How well does Fama-French Five-Factor model fit Chinese stock market?

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UNIVERSITY OF AMSTERDAM

Master Thesis Economic and Business Track: Quantitative Finance

How Well Does Fama-French Five-Factor Model Fit Chinese

Stock Market?

Name: HU YATING SID: 11926716 Supervisor: Dr. LIANG ZHOU Date: 30th_June, 2018

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Statement of Originality

This document is written by Student [HU YATING] who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

HU YATING 30th June, 2018

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Abstract

I conduct out-of-sample tests of the five-factor model as well as the three-factor model introduced by Fama and French for the Chinese A-share stock market. To make the

“imported” model more suitable for the Chinese market, I change the calculation of the size model from total market capability to the market capability in circulation. After adjustment, I find that during the timespan of the sample (2007-2017), the size factor is prominent in related with the average returns. Besides, the value factor also reveals considerable

explanatory power. The two additive factors—profitability and investment factor makes the five-factor model more superior than three-factor model but not in a large degree. Moreover, the profitability factor shows highly correlated with investment factor.

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1. Introduction

1.1. The popular excess return models—from CAPM to Fama-French

Five-Factor Model

In terms of estimating the expected excess return of the asset, it can be derived from CAPM (Capital Asset Pricing Model) developed by William Sharpe et.al in as early as 1964. It is the essential foundation of the modern financial market theory to explore the relationship between the risk and the expected return, with the straightforward formula as follows:

Rit－Rft = βi(RMt- Rft) + eit Rit: return rate of Asset i in time t

Rft: risk-free rate RMt: market return

βi: the covariance of asset return with the market return divided by the variance of the market return

eit: residual term

However, this model only takes the market risk premium into account, which means it is only able to explain the systematic risk factor. Consequently, CAPM is suspected to significantly fit the real equity world. To evaluate whether the CAPM function well in the U.S. stock market, Eugene Fama and Kenneth French tested plenty of stocks’ returns in NASDAQ and NYSE during 1963 and 1990. They find the CAPM appears to be unable

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to explain the stock returns in reality. Instead, they expand the traditional CAPM with two more factors involved in, and formed the three-factor model (1993) as follows:

Rit－Rft = ai + bi(RMt- Rft)+ siSMBt+ hiHMLt+ eit

SMBt : the size factor, which is the return on small capitalization minus the return on large capitalization;

HMLt: the value factor, which is the return gap between the high group with high B/P ratio and the low group with low BP ratio;

Although the Three-factor model developed by Fama & French is well-received by the world to explore the stock portfolio’s expected return, Fama & French keep polishing up the model with more explanatory variables, because available evidence also suggests that much of the variation in average returns related to profitability and investment is left unexplained by the three-factor model. In recent years, motivated by Miller and Modigliani’s clean surplus theory (1961) that depicts the relationship among the firm value and investment, profitability, and return rate, Fama and French added two more factors into the three-factor model with profitability and investment, to form the Five-factor model, based on the test in the performance of U.S. stock market from 1963 to 2013—

Rit－Rft = ai + bi(RMt- Rft)+ siSMBt+ hiHMLt+ riRMWt + ciCMAt+ eit,

RMWt: profitability factor, short for “Robust minus Weak”, the indicator is calculated as “operating profit/shareholders’ equity”;

CMAt : investment factor, short for “Conservative minus Aggressive”, the corresponding indicator is calculated as △Assett/Assett-1.

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1.2. Relevance

This five-factor model arouses the debates whether it really fits the real-world stock markets, especially outside of the U.S.. Correspondingly, the financial scholars have carried out researches to test its feasibility and the results vary. Nevertheless, I found that there are only a few articles talking about the Fama & French five-factor model’s

feasibility in Chinese A-share market, while A-share market is becoming a more and more important part in the international equity market, which increasingly attracts

attention from both at home and abroad. Besides, as an emerging capital market, Chinese market is noticed that investors’ capability to evaluate the true value of a listed company is restricted due to market imperfections. It has a different structure compared with the U.S., so that out-of-sample empirical asset pricing research is important in this case. Moreover, previous research work has been unable to provide consistent empirical evidence because of the variation in sample periods, firms and factor construction

methods, which leads to the comprehensive interpretation of empirical evidence difficult. As a Chinese financial student, I am interested in studying whether the five-factor model fits in Chinese stock market better than the three-factor model does, and how the five factors affect the expected return (based on the statistical results of each factor’s

coefficient). In order to test in which market the five-factor model can fit better. In terms of my unique contribution, first of all, only a few researches test the five-factor model on Chinese market. Moreover, Chinese stock market is getting more and more mature in recent years after undergoing frequent turbulences so that a research with the latest data makes more sense. Besides, it is possible to make some small adjustment in the

