Empirical Study on Five-Factor Model in Chinese A-share Stock Market

Empirical Study on Five-Factor Model in Chinese A-share Stock Market Supervisor: Prof. Dr. F.A. de Roon Student name: Qi Zhen Administration number: U165184 Student number: 2004675 Master of Finance Economics & Management School, Tilburg University

Abstract Fama and French (2015a) proposed the five-factor model based on the three-factor model. According to the previous study results, this paper considers to abandon the redundant investment factor and to add liquidity factor, and examine the performance of the new five-factor model in Chinese A-share stock market. The empirical result of GRS test and model regressions show that the five-factor model does not have better performance than three-factor model by adding profitability factor and liquidity factor. Moreover, there is no obvious value effect in Chinese stock market. Only the size factor has strong explanatory power for the average stock returns. The stock turnover ratio as the proxy for the liquidity has explanatory power for the stock return, but it is proved to be redundant which is absorbed by size and value factors. Key words: Asset pricing model, Five-factor model, Profitability factor, Liquidity factor, Chinese A- share stock market 2

Table of Contents 1. Introduction... 1 1.1 Background... 1 1.2 Objective... 2 1.3 Thesis Framework... 3 2. Literature Review... 3 2.1 Markowitz Mean-variance Analysis... 3 2.2 CAPM factor model... 3 2.3 Multi-factor Model... 4 2.4 Asset pricing model in China... 5 3 Research Methodology... 6 3.1 The five-factor model... 7 3.2 Portfolios and Factors construction... 8 3.3 Explanatory power of the model (GRS-F test)... 8 3.4 Regression... 9 4 Data... 9 4.1 Data Source... 9 4.2 Data Selection... 10 5. Summary statistics for portfolio returns... 11 5.1 Portfolios construction... 11 5.2 Analysis of average excess return on 25 portfolios... 12 5.3 Analysis of Average excess return on 32 portfolios... 14 6 Summary statistics for factor returns... 15 6.1 Factor construction... 15 6.2 Analysis of factor return and correlation... 16 7 Summary for model performance test... 19 7.1 GRS test... 19 7.2 Redundant factor... 21 7.3 Regression Analysis... 23 7.3.1 25 Size-B/M regression... 23 7.3.2 25 Size-OP regression... 25 7.3.3 25 Size Turnover regression... 26 7.3.4 32 portfolios regression... 28 8 Conclusion... 29 8.1 Results summary... 29 8.2 Limitation... 30 8.3 Future Study... 30 Appendix A... 31 References... 34 3

1. Introduction 1.1 Background Sharpe (1964) and Lintner (1965) proposed the Capital Asset Pricing Model based on the Markowitz s Modern Theory, which is used to reveal the obvious relationship between asset expected return and risk. But using the market risk premium as the only factor, CAPM faces many empirical challenges to explain the stock returns. Subsequently, more and more new factors are proposed trying to improve the performance of asset pricing model. However, there are still many financial anomalies which cannot be completely explained by the current asset models and experts keep discovering new variables to explain the anomalies. In 2015, Fama French proposed the five-factor model based on the famous three-factor model by adding two new factors, profitability factor and investment factor. Nevertheless, most of the asset pricing models are built on the samples in mature stock markets across the developed regions such as the United States, but whether the factor models can explain the stock returns in emerging countries such as China remains to be further studied. Actually, the explanatory power of the asset model needs to consider the stage of capital market development (Griffin, 2002)and specific market characteristics. Chinese stock market started late from the early 1990s which is an emerging market compared to the developed capital market. There are much differences between Chinese stock market and mature equity markets such as the investing environment, pricing mechanism, securities law and investor trading philosophy. Chinese capital market is growing rapidly in the past twenty years. Especially, after the Non- Tradable Shares (NTS) Reform issued by the CSRC in 2005, both the number of listed companies and investment scale have been in the great process of development. By the end of October in 2016, the number of the listed firm is 2,972 and the total market capitalization is 50.732 trillion on the A-Shares stock market. Before NTS reform, despite existing large number of private enterprises, State-Owned Enterprises play a leading role in Chinese stock market. Non-tradable shares took up 64% of total shares, and the tradable share only occupied one-third of the Chinese securities market. With the process of reform, more and more state-control shares have been freely tradable and enter the market, promoting market liquidity. Now it still exists partial non-tradable share in the market. Also, as an emerging capital market, highly speculative trading is another main characteristic of 1

Chinese A-share market due to the private investor leading structure. One of the notable features for Chinese stock market is the high proportion of individual investors rather than the institutional investors. In China, individual investors account for about half of the total investors and pricing mechanism is easily affected by private investors behavior instead of institutional investors. As a weak efficiency capital market, information asymmetry increases the trading cost of private investors and the herding behavior leading to the super high stock turnover ratio in recent years. Therefore, the stock turnover ratio becomes a new attracting factor that investors concerned about due to the extremely high ratio in the world. The trading motivation tends to focus on trend-following speculation. It is a very different situation for the developed stock market. As well known, the mature capital market is dominated by the institutional investors with rational decision-making, while it is not affected by individual investors. The common speculative behavior without value investment philosophy is likely to have a great effect on stock return. 1.2 Objective With the progress in the development of asset pricing models, lots of new factors are discovered by experts trying to explain the variation of stock return better. A number of studies find that the common risk factors would be different between China and United States due to the different stock environment. There are many controversies among scholars about whether the asset pricing model such as CAPM, three-factor or five-factor model can be applied in China stock market. Whereas, for almost all of the recent empirical studies, there is a common view that the investment factor mentioned in Fama French (2015) is a redundant factor in Chinese stock market. Thus, according to the specific feature of Chinese stock market and the results of previous researches, this paper will consider to abandon investment factor and to add liquidity factor into factor model, and focus on three main questions as follows. First, examine whether the five-factor model can capture the variation of stock return in the Chinese market, while using stock turnover ratio as a proxy for the liquidity factor instead of investment factor; Second, whether the new five-factor model has superior performance than the three-factor model; Third, examine whether exists redundant factors in this five-factor model. The sample covers 19 years spanning from July 1997 to June 2016, 228 months, which is longest time span with latest data for the study. Moreover, the research method adopted in this paper is following the article of Fama French (2015). 2

