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University of Amsterdam Bachelor thesis Economic & Business Track: Finance and Organization

The three-factor model and the five-factor model for the

Chinese stock market

By Inge Dontje 10783474 Supervisor: Dr. Liang Zou Date: 30 January 2017

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Declaration of own work

This document is written by Inge Dontje who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is 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. Inge Dontje 30 January 2017

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Abstract

This study researches the performance of the Fama and French three-factor model and the five-factor model for the Chinese Stock market in the period between 2006 and 2015. This study confirms that the three-factor model and the five-factor model are incomplete models to explain variation in average return for the Chinese stock market in this research period. The five-factor model performs better (but imperfect) than the three-factor model.

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Table of Content

Statement of Originality.………..…….2 Abstract……….………..…....3 Table of contents………..……..4 List of Table………..……..6 Chapter 1: Introduction………..………7 1.1 Chinese stock market………..……..7 1.2 Research………..7 1.3 Relevance of the study………..8 1.4 Outline of the study……….9 Chapter 2: Literature review……….10 2.1 Capital Asset Pricing Model………..10 2.2 Three-factor model……….10 2.3 Five-factor model……….11 2.4 Roll’s critique………..……12 2.5 Historical research on the Chinese stock market………..………13 Chapter 3: Methodology………..……14 3.1 Formation of the portfolios………..14 3.2 Regressions………..………15 3.3 GRS-test………..………17 Chapter 4: Data………..………19 4.1 Sample………..………..19 4.2 Data from Datastream……….19 4.3 Data from Computstat……….20 Chapter 5: Results………..………..21 5.1 Results of the CAPM..………21 5.2 Results of the three-factor model..……….22 5.3 Results of the five-factor model..……….23 Chapter 6: GRS-test………..…………..25 Chapter 7: Limitations………..……….26 Chapter 8: Conclusion………..……….28

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8.1 Conclusion………..……....28 8.2 Limitation………..…………28 8.3 Future research……….28 References………..………..29 Appendix 1………..………..31 Appendix 2………..………..35

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List of tables

Table 1: The research question Table 2: The hypotheses Table 3: Formation of 2x3 portfolios on size and M/B Table 4: Equations of the regression Table 5: Explanation of variables Table 6: Formation of 2x3 portfolios on size and OP Table 7: Formation of 2x3 portfolios on size and INV Table 8: Formula’s for the SMB and HML variable for the three-factor model Table 9: Formula’s for the SMB, HML, RMW and CMA variable for the five-factor model Table 10: Formula GRS-test Table 11: Equation return on equity Table 12: Results of the CAPM regression Table 13: Results of the three-factor model regression Table 14: Results of the five-factor model regression Table 15: GRS-statistics Table 16: List of companies which are included in the sample Table 17: Descriptive statistic of the regression factors in the Chinese stock market Table 18: Descriptive statistics of the portfolios Figure 1: ‘A’ share index time frame

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Chapter 1: Introduction

This chapter provide an introduction to this study. First, the Chinese stock market is discussed. Second, the research question and hypothesis are introduced. Also, the study relevance is explained. At last, the outline of this thesis is discussed. 1.1 Chinese stock market Comparatively with other stock markets is the Chinese Stock market a young market. In the recent years, the Chinese stock market has grown rapidly. It contains of two stock exchanges, namely the Shanghai Stock Exchange (SSE) and the Shenzhen Stock Exchange (SZE). The Shanghai Stock exchange was founded in 1990 with only eight listed stocks. At the moment, it has developed into a stock exchange which contains 1247 listed stocks. Likewise, the Shenzhen stock exchange has developed rapidly. The exchange was established in 1990 and has grown to an exchange with 1889 listed companies at the moment. There are two types of shares. The ‘A’ shares which are only tradable by Chinese citizens. They are denominated in Renminbi. And the ‘B’ shares which are only tradable by foreign citizens and resident of Hong Kong, Macao and Taiwan. They are denominated in Renminbi, but traded in US dollars. The ‘A’ and ‘B’ are legally equivalent, the shares have the same voting power and claims on dividends. For the Shanghai Stock Exchange, three representative indices are the SSE composite index, the SSE A-share index and the SSE 180 share index. The SSE composite index includes all shares on the Shanghai stock exchange, the SSE A-share index contains all A-shares on the Shanghai stock exchange, and the SSE 180 index contains the 180 most representative ‘A’ shares on the Shanghai stock exchange. 1.2 Research This thesis research if the Fama and French five-factor model performs better than the Fama and French three-factor model for the Chinese stock market. This will lead to the research question in table 1 on the next page.