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2. Literature Review

In the early stages, Fama and French test the three-factor model on the U.S. stock market. Specifically, they find that in terms of the significance of value factor, a portfolio with high B/M ratio outperforms a portfolio of low B/M stocks, which has been explained by the compensation for higher risk (Fama & French, 1992). Since the five-factor model is developed from Fama-French three-factor model, in 2016, they suggest that returns become less anomalous when the five-factor model is employed in the paper named

“Dissecting Anomalies with a Five-Factor Model”, which supports the superiority of the

Five-Factor model compared with the Three-Factor model. Fama and French (2015) argue that this new model is suitable for the international market instead of only being restricted in the U.S. stock market. In 2017, they update their research with the findings that average stock returns for North America, Europe, and Asia Pacific increase with profitability factor and are negatively correlated with investment factor. Meanwhile, in Japan, the relation between average returns and the level of B/M is strong, but show weak correlation in terms of profitability or investment. Moreover, it is worth to notice the puzzle of small stocks that behave as firms that invest a lot despite low profitability, which would be a noisy element to disturb the result. Studying relevant to Japanese equity market as well, Kubota, K., andTakehara, H. (2017) state that the original version of the Fama and French five-factor model is not the best benchmark pricing model for Japanese equity market during 1978 and 2014, because they find that the profitability factor and the investment factor are not statistically significant when conducting generalized method of moments (GMM) tests with the Hansen–Jagannathan distance measure. Xie and Qu (2016) find that the three-factor model fits the Shanghai Stock Exchange A-share market

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fairly well, after well-adjustment for the unique features of China’s stock market (by modifying the calculation of market capitalization and B/P ratio). They notice that there exist over-whelming proportion of non-tradable components in Chinese stock market especially before the equity reform in 2005. Even after reform the proportion of non-tradable shares dropped drastically, the percentage is still as large as approximately 20% in the market. This phenomenon is likely to disturb the relationship between firm size and the stock return, because the non-tradable stocks have adverse effect on operating income compared with the tradable stocks. As a result, Xie and Qu apply a different method from Fama& French’s to calculate the firm size indicator—to use “market value in circulation” to replace “total market value” . After modification, the results illustrated that size and value premiums are significant in China’s stock market, although there are modest differences among separate industrial sectors. However, Guo et al. (2017) find strong profitability pattern in average return while weak investment pattern in the five-factor model. The investment factor CMA is redundant in Chinese stock market. Besides, they also test the superiority of between the five-factor and the three-factor model. The results turn out to be in line with Fama & French with the Five-Factor model being better than the 3-factor model. Qi (2017) finds that, over the period 1997 to 2015, the five-factor model consistently outperforms the three-factor model in the Chinese equity market, and both value factor and profitability factor are essential to the return. It is worth to mention that the puzzle of small stocks is also evidenced in this paper. Fang & Yu (2002) argue that through 1996 to 2002, the size factor is essential for cross-sectional differences in the Chinese stock returns, while the B/M ratio factor appears to be useless when associated with the returns, which is contradictory to Fama & French’s finding on the U.S. market. They added free-float rate in the model as a proxy for company fundamentals, in order to offset the drawbacks stemming from the low accounting quality for Chinese firms and the

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large state-owned shares proportion. Their adjusted model is found to be powerful to explain the Chinese stock return, from 81% to 90%. Cakici et al. (2015) show that the decomposing the original Book-to-Market ratio (i.e., the decomposition into dB [change in book value of equity and dM [change in price]] in the sample from 1996 to 2012. It is another benefit from the decomposition that the dB can be statistically tested, which shows vital predictive power. The importance of change in book equity is consistent with the view that people pay more attention to the accounting information when evaluating the stocks from an emerging country. It provokes an implication to adjust the formula to calculate and make the Five-Factor model more feasible in the specific market.

In conclusion, firstly, the five-factor model are assumed to possess more explanatory power than the three-factor model in the same sample test. Secondly, the results of the suitability of five-factor model to a certain market tend to vary from country to country and time span. Thirdly, no matter in the three-factor model or in the five-factor model, the value factor (B/M) and size factor takes essential account. Fourthly, according to the previous findings, although the factors reveal different performance and significance, the additional factor--investment factor is redundant with high likelihood. In addition, due to the specialty of the Chinese market (because of different accounting style or stock market regulation rules), the factors in the model might be applied with some modifications in calculation which are different with Fama & French’s original suggestion, to make it fit better.