1.3 Thesis Framework The framework of the rest of the paper is arranged as follows. The second part introduces the development history of asset pricing model and the current state of factor models applied in China. Section 3 provides the research strategy and empirical techniques. Section 4 describes the data resources and selection. From section 5 to section 7, this paper illustrates the statistical summary about portfolio return, factor return, GRS-F test, redundant factor test, model regression details respectively. And section 8 is the conclusion. 2. Literature Review 2.1 Markowitz Mean-variance Analysis Modern Portfolio Theory started from Markowitz Mean-Variance analysis in 1952 which propose how to construct efficient portfolios and how to maximize returns based on investor s risk preference. Markowitz defined the expected return and risk as mean and variance, and provide the idea that diversification can reduce portfolios risk given the same expected return. It reveals the relationship between expected return and risk (variance) that the expected return is depended on the risk level based on the assumption that all the investors are risk-averse. If the investors expect higher returns, they need to take greater risk. Markowitz provides new enlightenment for investment behavior. 2.2 CAPM factor model On the basis of Markowitz, Traynor (1962), Sharpe (1964) and Lintner (1965) proposed the classic Capital Asset Pricing Model (CAPM). There is a reasonable relationship between expected return on assets and risk. As mention above, the risk is defined as the variance of asset return by Markowitz. Sharpe (1963) developed the definition of portfolio risk, that is, the weighted average of the variance of individual securities, plus the product of the covariance and weights of every asset. In CAPM, beta as the measurement of risk describes the ratio of asset risk relative to market risk. The expected return of an asset depends on the risk-free return and the return for taking on systematic risk, that is, beta times the market excess return. Investors can evaluate the theoretical value of the asset through CAPM under some constraints. Moreover, diversification can reduce the idiosyncratic risk, but the systematic risk cannot disperse by diversified portfolios. 3

Nevertheless, the performance of CAPM is not good enough in practice. A lot of empirical researches have indicated that the stock return cannot be entirely explained only by the market factor. It still exists many market anomalies observed on the stock market which mean we need to explore new factors to explain the stock volatility. 2.3 Multi-factor Model Ross (1976) proposed the famous Arbitrage Pricing Theory (APT) model that factors that explain asset value are not unique, and that expected returns can be explained by multiple factors. Although the APT is based on less assumption than CAPM model, it does not give specific factors driving asset prices. Then Barra (1976) model developed the multi-factor analysis as a risk model. Fama and French (1992a) examined the performance of Market beta, Book-to-market ratio, Market equity, Earning Price ratio and leverage in explanation for expected stock returns using the crosssectional regression method based on US market sample. They find that the market beta cannot explain the stock return variation, but other factors have good explanatory power in separate regression. The Size and BE/ME factor have strong explanatory power for the average expected returns, containing the influence of Earning Price ratio and leverage. The Fama and French (1993) established the three-factor model to explain the stock return variation which provides a structure for the study of the following factors. This paper added Size (market capitalization), and Book-to-market ratio based on the CAPM model and the empirical research proves that three-factor model has enough explanatory power not only for US market but also for other countries. The momentum factor means a tendency to continue in the direction of original movement. Carhart (1997)proposed the four-factor model on the basis of the three-factor model by adding the factor to capture the momentum anomaly in Jegadeesh and Titman(1993), and measures the momentum factor using eleven-month returns lagged one month as a proxy. Carhart s four-factor model, adding the PR1YR (momentum) factor, has improved the explanatory power of the three-factor model. This paper found that the stock with a higher return over a period would earn much more return than stock with a lower return in the future. Thus, momentum investor could earn a profit selling the stocks with a lower return, while buying the higher return in short-term. Fama and French (2015) adds profitability and investment factor into the three-factor model to improve the interpretation of market anomalies. The two new factors are defined as the difference 4

between robust and weak profitability and the difference between conservative and aggressive investment. The results in the paper indicate that the five-factor model has better performance than the three-factor model to explain the variation in average stock returns based on the US market sample. Moreover, the value factor becomes redundant after adding these two new factors. However, the fivefactor model cannot successfully explain the portfolio return of small stocks with high investment and low profitability. As mentioned in the Fama and French (2015), the momentum factor and liquidity factor are not considered in that paper, which are also important factors to explain the stock return. Liquidity is the ability of the market to trade assets at a reasonable price and can be described quantitatively from the following four aspects: breadth, depth, resiliency and immediacy. 1 Pástor and Stambaugh (2003) pointed out that the liquidity risk is a component of system risk which cannot be diversified and it plays an important in asset pricing model. The most common measure indicators are bid-ask spreads, turnover ratios and price impact measure. 2 Amihud and Mendelson (1986) use bid-ask spreads which describe the depth and breadth of liquidity based on the sample in US stock market and proposed the liquidity premium theory, indicating that the stock return increases with liquidity reduction. Since illiquidity produces the greater transaction costs, the investors would expect a higher return on assets. And the Haugen and Baker (1996) find that there is a significantly negative relationship between expected return and turnover ratio by Russell 3000 in US stock market and some other developed countries. Shingyang Hu(1997) and Datar, Naikand, Radcliff (1998), using turnover ratio as a measure of liquidity, also examine the liquidity premium theory. Amihud (2002), and Pastor and Stambaugh (2003) tend to use the price impact measure and prove the liquidity premium. 2.4 Asset pricing model in China Considering about the Chinese stock market-specific characteristic, many experts make a sustained effort to test whether these famous asset pricing models can capture the variation of stock return in Chinese stock market. Currently, academic researchers have not reached a consensus. To examine the performance of CAPM in Chinese stock market, Xiao and Sun (2000) suggest that 1 Su, D. & Mai, Y. (2004). Liquidity and Asset Pricing: An Empirical Exploration of Turnover and Expected Returns on Chinese Stock Market. Economic Research Journal (2), 95-105. 2 Sarr, A., & Lybek, T. (2002). Measuring liquidity in financial markets. Imf Working Papers, 02(2/232). 5