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Table 1: The research question Does the Fama and French five-factor model performs better than the Fama and French three-factor model for the Chinese stock market? To test the research question, four hypotheses will be examined. The first hypothesis follows from the three-factor model of Fama and French (1993), which consist of the variable excess market return, size and value. There will be tested if these three variables can explain the average excess portfolio return. The second hypothesis is derived from the five-factor model of the Fama and French (2015). The five-factor model consists of the variables excess market return, size, value, investment and profitably. And there will be tested if these variables are capable to explain the average excess portfolio return. Fama and French (2015) confirm that the five-factor model is better to explain the average excess portfolio returns than the three-factor model for the American stock market. This leads to the last hypothesis, which test if the five-factor model performs better than the three-factor model. The three hypothesis are shown in table 2. Table 2: The hypotheses Hypotheses 1: the variables excess market return, size and value explain average excess portfolio return Hypotheses 2: the variables excess market return, size, value, investment and profitability explain average excess portfolio return Hypotheses 3: the variables excess market return, size, value, investment and profitability explain average portfolio return better than the variables excess market return, size and value 1.3 Relevance of this study The Capital Asset Pricing Model and the three-factor model are two important asset pricing model. In Fama and French (2015) they introduces a new model which add two variables to the three-factor model, namely the five-factor model. They researched the New York Stock Exchange (NYSE), American Stock Exchange (AMEX) and the National Association of Securities Dealers Automated Quations stock exchange (NASDAQ). These are all based in America, which has a developed economy. They provide evidence that the five-factor model

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performs better than the three-factor model for the American Stock market. As stated above, the Chinese stock market had a lot of development in the recent years. It is an interesting case to look at the emerging and turbulence Chinese market. And test if the same conclusion, that the five-factor model performs better than the three-factor model, can be drawn. Since the five-factor model is relatively new, this study isn’t done for the Chinese market before. The most historical studies research the performance of the three-factor model on the Chinese stock market. The study of Xu & Zhang (2014) covers the period till 2013, but this period does not cover the Chinese stock market turbulence of 2015. So, it is an interesting case to include 2015. The relevance of this study is to research the performance of the new five factor model in a recent time period. This study covers the period between 31-12-2005 and 31-12-2015. 1.4 Outline of the thesis This chapter was the introduction to the research. The next chapter contains the literature review. In chapter three the methodology of this study will be explained. Chapter four gives a brief explanation on how to get the data for this study. Chapter five contains the regression results. Chapter six will cover the GRS-test. Chapter seven contains the limitations of this study. At last, chapter eight provide a conclusion for this study.

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Chapter 2: Literature review

This chapter contains the literature review of this study. First, the Capital Asset Pricing Model is explained. Second, the three-factor model is explained. Also, the five-factor model is discussed. Then Roll’s critique is mentioned. Finally, the historical researches on the Chinese market are discussed. 2.1 Capital Asset Pricing Model Berk and Demarzo (2014) state that the Capital Asset Pricing model (CAPM) is the most important model for the relationship between risk and return. The CAPM is developed independently by William Sharpe (1964) and John Lintner (1965). The CAPM predicts the expected return of an assets on its beta. The estimated market beta, together with the risk-free rate and the average market risk premium are used to calculate the cost of equity. The market portfolio is a value-weight portfolio which contains the non-diversifiable risk of risky assets, and the CAPM implies that the market portfolio is on the minimum variance frontier. The model state that investors should be compensated for the time value of their money and the systematic risk they are taking. The equation of the CAPM is in table 4. Besides that, the CAPM is the most important model for the relationship between risk and return, the empirical performance of the model is poor (Fama & French, 2004, p. 25). The poor performance of the CAPM may be caused by it simplifying assumptions. As well as difficulties which arise when implementing valid tests of the model. Black, Jensen and Scholes (1972), Blume and Friend (1973) and Stambaugh (1982) found that the relation between average beta and average historical return is too flat. Also, the more recent study of Fama and French (2004) confirms this finding. The predicted returns on the portfolios with the lowest beta are lower than the actual returns, and the predicted returns on the portfolios with the highest beta are higher than the actual return. 2.2 Three factor model Since the early 1980s, evidence appears that much of the variation in expected return is related to variables such as firm size and book to market equity. Banz (1981) provide evidence of the size effect on the New York Stock Exchange. The size effect is that average

