49 -4.61 -4.80 -6.35 -4.56 -4.54 Small 0.74 0.77 0.79 0.78 0.80 0.95 0.95 0.97 0.98 0.95 2 0.79 0.84 0.82 0.82 0.83 0.95 0.98 0.97 0.97 0.97 3 0.78 0.85 0.86 0.86 0.88 0.92 0.95 0.96 0.97 0.96 4 0.86 0.87 0.91 0.91 0.91 0.92 0.94 0.97 0.97 0.95 Big 0.93 0.93 0.82 0.95 0.92 0.91 0.93 0.87 0.93 0.86 Average R2 0.85 Average R2 0.95

Book-to-market equity (BE/ME) quintiles Table 6

Regression of excess stock returns on the excess market returns (RM-RF) and the mimicking returns for book-to-market equity (HML) factor; Regression of excess stock returns on the excess market returns (RM-RF) and the returns for size (SMB) factor:July

2005 to June 2014, 108 months.

R(t)-RF(t)=α+β[RM(t)-RF(t)]+hHML(t)+e(t)

R(t)-RF(t)=α+β[RM(t)-RF(t)]+sSMB(t)+e(t) Dependent variables: Excess returns on 25 stock portfolios formed on ME and BE/ME

t(h) t(s)

Adjusted R2 Adjusted R2

β β

t(β) t(β)

h s

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Size (ME)

quintiles Low 2 3 4 High Low 2 3 4 High

Small 0.94 0.96 0.94 0.99 1.00 35.52 38.11 47.05 55.08 39.72 2 0.98 1.01 0.97 1.03 0.99 39.95 58.21 50.96 48.75 61.79 3 0.95 0.99 1.02 1.03 1.02 30.72 42.59 46.38 54.93 55.56 4 0.95 0.97 1.04 1.07 1.05 33.22 39.68 53.87 52.51 50.60 Big 0.96 1.05 1.05 1.03 0.89 46.38 42.03 26.20 47.23 37.44 Small -0.03 -0.09 0.00 0.21 0.34 -0.38 -1.10 -0.03 3.63 4.35 2 -0.20 -0.14 0.14 0.10 0.42 -2.65 -2.47 2.27 1.57 8.44 3 -0.23 -0.27 0.05 0.29 0.45 -2.37 -3.70 0.75 4.83 7.88 4 -0.35 -0.26 0.01 0.25 0.54 -3.94 -3.40 0.16 3.92 8.22 Big -0.66 -0.32 -0.13 0.56 0.87 -10.17 -4.12 -1.05 8.17 11.63 Small 1.02 0.97 0.92 1.03 0.92 20.70 20.69 24.97 30.84 19.80 2 0.91 0.80 0.83 0.88 0.86 20.08 24.92 23.63 22.44 29.18 3 0.81 0.70 0.72 0.77 0.67 14.24 16.19 17.78 22.31 19.83 4 0.50 0.56 0.50 0.53 0.51 9.44 12.27 14.15 14.22 13.28 Big -0.28 -0.25 -0.47 -0.21 -0.26 -7.21 -5.45 -6.41 -5.19 -5.98 Small 0.95 0.95 0.97 0.98 0.96 2 0.96 0.98 0.97 0.97 0.98 3 0.93 0.96 0.96 0.97 0.97 4 0.93 0.95 0.97 0.97 0.97 Big 0.95 0.94 0.87 0.96 0.94 Average R2 0.96 h t(h) s t(s) Adjusted R2 β t(β) Table 7

Regression of excess stock returns on the excess market returns (RM-RF) and the mimicking returns for the size (SMB) and book-to-market equity (HML) factors:July 2005 to

June 2014, 108 months.

R(t)-RF(t)=α+β[RM(t)-RF(t)]+hHML(t)+sSMB(t)+e(t)

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*Details for Table 5, Table 6, and Table7 are listed as follows:

Each year t from 2005 to 2014, BE/ME (measured at the end of December year t-1) is used to rank stocks and split them to one of the five BE/ME quintiles. The same procedure is used to make the ME (measured at the end of June year t) quintiles. However, because there might be negative values for both NI and CFO, this paper first splits all sample stocks into two groups (group P and group Zero) based on their positive and negative values of NI and CFO. Group P contains stocks that with both positive NI and positive CFO values. The rest stocks are contained in the group Zero. Stocks in the group P are then ranked to make the five NI/CFO quintiles. Both net income and cash flow from operating activities are captured in financial statements at the end of December in year t-1 for each year of the nine-year period.