the market exposure β does not have explanatory power of stock average return by a cross-sectional test. Zhu and He (2002), Wu and Xu (2004) examine the applicability of the three-factor model in Chinese stock market, and both of them find the significant size effect and value effect. On the contrary, Huang et al. (2002) prove that the BE/ME factor is insignificant based on the sample of Shenzhen stock exchange data and concludes the three-factor model is invalid in China. And Pan and Xu (2011) also do not find an apparent positive relationship between stock return and book-to-market factor and using the Price earnings ratio instead of value factor to construct an alternative three-factor model. Zhou and Zhang (2016) suggests that the five-factor model basically explain the stock crosssectional return, but not perform as well as in US market. Meanwhile, Qi (2017) and Guo et al. (2017) also find the five-factor model has superior performance than three-factor model by adding the profitability factor, and the investment factor is redundant in Chinese stock market. CMA as the investment factor is the difference of returns between conservative stock and aggressive stocks. RMW as the profitability factor is the returns on portfolios with high profitability (Robust) minus the returns with low profitability (weak). Song et al. (2017) indicates that CMA is a redundant factor in China because most of the enterprise pursue the massive investment pattern leading to the less investment difference among the stocks. Moreover, Zhao et al. (2016) provide the empirical evidence that RMW and CMA are not helpful for interpretation of the return on the portfolios. In the Chinese stock market, individual investors have dominant roles in the stock market rather than institutional investors. The market speculation atmosphere is strong, leading to the characteristics of high stock turnover ratio. Sometimes high turnover rate represents a popular stock which is easily chased after by individual investors without value-based investment philosophy. Another particular situation is that there are non-tradable shares in China's stock market, which are not traded freely in the listed companies. Su and Mai (2004), using the turnover ratio as a proxy for the liquidity, finds that there is significant liquidity premium in China. The stocks with low turnover rate and high transaction costs have a higher expected return. Luo (2007) also obtain the similar result. 3 Research Methodology This research followed the approach of Fama and French (2015) to test the explanatory power of new five-factor model in the Chinese A-share stock market and the relationship between five factors and the average excess return of portfolios. 6

3.1 The five-factor model FF(2015) added two new factors into the three-factor model, namely profitability and investment, according to the derive formula based on dividend discount model (DDM), = ( )/( ) (1) In the equation (1), is the stock price for time t. is book equity for time t. is the equity earnings during the period +, is the change of book equity in time + ; r is the expected stock return in long term. As can be seen from the formula, fixing other variables, the expected return has positive relationship with expected profit, the higher ( ) with higher r. And the expected return is negative with investment, the higher ( ) with lower r. Then, the five-factor model was proposed using the market excess return factor, size, book-tomarket, profitability and investment factors, = + ( ) + + h + + + Where the is total return on portfolio i during time t, is risk free rate, is value-weighted market return. SMB, HML, RMW, CMA are referred to as premiums of size, value, profitability and investment patterns respectively. SMB represents the difference on stock return between small size firms and big size firms. HML is calculated by spread in returns between value stocks with high bookto-market ratio and growth stocks with low book-to-market ratio. RMW is the returns on portfolios with high profitability (Robust) minus the returns with low profitability (weak). CMA is the difference of returns between conservative stock and aggressive stocks.,, h,, are factor coefficients. represents the abnormal return cannot be explained by factors and the is the noise. However, based on the previous empirical evidence such as Lin (2017), Guo et al. (2017), CMA is generally proved as a redundant factor for Chinese stock market, indicating the CMA return is captured by other four factors. Therefore, according to the previous academic results, we decided to abandon the investment factor in this paper. The five-factor model focus on isolating asset pricing drivers but still missing an important system factor, liquidity, just as mentioned in FF(2015). Liquidity is another important stock characteristic in explaining returns which is gradually wide-accepted in academic researches. Amihud and Mendelson (1986) derived the relationship of expected return with bid-ask spread as a proxy for the cost of illiquidity and proposed the stock market liquidity premium theory. The assets with low liquidity have 7