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return falls from small stocks to big stocks, based on the level of market capitalization. Stattman (1980) find evidence for the value effect. The value effect is that stocks with high book to market ratio have higher average return than stocks with low book to market ratio. Fama & French (1992) provide more evidence that size, earnings-price, debt-equity and book to market ratio plays an important role at the prediction of expected return on assets. As a result, Fama & French (1993) create the three factor model which include two variables relating to size and book to market ratio to the CAPM. They provide evidence that most of the variation in expected return is captured for portfolios formed on size and book to market equity for the American stock market. The equation of the three-factor model is given in table 4. However, the three-factor model had some problems. These problems are caused by many anomaly variables. Novy-Marx (2013) provide evidence that profitability has explanatory power predicting average returns. Also Fama and French (2008) confirms a positive relation between profitability and expected returns. In Fama and French (2006) they confirmed that book to market ratio, expected profitability and expected investment are related to expected returns. They found a positive relation between profitability and expected return. And they found a negative relation between expected rates of investment and expected returns. Also, Titman, Wei and Xie (2004) emphasize the negative relation between capital investment and average return. All these papers provide evidence that the three-factor model is an incomplete model due to the important variables, profitability and investment, that are left unexplained. 2.3 Five factor model Fama and French (2015) introduced the five-factor model which include profitably and investment factors to the three-factor model. The equation is shown in table 4. They provide evidence that the five-factor model explains between 71% and 94% of the variation in expected return for the portfolios formed on size and book-to-market ratio, size and investment, and size and profitability. And they state that the five-factor model performs better than the three-factor model. However, their results suggest that the factor HML is superfluous. They find that the four factor model, where HML is excluded, performs the same as the five-factor model. The

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factor HML is important in portfolio tilts toward size, value, profitably and investment premiums. Another interesting conclusion is that portfolios of small stocks with negative factors of CMA and RMW are the main problem for the five-factor model. The model fails to capture low average stock return of small stocks that act like firms that invest a lot despite of the low profitability. In Fama & French (1993, 2015) the main problems of the asset pricing models are with the small stocks. 2.4 Roll’s critique As stated above, the market portfolio is a value-weight portfolio which contains the non-diversifiable risk of risky assets. The CAPM suggest that the market portfolio is on the minimum variance frontier. In the CAPM, three factor model and the five factor model proxies are used for the market portfolio. However, Roll (1977) state that, because of the use of market portfolio proxies, these models are incorrect. The problem is to find the right market portfolio for these models. The right market portfolio lies on the minimum variance frontier. So, if the market proxy lies on the minimum variance frontier, it can be used to explain variation in expected return. In this study the Shanghai ‘A’ share index is used as the market proxy. This index is a value-weighted index of all ‘A’ shares on the Shanghai Stock Exchange. 2.5 Historical research on Chinese stock market Wong, Tan and Wei (2006) investigates the effects of beta, size, book-to-market ratio and a variable specific for Chinese stock market on the A-shares of the Shanghai Stock Exchange. The period covered in this study is 1993 till 2002. They provide evidence that smaller firms and value firms have higher average return. However, they find that in the down market, the systematic risk is negative related to average stock return. Xu & Zhang (2014) studied the performance of the three factor model on the Chinese stock market for the period 1996 to 2013. They provide evidence that the three-factor model explains 93% of the variation in average return on the Chinese stock market. They state that the formation of the portfolios has a large effect on the results. Their study used the 5x5 portfolios and is based on the book-to-price ratio instead of the book-to-market ratio.