The 25 size-BE/ME portfolios are formed as the intersections of the five size and the five BE/ME groups. The 30 stock portfolios are constructed from the intersections of the five size quintiles and the six NI/CFO groups (group Zero and the five ranked NI/CFO quintiles of group P).

The small minus big (SMB) portfolio is used to reflect returns related to size and the high minus low (HML) portfolio is created to proxy returns related to BE/ME. The portfolio SMB for the 25 stock portfolios is the monthly difference between average returns (value-weighted) on small (S) and big (B) groups of the six size-BE/ME portfolios, while the HML portfolio is the monthly difference between average returns (value-weighted) on the high (H) and low (L) groups of the six size-BE/ME portfolios.

Return of the market portfolio, RM, used in this paper are monthly returns of the CSI All Share Index that is calculated from the last trading day of July in year t to the last trading day of June in year t+1 for each year in the nine-year period. The risk free rate, RF, in this paper, is the monthly rates of benchmark three-month term deposit rates announced by the People's Bank of China (PBOC).

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5.2. The three-factor model with NI/CFO factor

The Market – Panel B of Table 5 shows that the excess return on the market portfolio captures the common variation in stock returns. The t-values of slopes on RM-RF for the 30 stock portfolios range from 17.81 to 44.25. The biggest adjusted R2 value is 0.95, whereas the smallest adjusted R2 value is 0.75. In every NI/CFO quintile and group Zero, except for the largest-size quintile, both t-values and adjusted R2 values increase from smaller- to bigger-size portfolios. However, with the average adjusted R2 value of 0.84, evidence shows that there are still some common variation that cannot be captured by the one-factor model formed on the RM-RF factor. In addition, the adjusted R2 values which are larger than 0.90 are all included in the two biggest-size quintiles. Therefore, other factors should be added to the one-factor regression in order to explain the stock returns of the small-size portfolios with lower adjusted R2 values.

The Market and LMS (SMB) -- Table 8 shows that the two-factor models---one with the RM-RF

and LMS factors and the other with the RM-RF and SMB factors---perform well in explaining stock returns. First, for the regression formed on RM-RF and LMS factors, the t-values of slopes for the RM-RF factor range from 18.16 to 45.10. Values of the coefficient l for the LMS factor range from -0.42 to 0.96. In every size quintile but the smallest, both the slopes and the t-values for the LMS factor increase from the smaller- to larger-NI/CFO quintiles, except for the second smallest NI/CFO quintile. The slopes of the LMS factors in the biggest size quintile even turn out to be negative in the low-NI/CFO quintiles, and they increase from the smaller- to larger-NI/CFO quintiles to be positive in the largest two NI/CFO quintiles. The average value of adjusted R2 for the two-factor model formed on RM-RF and LMS is 0.86, which is slightly larger than that of the two-factor model formed on the RM-RF and HML factors. Moreover, under the 5% significance level, 96% of the l coefficients of the group P are significant, and more than 93% of them are significant for the whole 30 stock portfolios, which is much larger than the significant rate of the h coefficient for the HML factor in the two-factor regression formed on the RM-RF and HML factors.

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SMB factor are negative in the biggest size quintile. Values of t-statistics for slopes of the SMB factor, ranging from -11.28 to 25.04, in general, are with the same trend of their related slopes. The average adjusted R2 value is 0.95 for the two-factor regression formed on RM-RF and SMB factors, which means that the time-series regression has a great performance in explaining stock returns. The Market, LMS, and SMB – Table 9 shows that the three-factor model with the overall market factor, LMS and SMB factors as independent variables, captures common variation in stock returns. The t-values of slopes for the RM-RF factor range from 26.01 to 54.01. Except for the smallest size quintile and the middle size quintile, slopes of the LMS factor increase monotonically from negative values for the smaller-NI/CFO quintiles to positive values for the larger-NI/CFO quintiles. Values of t-statistics of the slopes for the LMS factor follow the same trend as their slopes, ranging from -10.67 to 5.46. Obviously, the value of slope for the SMB factor is inversely related to size. The t-values of the slopes for the SMB factor are all larger than 9.68, except for the negative t-values in the biggest size quintile. The average value of adjusted R2 for the three-factor model using the RM-RF, LMS and SMB factors as the explanatory variables is 0.95, which is slightly lower than that of the Fama and French three-factor model as previously examined.