a higher expected return, while the assets with high liquidity have a lower expected return. In stock market, stocks with low liquidity and high transaction cost would generate higher returns. Based on the trading frequency hypothesis, Shingyang Hu(1997) found that turnover is a good measure of liquidity to predict expected stock returns. It constructed an empirical model using stock turnover as proxy for liquidity and prove that the expected return is a decreasing function of turnover. Thus, this paper will add liquidity factor to the Fama-French model to test whether the factor can improve the model performance and use average daily stock turnover ratio trailing 12 months as proxy for liquidity factor. Therefore, the five-factor model used in this paper is = + ( ) + + h + + + In this equation, is value-weighted market return based on free-float market capitalization. The LIQ represents the stock liquidity that is a difference of returns between stocks with high turnover ratio and stocks with low turnover ratio. represents the liquidity exposure. 3.2 Portfolios and Factors construction All the listed firms are allocated into groups by common stock characteristics related to market, size, book-to-market, profitability and liquidity independently, using different breakpoints. The intersection of groups produces the value-weighted portfolios and construct the factors. This paper tries to use three sets of factors to explain the average excess return of two- and three-dimension portfolios. In order to understand the average excess return variation for portfolios, the study sorts all listed firms independently according to the five stock common characteristics. All the A-shares stock in the Chinese market are allocated into groups by breakpoints, and the intersection of size group and one or two other factor groups generate the value-weight two- or three-dimensional portfolios, 25 (5 5) and 32 (2 4 4) portfolios respectively. For the robustness of factor construction, to examine whether the way of stock allocation affects the model performance, the factors are formed on three versions of grouping structure, 2 3, 2 2 and 2 2 2 2. 3.3 Explanatory power of the model (GRS-F test) This paper uses GRS statistic proposed by (Gibbons, Ross, & Shanken, 1989) to test whether the alternative five factors capture all variation in average excess return for 25 and 32 value-weight 8

portfolios respectively. The null hypothesis of GRS-F test is α=0, which examines whether all intercepts of time-series regression of average excess portfolio returns are jointly zero. In theory, if the factor model can completely capture the variation of average excess return on portfolios, the alpha should be zero. If the F statistic of GRS test is large enough or p-value is under 0.05, the null hypothesis is rejected, and vice versa. Average absolute value of the intercept (alpha) across the portfolios is an important indicator to judge the performance of factor model. The alpha represents the unexplained proportion of variation of excess return. In practical, for the estimated intercept, alpha needs to be statistically insignificant with zero to prove the effectiveness of models. For the mean adjusted R-square, it examines the goodness of fit of time-series regression to find how well the five factors account for the variation of excess return. If the adding factors are efficient, the explanatory power of the model will increase, indicating that the factor exposures can explain stock excess return better. 3.4 Regression To estimate the performance of five factors further, this paper runs a regression of average excess return on portfolios against five factors Mkt, SMB, HML, RMW and LIQ. The analysis focuses on the comparison of intercept (alpha) between three-factor model and five-factor model with t-statistics and slopes for five factors to see how well the five factors explain the excess return. The common null hypothesis of the coefficient is zero. This paper will see the explanatory power of five factors and compare the results among competing factor models. 4 Data 4.1 Data Source This paper uses data from Chinese A-share stock markets including Shenzhen Stock exchange and Shanghai Stock exchange from July 1997 to June 2016 (228 months) in the China Stock Market & Accounting Research (CSMAR) database and RESSET database. Before December 1996, there was no 10% price fluctuation limit in Chinese stock market. In order to ensure the data consistency, this study starts from the year 1997. During these 19 years, Chinese stock market experienced two crashes in 2007 9

and 2015 respectively, and experienced one complete boom-and-bust cycle and is undergoing the second cycle now. In this paper, all listed firms in A-share stock market are considered except negative book value firms and financial firms. It also excludes the stock if the stock is missing the annual accounting data or the value of market capitalization in June. In China, the annual financial statements should be published within four months after the end of fiscal year. However, some listed companies do not comply with the deadline and delay the date of publication of the annual report. Thus, this paper chooses to use the accounting data of annual report in June of year t to guarantee the data credibility. There are 2,794 listed firms in 2016 and 353,306 observations in the final sample. 4.2 Data Selection This paper collects monthly data: stock return, value-weighted market return, risk-free rate, stock price, tradable shares, net asset value per share, operating profit per share, interest expense and daily stock turnover rate. The specific data description is shown as followed. Average market return is value weighted return based on free-float market capitalization and considered the reinvestment of cash dividend. The risk-free rate download from the database is threemonth fixed deposit rates. As we know, FF (1993) uses one-month Treasury bill rate as the risk-free rate for the three-factor model. However, the transaction of Treasury bill is not active in the Chinese market, and the interest rate is not market-oriented completely. China is a country with a high savings rate and the idea of saving against risk makes the majority of residents invest mainly in savings 3. This paper chooses to use tradable shares to calculate all the variables, although both non-tradable shares and tradable shares exist in the Chinese stock market. The net asset per share, which is book equity per share, is the quotient of shareholders equity and shares outstanding. Following the definition of operating profitability in FF (2015), operating profit per share is revenues minus cost of goods sold, selling, general, and administrative expenses and then divided by outstanding shares. As mentioned in the literature review, the most common indicators of liquidity are bid-ask spreads, turnover ratios, and price impact measure. Among these three indicators, turnover ratio measures the activity of stock trading, and the data is easy to obtain. So, this paper will choose average daily stock turnover ratio trailing 12 months as a proxy of liquidity. The share turnover ratio equals trading volume in a period divided by 3 Ma, J., & Yu, F. (2006). Research on Choosing Risk-free Return Rate in China. Communication of Finance and Accounting (1), 44-46. 10