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3. Data, Factor Definitions and Methodology

3.1. Sample selection and data source

The out-of-sample empirical research approach adopted in this paper is similar to the prior literatures, especially the model methods developed by Fama & French. When it comes to the sample market selection, actually the Chinese stock market includes A-share stocks which is traded only for domestic investors using RMB denomination and B-share stocks which is available for foreign investors using USD denomination. However, A-share market is drastically larger and with more trading volume than B-A-share market. Hence, I firstly narrow my study scheme to the A-share stocks. Specifically, the A-share stocks comprise four categories, i.e. Shanghai Stock Exchange (SSE) and Shenzhen Main Broad, Shenzhen Small and Medium-sized Enterprise Board (SMEB) and Growth

Enterprise Market (GEM) stocks. It is worth to note that among the four boards, both Shanghai and Shenzhen Main Board are more mature and representative than the SMEB and GEM, and they take larger weight in the all share index. Therefore, I choose all A-shares as my typical target sample for studying the Chinese stock market. I construct the sample accounting data as well as monthly stock price data from all firms listed in A-share markets over the period 01/01/2007-31/12/2017 in the database of the CSMAR (China Stock Market and Accounting Research) database developed by GTA. I begin in the year of 2007 to ensure that enough number of listed firms are included, with the period covering a time span of 132 months over 11 years, which is long enough to ensure adequacy and effectiveness when testing the model. Besides, the non-tradable share reform in Chinese market initiated from 2005 to 2006 have great impact on the proportion

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of the stock ownership (Jiang, Laurenceson, & Tang, 2008). Before the reform, the government-owned share proportion seems to have a linear and positive impact on firm performance, which lowering the market efficiency and leading to the difference in the stock return performance pattern between ex- and post-reform period. Hence, in the purpose of more consistency, the period before 2007 is not included in the sample for this paper. In addition, the sample period goes through the bear market after 2008, the super bull market in 2015 and the following turbulence period, covering an all-round market cycle.

For the risk-free rate selection, there are numerous feasible benchmarks, such as 1-month Chinese government bonds, 1-month SHIBOR, or deposit rate released by People’s Bank of China. Most of the papers that study the similar topic tend to choose 3-month deposit rate as the suitable criteria, because it is more stable and transparent as well as meaningful due to the enormous deposit volume in China, which can reflect the base risk-free rate in Chinese market to a large extent. Therefore, I also adopt the 3-month deposit rate as the risk-free rate.

To make the dataset cleaner and reduce the possible noise for the output, I would like to deal the data with some criteria. Firstly, for each time t, firms that got public less than three months will be excluded because the underpricing of IPO tend to cause the

abnormal returns on the certain stocks. Secondly, the firms with negative book value will be dropped from the dataset since the negative B/M ratio is meaningless for the sense of value. Fama-French library provides comprehensive datasets for other markets, and detailed instructions to build up the model. However, I would like to adjust the calculation of size factor following the methods adopted by Xie and Qu (2016), regarding of the still considerable proportion of non-tradable stocks in the listed firms in Chinese stock market.

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1) market factor indicator: All A-share index adjusted by corresponding risk-free rate 2) size factor indicator: market capitalization in circulation

3) value factor indicator: book-to-market ratio (B/M)

4) profitability factor indicator: Return on Equity= Net income/Equity 5) investment factor indicator : △Assett/Assett-1

6) risk-free rate: 3-month deposit rate determined by People’s Bank of China, transferred to monthly-rate scale

7) calculate the factors and assign to different portfolio group every month.

3.2. Main hypothesis

Based on the previous empirical studies, I make several hypothesis as follows:

Hypothesis 1: The intercept is equal to 0, which implied the excess return is explained sufficiently by these specific factors in the model.

Hypothesis 2: The amount of uncertainty left is lower for the five-factor model than the three-factor model, which indicates that the five-factor model outperforms the three-factor model.

Hypothesis 3: All the five factors in Fama & French five-factor model are significant in fitting Chinese A-share market so that the model has strong explanatory power.

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3.3. Factor and portfolio construction

In order to test the hypothesis effectively, it is an intuitive approach to classify the stocks into different groups in a gradient order based on the respective breakpoint for each factor, so that various levels of portfolios with different characteristics are constructed, e.g. a portfolio consisting of big-size, low-B/M ratio, strong-profitability and conservative-investment firms’ stocks, or, a portfolio comprising small-size, high-B/M ratio, strong-profitability and aggressive-investment firms’ stocks, etc..After the “layering” procedure, the corresponding portfolio can be derived. Afterwards, by comparing the monthly return gap between different portfolio’s with different tags, the so-called efficiency of a certain factor is dipped out. The larger the gap, the more profound of the effect generated by the factor.

To accommodate to the logic above, I will follow the methods provided by Fama & French to classify the groups for each factor, i.e. 2x3 methods, which is to rank the portfolios and use certain quantiles as the threshold based on two dimensions each time. One dimension is fixed to be the size factor, and another dimension is value factor, profitability factor, or investment factor.