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Size (ME)

quintiles 0 Low 2 3 4 High 0 Low 2 3 4 High Small 1.05 1.05 1.00 1.04 1.06 1.03 0.98 0.97 0.93 0.96 1.01 0.96 2 1.10 1.08 1.01 1.04 1.04 1.00 1.03 1.02 0.95 0.99 0.99 0.94 3 1.08 1.11 1.04 1.06 1.05 1.03 1.02 1.05 0.99 1.01 1.01 0.99 4 1.11 1.16 1.06 0.98 0.98 1.03 1.08 1.12 1.03 0.95 0.94 1.00 Big 1.04 0.95 0.92 0.93 0.94 1.01 1.05 0.98 0.93 0.97 0.95 1.03 Small 19.00 18.58 19.13 18.16 21.87 19.37 33.82 41.15 38.49 36.65 34.04 34.55 2 21.93 23.46 21.23 23.96 23.82 22.38 46.66 50.76 50.22 43.59 35.41 45.96 3 23.58 24.84 26.95 27.37 26.92 28.20 43.50 41.22 51.84 47.35 51.40 46.87 4 32.54 28.48 35.60 33.65 28.64 31.17 46.70 37.54 49.67 46.84 40.07 40.16 Big 33.05 27.09 25.74 23.47 45.10 42.11 34.95 27.81 25.62 29.62 45.81 41.78 Small 0.37 0.48 0.63 0.48 0.96 0.75 0.94 1.03 0.95 1.02 0.88 0.95 2 0.43 0.44 0.54 0.63 0.90 0.93 0.90 0.84 0.89 0.78 0.78 0.89 3 0.54 0.42 0.77 0.71 0.82 0.87 0.81 0.74 0.75 0.71 0.77 0.71 4 0.55 0.44 0.40 0.60 0.72 0.85 0.56 0.58 0.46 0.50 0.59 0.59 Big -0.28 -1.60 -0.42 -0.16 0.22 0.33 -0.23 -0.75 -0.19 -0.46 -0.12 -0.13 Small 1.64 2.07 2.98 2.05 4.87 3.48 17.17 23.02 20.85 20.54 15.73 18.08 2 2.08 2.31 2.79 3.54 5.09 5.10 21.60 22.05 25.04 18.29 14.77 22.93 3 2.93 2.30 4.92 4.49 5.12 5.82 18.26 15.38 20.71 17.65 20.72 17.87 4 3.94 2.67 3.27 5.04 5.17 6.28 12.83 10.38 11.76 12.98 13.31 12.44 Big -2.17 -11.20 -2.87 -1.01 2.65 3.40 -4.09 -11.28 -2.74 -7.40 -3.02 -2.80 Small 0.78 0.77 0.78 0.76 0.83 0.79 0.94 0.96 0.95 0.95 0.94 0.94 2 0.82 0.84 0.81 0.85 0.85 0.84 0.97 0.97 0.97 0.96 0.94 0.97 3 0.84 0.86 0.88 0.88 0.88 0.89 0.96 0.95 0.97 0.96 0.97 0.96 4 0.91 0.89 0.92 0.92 0.89 0.91 0.96 0.94 0.96 0.96 0.95 0.95 Big 0.91 0.88 0.86 0.84 0.95 0.94 0.92 0.88 0.86 0.89 0.95 0.94 Average R2 0.86 Average R2 0.95 t(l) t(s) Adjusted R2 Adjusted R2 β β t(β) t(β) l s

Earnings quality (NI/CFO) quintiles Table 8

Regression of excess stock returns on the excess market returns (RM-RF) and the mimicking returns for earnings quality (LMS) factor; Regression of excess stock returns on the excess market returns (RM-RF)

and returns for the size (SMB) factor:July 2005 to June 2014, 108 months.

R(t)-RF(t)=α+β[RM(t)-RF(t)]+lLMS(t)+e(t) R(t)-RF(t)=α+β[RM(t)-RF(t)]+sSMB(t)+e(t) Dependent variables: Excess returns on 30 stock portfolios formed on ME and NI/CFO

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Size (ME)