the outstanding shares. 5. Summary statistics for portfolio returns Following FF (2015), average monthly excess returns of portfolios divided by two- and three- dimensions of stock characteristic, demonstrating the factor effects intuitively. 5.1 Portfolios construction The first step is to calculate the variables. The method of measuring the market premium, size, value, profitability and liquidity patterns are shown as follows. Market premium (Rm-Rf) is average monthly market return based on free-float market capitalization minus risk-free rate. Market capitalization (Size) is stock price times outstanding shares at the end of June in year t. The book-tomarket ratio is the book equity at the end of December in year t-1 divided by market capitalization at the end of December in year t-1. Operating profitability equals operating profit per share times outstanding shares and minus interest expense, and then divided by book equity at the end of December in year t-1. Turnover ratio is the average stock daily turnover rate over the past twelve months before constructing the portfolios. For the second step, the paper constructs 25 portfolios by the intersections of size and one other factor. At the end of June in calendar t, all stocks are allocated into five Size groups (small to big), five B/M groups (low to high), five OP groups (robust to weak) or five Turnover groups (illiquidity to liquidity) separately using equal breakpoints. For the 5 5 Size-BM, the intersection of Size and B/M sorts produce 25 value-weight portfolios. Holding these 25 portfolios for 12 months, from July in the calendar year t to June in year t+1, then it gets the time-series monthly returns of the value-weighted portfolio in excess of the risk-free rate. This process is repeated for every twelve-month from July 1997 to June 2016, then obtain the time series of Size-B/M portfolio excess return for 228 months. The 5 5 Size-OP, Size-Turnover portfolios excess return is created in the same way. The third step is to construct 32 portfolios. For the three-dimension sorting, 2 4 4 portfolio, the stocks are allocated into two Size groups using the median as a breakpoint, while sorting the other three variables B/M, OP and Turnover in quartile independently. The Size group combines with each of pairwise of the other three variables and get the three versions of 32 value-weight portfolios: 2 4 4 Size-BM-OP, Size-BM-Turnover, Size-OP-Turnover. Table 2 shows the results of the time series of 11

three versions of 32 portfolios excess return of 228 months by the same method of 25 portfolios. 5.2 Analysis of average excess return on 25 portfolios The results of average time series excess returns for 25 portfolios are shown in Table1. Generally, it is clear that there is an apparent Size effect for every three version of 25 value-weight portfolios in each B/M, OP or Turnover column. And there are general trends for profitability and turnover for most portfolios. Compared with U.S. market, the Chinese stock market has a larger monthly average excess return for portfolios. Panel A of Table 1 illustrates the result of 25 portfolios average excess returns formed on Size-BM sort. The table clearly demonstrates that there is an obvious Size-effect in each B/M column, since the average monthly excess return is monotonically decreased from small size portfolio to big size portfolio. Fama French (1993) indicates the problems that the smallest extreme growth stocks have lower excess return compared to the large stocks which cannot explain by the three-factor model. However, this problem does not exist in Chinese stock market. Nevertheless, there is no typical general trend shown in every Size quintile B/M effect. This result is consistent with Chen et al. (2008) which suggest that if keeping the portfolios just for one year, there is no BM effect in Chinese stock market. Instead, if holding the portfolios two or three more years, it exists value premium in A-share stock market because the stock returns are also affected by great market fluctuation in the Chinese market. The significant volatility in 2007 and 2015 weakened the BM effect. Panel B illustrates the result of 25 portfolios average excess returns formed on Size-OP sort. Also, it can be noticed that average excess return keeps a downward tendency while size goes up. In each size quintile, there are at least three portfolios exhibit general upward trend in average excess returns as OP goes up except the second size quintile. And the last two size quintile shows a more obvious increasing trend. It is more likely that, for small size companies, investors do not pay attention to profitability. However, for big size firms, investors tend to care about the ability to generate gains. It is reasonable that small companies have to face more challenges than large enterprises such as cash-flow problems, relative high financing cost and the ability to take risks. Investors need to balance the profitability and these potential risks of small firms. Panel C illustrates the result of 25 portfolios average excess returns formed on Size-Turnover sorts. It is not surprising finding the obvious size effect in every turnover column except one portfolio in the 12

low turnover group, 4.347%. As can be seen from the table, the highest turnover portfolios have lower average return than lowest turnover portfolios which is consistent with liquidity premium theory. Table 1 Average monthly excess return for 25 portfolios are constructed by the intersection of Size group and one of other factor groups (B/M, OP and Turnover). The data ranges from July 1997 to June 2016 (228 months) from Chinese A-share stock market. At the end of June in calendar t, all stocks are allocated into five Size groups (small to big), five B/M groups (low to high), five OP groups (robust to weak) or five Turnover groups (illiquidity to liquidity) separately using equal breakpoints. B/M represents book value at the end of December in year t-1 divided by market capitalization at the end of December in year t-1. Operating profitability equals operating profit per share times outstanding shares and minus interest expense, and then divided by book equity at the end of December in year t-1 4. Turnover ratio is the average stock daily turnover rate over the past twelve months before constructing the portfolios. The table illustrates monthly average return of 25 portfolios minus the three-month fixed deposit rates. Low 2 3 4 High Panel A:Size-B/M portfolios small 3,112 3,033 2,954 2,903 3,534 2 2,915 3,101 2,231 2,512 1,984 3 1,785 2,113 1,713 1,787 1,794 4 1,613 1,520 1,658 1,735 1,574 Big 0,757 0,720 0,846 0,757 0,754 Panel B:Size-OP portfolios small 3,523 2,883 2,594 2,772 3,106 2 2,611 2,479 2,570 2,249 2,232 3 2,008 1,714 1,939 1,950 1,705 4 1,353 1,443 1,526 1,604 1,735 Big 0,439 0,741 1,054 1,077 0,744 Panel C:Size-Turnover small 3,057 2,719 2,820 2,993 2,556 2 4,347 2,269 2,218 2,218 2,200 3 1,794 1,892 1,969 2,099 1,605 4 1,557 1,709 1,957 1,442 1,361 Big 0,588 0,820 0,806 1,122 1,025 However, it is interesting to discover that the average excess return roughly rises with increasing turnover rate except for the second size quintile. In fact, the individual investors have dominant roles in the stock market rather than institutional investors in Chinese stock market. The herd behavior and the information asymmetry causes the long-term holdings would take more risk. Sometimes high turnover rate represents a hot stock which is chased after by individual investors without value-based investment philosophy. However, in the highest turnover rate column, investors are aware of the high risk of the stocks with over-reaction of stock price, the stock price will probably be reversed leading to a lower 4 The calculation followed the approach in Fama and French (2015). 13