To start with the 2x3 Size-B/M matric, I will divide the sample stocks into two levels based on size (with threshold of the median), and three levels based on B/M ratio ranking (with thresholds of 30th percentile and 70th percentile). In detail, the small-size is marked as “S” and big size is marked as “B”. Similarly, the high B/M is labeled as “H”, the medium B/M is labeled as “M”, and the low B/M is with “L”, respectively. Eventually, based on the 2x3 size-B/M matric, I can get 6 groups of portfolios named SH, SM, SL, BH, BM, and BL (a straightforward display of the classification is shown in Table 1) .

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High B/M Medium B/M Low B/M

Small size SH SM SL

Big size BH BM BL

Similarly, with the same percentile threshold, the profitability factor can be classified into three levels as well: Strong (R), medium (N), and Weak (W); and the investment factor is divided into Conservative (C), medium (O), and Aggressive (A). Therefore, the formation of 2x3 portfolios on size-profitability as well as size-investment is illustrated respectively in Table 2 and Table 3.

Table 2: 2x3 Size-Profitability

Strong Profitability Medium Profitability Low Profitability

Small size SS SN SW

Big size BS BN BW

Table 3: 2x3 Size-Investment

Conservative Inv Medium Inv Aggressive Inv

Small size SC SO SA

Big size BC BO BA

After constructing the diversified groups, the factors in the five-factor model are calculated as follows.

Size factor: SMB=(SMBB/M +SMBprofitability+SMBinvestment)/3, in which SMB B/M =(SH+SM+SL)/3-(BH+BM+BL)/3;

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SMBinvestment=(SC+SO+SA)/3-(BC+BO+BA)/3; Value factor (B/M): HML=(BH+SH)/2-(BL+SL)/2; Profitability factor: RMW=(BR+SR)/2-(BW+SW)/2; Investment factor: CMA=(BC+SC)/2-(BA+SA)/2

To sum up, in this paper, the factors are interpreted as follows.

SMB(small minus big): average monthly return on the small-size stocks minus the average monthly return on the large-size stocks;

HML(high minus low): average monthly return on the high-B/M stocks minus the average monthly return on the low-B/M stocks;

RMW(robust minus weak): average monthly return on the robustly profitable firms’ stocks minus the average monthly return on the weakly profitable firms’ stocks;

CMA(conservative minus aggressive): average monthly return on the low-asset-growth rate firms’ stocks minus the average monthly return on the high-asset-growth-rate firms’ stocks.

Now that the SMB, HML, RWM, CMA as well as Rm are constructed clearly, the following step is to repeat the calculation of the five independent variables in a monthly-base from 2007 to 2017. Then, the needed sample of time-series on the five factors is constructed.

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4. Five-Factor Model Performance Summary

4.1. Characteristics of the five factors

In the last section, the five factors have been calculated based on the time series during 2007-2017. Hence, to understand the basic feature of the five factors in Chinese stock market, I plot the factors in Chart 1. It is apparent that the market risk premium tends to outweigh other factors’ values in terms of scale. Among the rest four factors, SMB and HML, as the two shared factor existing in both three-factor model and five-factor model, they tend to have larger absolute value than RMW and CMA’s. RMW and CMA, which are the two controversial factors, their absolute values seem to be comparatively trivial but still cannot be neglected. Besides, the pattern of RMW and CMA appear to be highly correlated.

Chart 1:

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Afterwards, based on the first month in the sample (01/2007), I plot the cumulative line chart for the five factors, as shown in Chart 2. The market factor, which is the Chinese A-share index return adjusted by the risk-free rate, can reflect the completed market

performance during 2007 and 2017 as a whole. The size factor, SMB, climes upwards steadily except for some retracement during 2015 and 2016, implying that the size factor maintains crucial for the return over the sample period. The value factor, HML, shows turbulence, but it is able to keep growing within several sub-periods, such as 2009-2012, 2015-2017. In terms of the two controversial factors, CMA shows a gradually slight growth pattern but remains in a small scale, while the RMW is anti-common sense to some degree, which reveals that the profitable companies in general do not outperform the less profitable companies. This abnormal pattern is estimated to result from the multicollinearity or the specialty of the Chinese stock market, and some adjustment is probable to be done on the RMW factor.

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 2007-01 2007-06 2007-11 2008-04 2008-09 2009-02 2009-07 2009-12 2010-05 2010-10 2011-03 2011-08 2012-01 2012-06 2012-11 2013-04 2013-09 2014-02 2014-07 2014-12 2015-05 2015-10 2016-03 2016-08 2017-01 2017-06 2017-11 Market Risk Premium SMB HML RMW CMA

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Chart 2:

Cumulative monthly data for the five factors during 2007-2017.