quintiles 0 Low 2 3 4 High 0 Low 2 3 4 High Small 0.98 0.98 0.93 0.96 1.01 0.96 36.48 45.47 38.97 39.47 34.52 34.42 2 1.04 1.03 0.95 0.99 0.99 0.94 50.62 54.01 52.26 43.41 36.18 46.97 3 1.02 1.05 0.99 1.01 1.01 0.99 43.81 42.00 52.59 47.51 52.55 49.41 4 1.08 1.12 1.03 0.95 0.94 1.00 46.63 37.39 49.42 47.88 41.10 43.01 Big 1.05 0.98 0.93 0.96 0.95 1.03 34.88 40.30 26.01 29.89 49.87 47.02 Small -0.50 -0.46 -0.19 -0.44 0.27 -0.05 -4.20 -4.86 -1.86 -4.15 2.08 -0.44 2 -0.39 -0.32 -0.25 -0.04 0.29 0.22 -4.37 -3.81 -3.07 -0.36 2.45 2.45 3 -0.16 -0.24 0.17 0.13 0.21 0.32 -1.55 -2.20 2.07 1.38 2.46 3.62 4 0.09 -0.06 0.01 0.21 0.26 0.42 0.93 -0.43 0.14 2.46 2.61 4.13 Big -0.10 -1.14 -0.31 0.26 0.38 0.52 -0.74 -10.67 -1.96 1.83 4.58 5.46 Small 1.03 1.11 0.98 1.10 0.83 0.96 18.64 25.26 20.12 21.93 13.88 16.74 2 0.97 0.90 0.94 0.79 0.72 0.85 23.23 23.05 25.14 16.89 12.94 20.63 3 0.84 0.79 0.71 0.69 0.73 0.65 17.51 15.27 18.53 15.76 18.55 15.94 4 0.54 0.59 0.46 0.46 0.54 0.51 11.43 9.68 10.71 11.26 11.56 10.66 Big -0.21 -0.54 -0.13 -0.50 -0.19 -0.23 -3.46 -10.76 -1.78 -7.60 -4.83 -5.05 Small 0.95 0.97 0.96 0.96 0.94 0.94 2 0.97 0.97 0.97 0.96 0.94 0.97 3 0.96 0.96 0.97 0.96 0.97 0.97 4 0.96 0.94 0.96 0.96 0.95 0.96 Big 0.92 0.94 0.86 0.89 0.96 0.95 Average R2 0.95 β t(β) Table 9

Regression of excess stock returns on the excess market returns (RM-RF) and the mimicking returns for the size (SMB) and earnings quality (LMS) factors:July 2005 to June 2014, 108 months.

R(t)-RF(t)=α+β[RM(t)-RF(t)]+lLMS(t)+sSMB(t)+e(t)

Dependent variables: Excess returns on 30 stock portfolios formed on ME and NI/CFO Earnings quality (NI/CFO) quintiles

l t(l)

s t(s)

Adjusted R2

*Details for Table 8 and Table 9 are presented as follows:

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income and cash flow from operating activities are captured in financial statements at the end of December in year t-1 for each year of the nine-year period. The 30 stock portfolios are constructed from the intersections of the five size quintiles and the six NI/CFO groups (group Zero and the five ranked NI/CFO quintiles of group P).

The small minus big (SMB) portfolio is used to reflect returns related to size and the large minus small (LMS) portfolio is related to earnings management factor (NI/CFO). The portfolio SMB for the 30 stock portfolios is the monthly difference between average returns (value-weighted) on small (S) and big (B) groups of the eight size-NI/CFO portfolios. Monthly difference between average returns (value-weighted) on the large (L) and small (S) groups of the eight size-NI/CFO portfolios forms the large minus small (LMS) portfolio.

Return of the market portfolio, RM, used in this paper are monthly returns of the CSI All Share Index that is calculated from the last trading day of July in year t to the last trading day of June in year t+1 for each year in the nine-year period. The risk free rate, RF, in this paper, is the monthly rates of benchmark three-month term deposit rates announced by the People's Bank of China (PBOC).

The adjusted R2 is adjusted for degrees of freedom.

6. Discussion and conclusion

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Secondly, Foye et al. (2013) defined the NI/CFO factor related to the earnings management as a risk factor. They found that NI/CFO factor has strong explanatory ability for the higher NI/CFO portfolios. In this paper, the results of both the two-factor and three-factor regression models (as illustrated in Section 5.2), which include the LMS factor related to the NI/CFO ratio as the explanatory variable, confirm the aforementioned findings of Foye et al. (2013) that NI/CFO factor shows more explanatory power for the higher NI/CFO portfolios. They believe that because investors perceive big differences between net income and cash flow from operating activities as a signal of accounting manipulation, and the large NI/CFO ratio is often a representativeness of big differences that are attributable to the accounting manipulation, therefore, firms with high NI/CFO ratios can be related to a high probability of facing earnings management problem. Thus, firms with large NI/CFO ratios are riskier, and need higher returns to compensate. In my opinion, treating the earnings management factor as a risk factor can be a reasonable explanation.

However, the overreaction of investors for both good and bad news can be another explanation for the high returns of high-NI/CFO stocks. Investors extrapolate past performance and act overly pessimistic to the high-NI/CFO stocks or overly optimistic to the low-NI/CFO stocks. These behaviors can lead to situations that high-NI/CFO stocks are underpriced and the low-NI/CFO stocks are overpriced. Therefore, the high-NI/CFO stocks may probably outperform the low-NI/CFO stocks in the coming future. In addition, the reason for a high NI/CFO ratio can also be that the firm is experiencing the growth phase with more expenses to pay. The growth of a firm can then attract more profitable opportunities in the coming future. Thus, the high-NI/CFO can also be a positive signal of development that is not perceived by many investors.