average return. Therefore, in the extreme high and low turnover ratio quintile, the results show the liquidity premium effect. Meanwhile, to some extent, the turnover ratio also represents speculation degree, which is in line with the actual situation in Chinese stock market. 5.3 Analysis of Average excess return on 32 portfolios To better undertand the factor effects, this paper uses the three-dimension sorting, 2 4 4 portfolio, controlling one more variable than 5 5 portfolios. And the results in Table 2 confirm the outcomes of 25 portfolios. In Table 2, there is an evident Size effect for all versions of portfolios. The small size stocks have greater excess return than the big size stocks. In Size-BM-OP sorts, controlling for BM or OP, there is still no apparent value effect. Basically, the excess return goes up along with the OP increases exclude the highest profitability quintile. In Size-OP-Turnover sorts, it is interesting to note that there is an opposite tendency for returns of turnover ratio in different size groups. For small stocks, the average return generally decreases with the turnover rate increase, that is liquidity premium. In contrary, for big stocks, the average return roughly goes up with turnover rate increases except for the third row. The speculation behavior is more obvious in large size groups. Moreover, in Size-BM- Turnover sorts, it shows the similar results that the tendency of average returns goes down with turnover rate goes up just for the first two columns under the control of the Size and BM, whereas the tendency reverses in other columns. Table 2 Average monthly excess return for 32 portfolios are constructed by the combination of Size group combines with each of pairwise of the other three variables. The data ranges from July 1997 to June 2016 (228 months) from Chinese A-share Small Panel A: Portfolios formed on Size, B/M and OP B/M Low 2 3 High Low 2 3 High Low OP 3,111 2,796 2,334 2,526 0,984 1,074 1,115 1,023 2 2,058 3,224 2,504 1,996 1,218 1,368 1,208 1,234 3 2,161 2,653 2,575 2,104 1,082 1,405 1,244 1,234 High OP 2,352 2,227 2,304 2,410 0,839 0,920 0,894 0,530 Panel B: Portfolios formed on Size, BM and Turnover B/M Low 2 3 High Low 2 3 High Low Turn 3,138 3,670 2,276 1,876 0,611 0,932 0,939 0,752 2 2,229 2,470 2,379 2,264 1,054 1,142 1,311 1,687 3 2,393 2,805 2,458 2,071 1,114 1,257 1,208 1,139 High Turn 2,095 2,279 2,486 2,450 1,126 1,065 1,601 0,747 Panel C: Portfolios formed on Size,OP,Turnover OP Low 2 3 High Low 2 3 High Low Turn 3,242 3,380 2,254 2,647 0,855 0,965 1,252 0,562 2 2,176 2,263 2,301 2,441 1,296 1,351 1,383 1,116 3 2,527 2,384 2,676 2,007 1,564 1,212 1,223 1,113 High Turn 2,394 2,093 2,233 1,894 1,092 1,391 1,155 1,199 14 Big

stock market. At the end of June in calendar t, all stocks are allocated into two Size groups using the median as a breakpoint, while sorting the other three variables B/M, OP and Turnover in quartile independently. The table illustrates monthly average return of 32 portfolios minus the three-month fixed deposit rates. 6 Summary statistics for factor returns Following the FF (2015), to examine whether the way of stock allocation affects the model performance, the factors are formed on three versions of grouping structure, 2 3, 2 2 and 2 2 2 2. The details of factor construction are in Table 3. 6.1 Factor construction The five factors in the model include market factor (Mkt), size factor (SMB), value factor (HML), profitability factor (RMW) and liquidity factor (LIQ). The average market return is value weighted return based on free-float market capitalization, and Mkt is average market return in excess of the riskfree rate. The other four factors constructed by Size, B/M, OP and Turnover breakpoints. All the listed firms are sorted by five characteristics independently. The 2 3 portfolios are built on the intersection of Size factor by median with one of the other three factors which divided by 30 th, 70 th percentiles. To create and HML factor in 2 3 sorts as example, at the end of June in year t, all the stocks are allocated into two groups using Size median, and independently distributed into three groups by B/M in 30 th and 70 th percentiles. The intersection of Size and B/M groups generate six valueweight portfolios. is the difference between average return of three small size portfolios and average return of three big size portfolios. HML is the difference of monthly average return of two high B/M stocks with monthly average return of two low B/M stocks. In the same way, the Size-OP and Size-Turnover portfolios are constructed on the Size by median combined with one of other two factors by 30 th and 70 th percentiles. RMW is the average return of firms with robust minus the average return of firms with weak profitability. LIQ is the average return of portfolios with high turnover ratio minus the average return of portfolios with low turnover ratio. And and are also constructed accordingly. SMB is the average of, and. The 2 2 portfolios are constructed on the Size group combined with one of the other three variables to produce four value-weight portfolios. All the stocks are sorted independently into two groups by median. SMB, HML, RMW and LIQ are calculated by Size-B/M, Size-OP and Size-Turn portfolios in 15