Speaking of building up a multi-factor model for evaluating the portfolio return, it is able to lower the value of the intercept with adding more and more factors into the model, which manipulates an “econometrics trick” to pretend the model owns strong explanatory power. However, this trick will also lower the significance of other coefficients because of the possible multicollinearity. Added two more factors, the five-factor model is usually suspected to encounter this issue. Hence, I conducted the correlation analysis between each factors and the result is presented in Table 4. From the statistics below, we can see the profitability factor (RMW) have strong correlation with the size factor (SMB) and investment factor (CMA). It is understandable that the RMW and CMA are negatively correlated in high degree—if the asset increment of a firm is largely dependent on the retained net income, then an aggressive firm is highly probable to be a more profitable firm as well. Therefore, I might adjust the CMA factor in the model to reduce the effect from the multicollinearity.

-1 -0.5 0 0.5 1 1.5 2 2.5 2007-01 2007-07 2008-01 2008-07 2009-01 2009-07 2010-01 2010-07 2011-01 2011-07 2012-01 2012-07 2013-01 2013-07 2014-01 2014-07 2015-01 2015-07 2016-01 2016-07 2017-01 2017-07 Market Risk Premium SMB HML RMW CMA

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Table 4: Correlation matrix between the factors Rm SMB HML RMW CMA Rm 1 0.146379759 0.063569 -0.356846108 0.174136227 SMB 0.146379759 1 0.573325 -0.769540866 0.386486798 HML 0.063568679 0.573325107 1 -0.231927454 -0.148995257 RMW -0.356846108 -0.769540866 -0.23193 1 -0.652036142 CMA 0.174136227 0.386486798 -0.149 -0.652036142 1

4.2. Comparison between three-factor model and five-factor model

No matter three-factor model or five-factor model or even other multi-factor model, all of their fundamental purpose is to dig out more explanatory factors to explain the excess return. In order to test whether the five-factor model fits the Chinese stock market better than the classical three-factor model, I would like to test the three-factor first, then the four four-factor models (each consists of market factor and three of the other factors), and finally comes the five-factor model.

I will adopt the popular method named GRS test accepted by other scholars to study the same question. It is one type of F-statistics tests developed by Gibbons, Ross, & Shanken (1989) to examine whether the "𝛼_!"𝑠 for the N assets all equal to 0. The GRS statistics are calculated with the following formula and the GRS critical value follows the FN,T-N-1 distribution.

𝐺𝑅𝑆 = _𝑵𝑻 𝑻−𝑵−𝑳_{𝑻−𝑳−𝟏} 𝜶′𝚺−𝟏𝜶

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The rule for the GRS test is that, the larger of the GRS-statistics, the probability of wrongly rejecting the hypothesis that all the 𝛼! =0 is smaller.

In short, I will run the regressions for each portfolio under the 2x3 classification methods respectively, and then use the GRS to test the 𝛼 and the related p-value. Besides, the average of the 𝛼_! under each group method is recorded as 𝐴 𝛼_! , which is better when smaller. The comprehensive result is displayed in Table 5.

Table 5 :

The GRS test on the intercepts from each regression of the portfolio, displayed separated under different 2x3 methods.

Factors applied GRS p_GRS A(|ai|)

A：size-B/M group three-factor model Rm SMB HML 3.02 0.02% 0.0055 four-factor model Rm SMB HML RMW 2.79 1.54% 0.0048 Rm SMB HML CMA 2.45 0.80% 0.0046 Rm SMB RMW CMA 3.32 0.00% 0.0081 Rm HML RMW CMA 3.89 0.00% 0.0094

five-factor model Rm SMB HML RMW CMA 2.01 1.45% 0.0043

B:size-profitability group three-factor model Rm SMB HML 4.87 0.00% 0.0073 four-factor model Rm SMB HML RMW 2.98 0.47% 0.0065 Rm SMB HML CMA 3.34 0.12% 0.0061 Rm SMB RMW CMA 3.24 0.29% 0.007 Rm HML RMW CMA 3.51 0.00% 0.0089

C:size-investment group three-factor model Rm SMB HML 3.95 0.00% 0.0061 four-factor model Rm SMB HML RMW 2.14 0.18% 0.0052 Rm SMB HML CMA 2.35 0.06% 0.0049 Rm SMB RMW CMA 3.19 0.18% 0.0068 Rm HML RMW CMA 3.22 0.00% 0.0085

Firstly, as illustrated in the table above, it is obvious to see that within each group, the four-factor model without size factor (SML) always has a higher GRS statistics and larger

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𝐴 𝛼_! than other models. In short, the size factor is a crucial factor to build up a such capital return model for Chinese stock market. This outcome is similar to Fama & French’s test in the U.S. equity market. It also reversely evidences the correctness to use size factor as the fixed dimension to conduct the portfolio classification.