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management factor related to the NI/CFO ratio shown in Section 5.2 is then explained. However, the comprehensive results of different time-series regressions mentioned above indicate that the variation in stock returns captured by the earnings management factor may be included in variation that is captured by the SMB factor.

In general, the findings of this paper are shown to have practical implications. As the average returns of different portfolios shown in Table 3 (analysis can be found in Section 4.2.1 and Section 4.2.2), obviously, there is a negative relation between size and average stock returns of A shares for the emerging market of China. This result indicates that these models and factors can actually help in building more profitable investment portfolios. The portfolio formed on the basis of the optimized combination of the risk factors can probably outperform the market. Besides, the remarkable explanatory power of the overall market factor, which is related to the excess return of the CSI All Share Index in this paper, may encourage the usage of different stock indexes as basic indicators for the stock returns. It seems to be interesting to study other indexes and try to find out the most typical index for the stock market of China. And for the earnings management factor discussed above, whether it is a risk factor or a product of the pricing inefficiency, it can be useful to investors who are interested in investing in the stock market of China and further research for this earnings management factor is worthwhile. Finally, the explanatory power of the BE/ME factor is not very strong, however, the Fama and French three-factor model, on average, gives the best performance in capturing common variation in stock returns of A shares of China.

7. References

Ball, R., 1978. Anomalies in relationships between securities' yields and yield-surrogates. Journal of Financial Economics 6, 103-126.

Banz, R.W., 1981. The relationship between return and market value of common stocks. Journal of Financial Economics 9, 3-18.

Basu, S., 1977. Investment performance of common stocks in relation to their price-earnings ratios: A test of the efficient market hypothesis. The Journal of Finance 32, 663-682.

Black, F., 1993. Beta and return. The Journal of Portfolio Management 20, 8-18.

Bondt, W.F.M.D., Thaler, R.H., 1987. Further evidence on investor overreaction and stock market seasonality. The Journal of Finance 42, 557-581.

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Fama, E.F., 1965. The behavior of stock-market prices. The Journal of Business 38, 34-105.

Fama, E.F., 1970. Efficient capital markets: A review of theory and empirical work*. The Journal of Finance 25, 383-417.

Fama, E.F., French, K.R., 1992. The cross-section of expected stock returns. The Journal of Finance 47, 427-465.

Fama, E.F., French, K.R., 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, 3-56.

Fama, E.F., French, K.R., 1998. Value versus growth: The international evidence. The Journal of Finance 53, 1975-1999.

Foye, J., Mramor, D., Pahor, M., 2013. A respecified fama french three-factor model for the new european union member states. Journal of International Financial Management & Accounting 24, 3-25.

Giles, D., July 3, 2013. The adjusted R-square, again. Econometrics Beat: Dave Giles’ Blog. htt p://davegiles.blogspot.nl/2013/07/the-adjusted-r-squared-again.html.

Giles, D., August 3, 2013. Unbiased model selection using the adjusted R-squared. Econometric s Beat: Dave Giles’ Blog. http://davegiles.blogspot.nl/2013/08/unbiased-model-selection-usin g-adjusted.html.

Kloek, T., 1975. Note on a large-sample result in specification analysis. Econometrica 43, 933-936. Lakonishok, J., Shleifer, A., Vishny, R.W., 1994. Contrarian investment, extrapolation, and risk. The

Journal of Finance 49, 1541-1578.

Li, Y., Niu, J., Zhang, R., Largay, J.A., 2011. Earnings management and the accrual anomaly: Evidence from china. Journal of International Financial Management & Accounting 22, 205-245.

Reinganum, M.R., 1981. Misspecification of capital asset pricing: Empirical anomalies based on earnings' yields and market values. Journal of Financial Economics 9, 19-46.

Rosenberg, B., Reid, K., Lanstein, R., 1985. Persuasive evidence of market inefficiency. The Journal of Portfolio Management 11, 9-16.

Sharpe, W.F., 1964. Capital asset prices: A theory of market equilibrium under conditions of risk*. The Journal of Finance 19, 425-442.

Schmidt, P., 1974. A note on theil's minimum standard error criterion when the disturbances are autocorrelated. The Review of Economics and Statistics 56, 122-123.

Sloan, R.G., 1996. Do stock prices fully reflect information in accruals and cash flows about future earnings? The Accounting Review 71, 289-315.

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