the same way as 2 3 sorts. For 2 2 2 2 portfolios, controlling jointly for four variables, every variable is sorted into two group independently, and the intersection of these portfolios produce 16 value-weighted portfolios. Then the factor can be calculated by the same way as above. Since 2 2 2 2 sorts are controlled in four dimensions, it leads some portfolios to lose a lot of stocks. Table 3 Construction of factors includes size factor (SMB), value factor (HML), profitability factor (RMW) and liquidity factor (LIQ). Stock turnover is the proxy for liquidity factor. The 2 3 portfolios are constructed on the intersection of Size factor by median with one of the other three factors which divided by 30th, 70th percentiles. The 2 2 portfolios are formed on the Size group combined with one of the other three variables by median. For 2 2 2 2 portfolios, controlling jointly for four variables, every variable is sorted into two group independently. The letters represent the way to deal with the group allocation. For the size factor, S is referred to small, B is big. In the 2 2 and 2 3 sorts, for the B/M group, H, N, L are referred to high, neutral and low respectively. For the OP group, R, N, W represent robust, neutral and weak. For the LIQ group, LI, N, Q represent liquidity, neutral and illiquidity. The combination order in 2 2 2 2 portfolios is size group, B/M group, OP group and LIQ group. Sort Breakpoints Factors and their components 2 3 sorts on Size and B/M, or Size and OP, or Size and Turnover Size: median SMBB/M=(SH+SN+SL)/3-(BH+BN+BL)/3 SMBOP=(SR+SN+SW)/3-(BR+BN+BW)/3 SMBTurno ver=(sli+sn+sq)/3-(bli+bn+bq)/3 SMB=(SMBB/M+SMBOP+SMBTurnover)/3 B/M:30th and 70th percentiles HML=(SH+BH)/2-(SL+BL)/2 OP:30th and 70th percentiles RMW=(SR+BR)/2-(SW+BW)/2 Inv:30th and 70th percentiles LIQ=(SLI+BLI)/2-(SQ+BQ)/2 2 2 sorts on Size and B/M, or Size and OP, or Size and Turnover 2 2 2 2 sorts on Size, B/M, OP and Turnover Size: median B/M: median OP: median Turnover: median Size: median B/M: median OP: median Turnover: median SMB=(SH+SL+SR+SW+SLI+SQ)/6-(BH+BL+BR+BW+BLI+BQ)/6 HML=(SH+BH)/2-(SL+BL)/2 RMW=(SR+BR)/2-(SW+BW)/2 LIQ=(SLI+BLI)/2-(SQ+BQ)/2 SMB=(SHRLI+SHRQ+SHWLI+SHWQ+SLRLI+SLRQ+SLWLI+SLWQ)/8 -(BHRLI+BHRQ+BHWLI+BHWQ+BLRLI+BLRQ+BLWLI+BLWQ)/8 HML=(SHRLI+SHRQ+SHWLI+SHWQ+BHRLI+BHRQ+BHWLI+BHWQ)/8 -(SLRLI+SLRQ+SLWLI+SLWQ+BLRLI+BLRQ+BLWLI+BLWQ)/8 RMW=(SHRLI+SHRQ+SLRLI+SLRQ+BHRLI+BHRQ+ BLRLI+BLRQ)/8 -(SHWLI+SHWQ+SLWLI+SLWQ+BHWLI+BHWQ+ BLWLI+BLWQ)/8 LIQ=(SHRLI+SHWLI+SLRLI+SLWLI+BHRLI+BHWLI+BLRLI+BLWLI)/8 -(SHRQ+SHWQ+SLRQ+SLWQ+BHRQ+BHWQ+BLRQ+BLWQ)/8 6.2 Analysis of factor return and correlation Table 4 presents the result of descriptive statistics for five-factor returns and correlation. In Panel A, for SMB factor, the mean and standard deviation is similar in the three version sorts. The significant and positive size premium prove that the small size firm gains higher average return than a big firm. And the SMB is the only significant factor. For HML factor, the B/M premium is positive but not 16

significant. The mean of HML drops from 0.137 of the 2 3 version to 0.08 of 2 2 and 0.089 of 2 2 2 2 version due to better diversified in 2 2 and 2 2 2 2 portfolios, and the 2 3 sorts just use the data lower than the 30th and higher than the 70th percentiles of B/M. Thus, the spread of B/M premium of 2 3 sort is greater than the two others version. For RMW factor, there are similar mean and standard deviation for three version sorts. RMW factors are negative insignificant which have the different result with FF (2015). This result indicates that stocks with robust profitability do not have higher average return than the stocks with weak profitability in Chinese stock market. For LIQ factor, as the proxy for liquidity, the mean and standard deviation of the three version portfolios sort are similar except the 2 2 sort which the average LIQ percent return is negative. In Panel B of Table 4 shows the correlation of five factors by different version respectively. The correlations of five respective factors between the 2 2 and 2 3 sorts are high, 0.999 for SMB, 0.964 for HML, 0.969 for RMW and 0.946 for LIQ. The correlation for SMB is extremely high because the size is allocated by median for three version sorts and use all the stocks. The correlation for HML, RMW and LIQ is smaller since they are allocated by the 30 th and 70 th breakpoint in 2 3 sorts and 40% stocks are not used. The correlations of joint controls HML with the other two versions sort are much lower and have almost identical value, 0.892. It implies that some portfolios lose many stocks. Panel C describe the correlation between the factors. Most of the estimated correlation coefficients are significant at 99% confidence level. The HML and RMW have a negative relationship with market factor and SMB. LIQ is positively related to the market and SMB factors. As we know, the absolute value of correlation coefficients between 0.7 to 0.9 is strongly correlated and between 0.5 to 0.7 is moderate. The coefficients from 0.3 to 0.5 are a weak correlation, and the magnitude under the 0.3 is very low. The correlations of size factor with the excess market return are close to zero which have little correlation, 0.07 in the 2 2 and 2 3 sort and 0.006 in 2 2 2 2 sorts. Since stocks with small size are likely to be growth stocks, it is reasonable that SMB and HML have a negative relationship. It is noteworthy that the correlations between SMB and RMW are high, around -0.7 for three versions sort. The small firms tend to have weak operating profitability. The stock turnover rate premium positively related to excess market premium with little correlation, and have a positive relationship with size premium with moderate correlation which indicates that small size companies tend to have a high turnover ratio. 17