Secondly, within each group, the GRS-statistics value for the five-factor model is smaller than that of the three-factor model and the corresponding 𝐴 𝛼_! is also smaller. Hence, the five-factor model fits better to the Chinese stock market than the three-factor model does. Thirdly, what is worth to notice that, several four-factor models that consist of the factors randomly also show considerable performance in the respect of explanatory power, with a 𝐴 𝛼_! observed. For instance, in Group C (classifying the portfolio based on the 2x3 size-investment method), the four-factor model comprising Rm, SMB, HML and CMA reveals a similar 𝐴 𝛼_! value with the five-factor model. Combined this finding with the

multicollinearity issue and the correlation matrix mentioned in previous sections, I would rather modify the RMW factor to reduce the effect of multicollinearity—

Make RMWO=RMW-𝑅𝑀𝑊, in which 𝑅𝑀𝑊𝑂𝑡= ai + bi(RMt- Rft)+ siSMBt+ hiHMLt+ ciCMAt. Therefore, the modified five-factor model is:

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5. Regression Details and Result Interpretation

After employed the modification on the RMW factor, I would like to use the modified model to test how well the five-factor model fit the Chinese market. Recalling the 2x3 classification methods applied in the previous sections, I will run the regression on the modified model based on the 2x3 size-B/M portfolios, 2x3 size-profitability portfolios and 2x3 size-investment portfolios respectively. In detail, the logic of interpretation of the regression result is—the coefficient for a certain factor represents the correlation between the corresponding portfolio and this factor, which indicates the consistency between the feature of the group and the feature of the factor. For instance, the size factor presents the size premium and the preference for investing in small-size stocks.

5.1. 2x3 Size-B/M portfolios

As shown in Table 6 below, from left to right, the title “small” and “big” stand for the increase of the firms’ size, while from top to down, the B/M ratio rises

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correspondingly. The coefficients are recorded as “β” in the left part of the table and the related t-values are in the right part of the table.

Table 6 :

Regression result of 2x3 size-B/M group (left-hand side is the coefficients, and right-hand side is the t-value).

size-B/M group

Small Big Small Big

α t(α) Low 0.0024 0.0011 1.24 -2.73 Medium 0.0008 -0.0002 0.65 -1.34 High 0.0032 -0.0025 1.44 -0.87 β_Rm t(β_Rm) Low 1.25 1.09 45.22 46.61 Medium 1.23 1.28 48.91 45.78 High 1.11 1.19 46.53 52.42 β_SMB t(β_SMB) Low 2.89 0.65 15.83 5.46 Medium 2.97 0.27 19.32 6.53 High 2.78 0.44 20.35 6.29 β_HML t(β_HML) Low -0.48 -0.95 -6.38 -13.24 Medium -0.23 -0.31 -2.58 -2.41 High 0.37 0.75 4.95 8.09 β_RMWO t(β_RMWO) Low -0.56 -0.13 -5.06 -1.56 Medium -0.27 -0.04 -1.45 -0.89 High -0.14 -0.28 -2.68 -2.06 β_CMA t(β_CMA) Low 0.88 0.51 2.75 1.99 Medium 0.27 0.22 0.98 0.73 High 0.32 0.38 1.3 1.55

According to the statistics generated in the table above, some conclusion can be drawn in general.

1) The Five-factor model after modification with the profitability factor (RMW) is basically capable to explain the excess returns in a sufficient degree, since the “α”s in each portfolio are relatively small enough. Given that the Hypothesis 1 estimates that the intercept equals to 0, which is to test whether “α”=0, and in this case, most of the

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absolute t-statistics values for “α”s are smaller than the absolute t-critical value at 5% significance, referring to that the intercept is significantly as small as 0.

2) The portfolio’s return is closely related with the market factor, with the observation that β_Rm for each portfolio are all near to 1. Compared with β values of other factors, it can be seen that the market factor is related with the portfolio return most closely. This phenomenon indicates that although CAPM model has been evidenced to have lots of flaws in practice, it is meaningful in roughly predicting the portfolio returns with less workload put in and more time efficiency saved, which can also explain for its long-lasting popularity till now.

3) For the size factor, by comparing the column tagged with “small” and that tagged with “big”, we can see the coefficients, “β_SMB” for small-size firms are all significantly larger than the big-size firms’. Moreover, by comparing the all the factors except for market factor, the t-values for the small-size firms are highest in the size factor, which implies that, the stock returns on small-size firms can be explained by the size factor to a large extent.

4) For the value factor (B/M), its β increases from negative value to positive value with the B/M ratio from low to high. For the portfolios classified in high B/M ratio, their positive “β_HML”s rise when the size move from small to big. On the other hand, for the portfolios that have lower B/M ratio, the absolute values of their negative “β_HML”s increase with the size scale. In summary, the HML factor obtains more explanatory power for the big-size stocks.

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6) The “β_CMA”s illustrate modest declining tendency respectively from top to down. The related t-values are also not significant enough. This phenomenon can be estimated as, the small-size firms with low B/M tend to have a more conservative investment style so that their asset growth rates are slower. This phenomenon might result from the

common scene of “shell game” or backdoor listing in China (Sun & Tong, 2000). That is, some tiny firms with little asset incremental might have high valuation (low B/M) owing to its “shell value premium”, as long as they are attracted to the private companies seek a fast-path for reverse-merge.

5.2. 2x3 Size-Profitability portfolios

As shown in Table 7 below, from left to right, the title “small” and “big” stand for the increase of the firms’ size, while from top to down, the profitability rises correspondingly. The coefficients are recorded as “β” in the left part of the table and the related t-values are in the right part of the table.

Table 7 :

Regression result of 2x3 size-Profitability group (left-hand side is the coefficients, and right-hand side is the t-value).

size-profitability group

α t(α) Low 0.0034 -0.0028 2.21 -1.85 Medium 0.0006 -0.0019 1.05 -2.55 High -0.0015 0.0004 -1.44 0.89 β_Rm t(β_Rm) Low 1.03 0.99 49.53 31.95 Medium 1.01 1.02 45.04 48.22 High 1.05 1.01 37.4 53.24 β_SMB t(β_SMB) Low 1.49 0.34 20.53 3.42 Medium 1.58 -0.05 22.77 -0.84 High 1.88 -0.18 16.94 -3.66 β_HML t(β_HML) Low -0.15 -0.26 -2.98 -2.24 Medium -0.24 -0.08 -3.16 -1.53 High -0.03 -0.15 -0.55 -1.97 β_RMWO t(β_RMWO)

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Low -0.75 -0.71 -8.94 -6.12 Medium 0.35 -0.33 0.75 -4.97 High 0.46 0.05 3.19 4.05 β_CMA t(β_CMA) Low 0.54 0.13 2.85 1.58 Medium 0.08 0.22 0.67 1.23 High -0.76 0.56 -0.83 1.69

Based on statistical analysis, Table 7 shares some similar pattern with Table 6. However, it still reveals inspiring features. The general conclusion drawn from Table 7 is listed below.

1) Similar with Table 6, the model after small modification can explain the excess return sufficiently. The intercept for all groups are all fairly small, with most of the corresponding absolute t-statistics values for “α”s are smaller than the absolute t-critical value at 5% significance level, implying that the intercept is significantly as low as 0.

2) When it comes to the market factor, it is the same case in this scenario—the portfolio return follows tightly with the market, with the values of “β_Rm” are all around 1. Generally speaking, among other factors, the market factor dominates the change of portfolio return.

3) For the size factor, the groups with small-size have comparatively large positive “β_SMB”, whilst groups with big-size have small negative “β_SMB”. When the coefficients for all of the factors in the small-size group are taken into comparison, only the “β_SMB”s show large value and the corresponding t-values are fairly big as well. It is supposed to evidence that, the returns on the small-size firms’ stock are mainly determined by the size factor.

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4) Regarding of the value factor analysis, the “β_HML”s do not reveal distinctive discrepancy among different groups.

5) For the vertical analysis of the profitability factor, its coefficients from different groups seem to rise and turn negative to positive, complying with the profitability moving from low to high. On the other hand, for the horizontal analysis between the small-size group versus the big-size group, the “β_RMWO”s are larger for the small-size group and are lower for the big-small-size group. To sum up, for the portfolios located in the same profitability group, return on the portfolios consisting of small-size firms’ stocks are more positively correlated with the RMW factor.

6) Last but not least, the discrepancy and the pattern of the coefficients of the

investment factor are thought-provoking. In the column of small size, the “β_CMA”s show declining trend as long as the profitability moving from low to high; while in the column of big size, the “β_CMA”s seem to grow with the level of profitability. In other words, it is intuitive to interpret that the small-size firms which are less profitable are apt to have more conservative investment style. Moreover, it is

interesting to see that the big-size firms with high profitability seem to be even more conservative in the aspect of investment. The reason behind is assumed to be the top large-firms in China are or were state-owned, which inherit the conservative

investment style even though they are profitable (Cull et al., 2015)

5.3. 2x3 Size-Investment portfolios

As shown in Table 8 below, from left to right, the title “small” and “big” stand for the increase of the firms’ size, while from top to down, the investment rises

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correspondingly. The coefficients are recorded as “β” in the left part of the table and the related t-values are in the right part of the table.