Table 4 summary statistics for factor returns. July 1997-June 2016, 228 months. At June at the end of year t, all the listed firms are sorted by stock characteristics (size, B/M,OP, turnover) independently. is the monthly average market return based on free-float market capitalization in excess of risk-free rate. SMB represents the difference on stock return between small size firms and big size firms. HML is calculated by spread in returns between value stocks with high book-to-market ratio and growth stocks with low book-to-market ratio. RMW is the returns on portfolios with high profitability (Robust) minus the returns with low profitability (weak). LIQ represents a difference of returns between stocks with high turnover ratio and stocks with low turnover ratio. Panel A: Average, standard deviation, and t-statistic for monthly return 2 3 2 2 2 2 2 2 stats Rm Rf SMB HML RMW LIQ Rm Rf SMB HML RMW LIQ Rm Rf SMB HML RMW LIQ mean 0,810 1,130 0,137-0,149-0,083 0,810 1,150 0,080-0,093 0,017 0,810 1,110 0,089-0,064-0,076 sd 8,350 4,630 3,110 3,230 4,311 8,350 4,800 2,380 2,370 2,859 8,350 3,960 2,110 2,240 2,662 t 1,50 3,79 0,68-0,71-0,29 1,50 3,70 0,52-0,61 0,09 1,50 4,31 0,65-0,44-0,43 Panel B: Correlation beween different version of the same factor SMB HML RMW LIQ 2 3 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 3 1 0,999 0,971 1 0,964 0,892 1 0,969 0,924 1 0,946 0,929 2 2 0,999 1 0,971 0,964 1 0,892 0,969 1 0,968 0,946 1 0,923 2 2 2 2 0,971 0,971 1 0,892 0,892 1 0,924 0,968 1 0,929 0,923 1 Panel C: Correlation between different factors 2 3 2 2 2 2 2 2 Rm Rf SMB HML RMW LIQ Rm Rf SMB HML RMW LIQ Rm Rf SMB HML RMW LIQ Ri Rf 1 0,072-0,124-0,255 0,077 Ri Rf 1 0,074-0,140-0,262 0,164 Ri Rf 1 0,006-0,068-0,068 0,110 SMB 0,072 1-0,443-0,737 0,487 SMB 0,074 1-0,364-0,732 0,560 SMB 0,006 1-0,388-0,659 0,396 HML -0,124-0,443 1 0,176-0,324 HML -0,140-0,364 1 0,115-0,351 HML -0,068-0,388 1 0,229-0,364 RMW -0,255-0,737 0,176 1-0,377 RMW -0,262-0,732 0,115 1-0,429 RMW -0,068-0,659 0,229 1-0,396 LIQ 0,077 0,487-0,324-0,377 1 LIQ 0,164 0,560-0,351-0,429 1 LIQ 0,110 0,396-0,364-0,396 1 18

7 Summary for model performance test 7.1 GRS test As can be seen in table 5, this paper tries to use two-, three-, four- and five-factors to explain the average excess return of 25 and 32 portfolios. The two-factor model consists of the market and SMB factor. Threefactor models are composed of market premium and SMB factor with one of other three variables. Four-factor models consist of market and SMB with two of other three factors. And five-factor model is comprised of all of the factors. The four versions of 25 and 32 portfolios need to be explained by three sets of factors. The effect of adding new factors could be assessed by comparing different versions of factor models. As mentioned in methodology, the GRS test examines the performance of factor models. If the factor models have strong explanatory power for the average portfolio excess return, all intercepts of time-series regression of average excess portfolio returns would be jointly zero insignificantly in theory. Unfortunately, in Table 5, GRS-F rejects most of the models at 5% significance level except for some models explained by 2 2 2 2 sorts. Even for the portfolios of size-bm-op and size-op sorts, the p-value is at three decimal digits. The results conclude that these factor models cannot capture the variation of average excess return completely. However, on the other hand, comparing the explanatory performance across competing models, it shows that most of the five-factor models have slightly lower GRS statistic than classical three-factor models by adding RMW and LIQ factors. Moreover, it shows that factor models have better explanatory power for the average excess return of portfolios when the model contains the factors of control variables. For example, in 25 Size- B/M portfolio, all the models contain the HML factor would have relatively low GRS statistic than other models, whereas the models with HML factor have inferior performance to explain the Size-OP portfolios compared to the models with RMW factor. It is undeniable that factors are good at explaining their own performance. The mean adjusted R-square statistic is another explanatory power measurement to judge how much proportion of the response variable variation can be explained by factors. The adjusted R-square is only depended on the explanatory power of the factors which have been taken into account the number of variables. If the newly added variable improves the model performance, the statistical number would increase and vice versa. As is exhibited in the table, the adjusted R-square statistic for most models is above 0.8 which implies that more than 80% of portfolios variation could be explained by factors. The range of adjusted R-square for 25 portfolios raises from 82.2% for the three-factor model to 87.9% for the five-factor model, while the range for 32 portfolios is from 77.3% to 85%. The goodness of fit for 25 portfolios is better than 32 portfolios. Since controlling one more factor, the less diversified portfolios lead to the reduction of the explanatory power of variables. Comparing the performance of the five-factor model with the three-factor model, the adjusted R- squared statistic increases after adding new factors, and all the five-factor models outperform the corresponding three-factor models by higher mean adjusted R-square. The smallest improvement in R-square is 1.3%, and the biggest one is 2.9%. The average square error is small, around 0.003 for all. 19