Table 8:

Regression result of 2x3 size-investment group (left-hand side is the coefficients, and right-hand side is the t-value).

size-investment group

α t(α) Low -0.0002 -0.0031 -2.02 -1.87 Medium -0.033 -0.0019 -1.38 -2.24 High -0.0031 0.0015 -1.29 -0.96 β_Rm t(β_Rm) Low 1.01 1.03 47.21 42.56 Medium 1.01 1.02 45.98 55.08 High 1.02 1.03 43.57 57.24 β_SMB t(β_SMB) Low 1.35 0.22 19.52 4.14 Medium 1.41 -0.06 20.69 -3.20 High 1.66 -0.12 17.53 -2.98 β_HML t(β_HML) Low -0.14 -0.09 -2.36 -1.52 Medium -0.09 -0.01 -3.15 -1.63 High -0.25 -0.11 -4.08 -5.56 β_RMWO t(β_RMWO) Low -0.47 -0.35 -5.24 -4.58 Medium -0.21 -0.14 -4.12 -2.97 High 0.15 0.11 2.01 1.98 β_CMA t(β_CMA) Low 0.64 0.85 3.55 3.79 Medium 0.39 0.45 1.45 0.92 High -0.61 -0.19 -3.26 -0.54

According to the information provided by Table 8, it also shows similarity with Table 6 and Table 7. The comprehensive interpretation is summarized below.

1) The modified five-factor model reveals substantial explanatory power on the excess return. The 𝛼 for all groups are all fairly small, with most of the corresponding absolute t-statistics values for “𝛼”s are smaller than the absolute t-critical value at 5% significance level, indicating that the intercept is significantly as low as 0.

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2) The market factor still holds a dominant place—the portfolio return follows closely with the market, with the values of “β_Rm” are all around 1.

3) As a vital factor, size factor still performs impressive especially for the small-size groups.

4) The coefficients for the value factor are relatively not significant.

5) In terms of the “β_CMA”, it gradually decreases to negative value when the

investment factor changes from low to high (conservative to aggressive). Besides, for the portfolios tagged with high-asset-growth-rate, the small-size group has a lager coefficient than the big-size one.

6. Conclusion

6.1. Research conclusion

In general, the optimal question can be answered after the analysis conducted. Fama-French Five-Factor model adjusted in the calculation of market capability (i.e. replacing total market capability in the baseline model with the market capability in circulation) fits the Chinese stock market well during the sample period from 2007 to 2017, and reveals stronger explanatory power than the three-factor model, even though the degree of superiority is not large.

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The equity reform in 2005 and the continuous improvement in the market liberalization enhance the efficiency in Chinese stock market as well as reduce its speculative feature. Besides, its defective accounting standards which keeps being reviled in the earlier stages are converging to the IFRS (Chen, Ding, & Xu, 2014). As a result, both the financial report quality and auditing quality are getting polished up. Therefore, although the

Chinese stock market is still classified as an emerging market, it is becoming increasingly mature for the investors to pay attention to and for the capital models to be employed in.

Specifically, for the Fama-French Five-factor model, the size factor is effective in the Chinese A-share stock market. That is, the small-size firms’ stock generates size-premium on the return. Moreover, since the A-share index is a composite index, so that the

portfolio return is closely related with the average market return. Therefore, the counter-cyclical investment in China is more difficult to implement. In addition, as another shared factor existing both in the three-factor model and the five-factor model, value factor plays a non-ignorance role, especially for the investors consider to invest in the big-size firms’ stocks with high B/M ratios. In conclusion, Fama-French Three-Factor model can be reasonably applied into the Chinese stock market. With two more factors added in, the five-factor model shows more estimative power, even though the profitability factor and the investment factor are not so profound as the size valuation. These five factors obtain important instructive meaning for the investors.

6.2. Possible extensions

During the process of the research, I realize that although the baseline of Fama-French multi-factors models is straightforward and easy to obtain, scholars strive to “localize”

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the model into a specific market, especially for the emerging market. Hence, the possible extensions can be implemented into two dimensions.

1) Extension on the selection of factors: It is well-known that the Fama-French multi-factor models are developed step by step by testing numerous multi-factors to the cross-sectional regressions. The factors evidenced to be statistically significant are then adopted into the final model. This research method inspires a loads of scholars to test other remarkable factors to modify the baseline models. For instance, the famous Pástor-Stambaugh model (Pástor,& Stambaugh, 2003) is also well-received in the worldwide, which combines the factors from Fama-French Three-Factor model and the liquidity factor. Besides, the momentum factor also arouses the scholars’ interest to study on (Beigi, Hosseini,& Qodsi, 2016).

2) Decomposition of the samples into subsamples in regarding of heterogeneity: Take the Chinese stock as an example—in terms of dividing vertically, it is feasible to only choose one board, such as Shenzhen Mainboard, Medium-sized Enterprise Board (SMEB) or B-share board. For dividing the sample horizontally, it is workable to select several industry sectors instead of the entire market and make comparison among various sectors.

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How well does Fama-French Five-Factor model fit Chinese stock market?

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