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Xie & Qu (2016) provide an empirical study on the application of CAPM and the three-factor model on the Chinese stock market. Their sample consist of monthly data from the SSE A-share market between 2005 and 2012. Compared with the CAPM, the three-factor model shows a large increase of the 𝑅#. With an average 𝑅# of 87.36%, they conclude that

the three-factor model can explain the average return better than the CAPM for the Chinese stock market. This study in done in 2016, however they don’t study the Fama and French five factor model.

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Chapter 3: Methodology

In this chapter the methodology for the study is discussed. The formation of the portfolios, the regressions, the calculation of the variable factors and the GRS-test will be explained. 3.1 Formation of the portfolios Fama & French (1993, 2015) make use of portfolios to regress the three-factor and five-factor model. In their studies, they sort the stocks into 25 value-weighted portfolios. They sort the stocks into five size groups and five book-to-market (B/M) groups, and call them the 5x5 size-B/M sorts. In this study, the 2x3 size-M/B sorts will be used. The stocks will be divided in two size groups, and three market-to-book (M/B) groups. The size groups, small and big, are created using the market capitalization. The stocks are ordered from low to high market capitalization. To allocate the stock to two size groups, the Shanghai Stock Exchange median is used. The stocks that are allocated within the 50th percentile are called small stock, and the stocks that are allocated above the 50th percentile are called big stocks. The M/B groups are created using the market-to-book ratio. As well as the size groups, the stocks are order from low to high market-to-book ratio. To allocate the stock to three M/B groups, the Shanghai Stock Exchange 30th and 70th percentiles are used. The stocks who lie within the 30th percentile are called value stocks. The stocks who lie between the 30th percentile and 70th percentile are called the neutral stocks. And the stocks who lie outside the 70th percentile are called the growth stock. This is different then the method used in the Fama & French (1993,2015) because in this study we make use of the market-to-book ratio instead of the book-to-market ratio. So the stocks with the lowest M/B ratio are called value stocks, and the stock with the highest M/B ratio are called growth stocks. This allocation of stocks will lead to 6 portfolio’s formed on size and M/B ratio, as shown in table 3. Table 3: Formation of 2x3 portfolios on size and M/B

Value Neutral Growth

Small SV SN SG

Big BV BN BG

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3.2 Regressions In this study, there will be three regressions. The CAPM-regression, the three-factor regression and the five-factor regression. The equations of the regressions are shown in table 4. The explanations of the variables are shown in table 5. Table 4: Equations of the regression CAPM Three-factor Five-factor 𝑅$ = 𝑎' + 𝑏' 𝑅*− 𝑅, + 𝑒' 𝑅$ = 𝑎' + 𝑏' 𝑅*− 𝑅, + 𝑠'𝑆𝑀𝐵 + ℎ'𝐻𝑀𝐿 + 𝑒' 𝑅$ = 𝑎' + 𝑏' 𝑅*− 𝑅, + 𝑠'𝑆𝑀𝐵 + ℎ'𝐻𝑀𝐿 + 𝑐'𝐶𝑀𝐴 + 𝑟'𝑅𝑀𝑊 + 𝑒' Table 5: Explanation of variables Rp Rf Rm SMB HML RMW CMA e Average excess portfolio return The risk-free return Return on the market proxy The return on a diversified portfolio of small stock minus the return on a diversified portfolio of big stocks The return on a diversified portfolio of high book-to-market ratio minus the return on a diversified portfolio of low book-to-market ratio The return on a diversified portfolio of stocks with robust profitability minus the return on a diversified portfolio of stock with weak profitability The return on a diversified portfolio of stocks with high investment opportunities minus the return on a diversified portfolio of stocks with low investment opportunities Residual

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The variables SMB, HML, RMW and CMA make use of portfolios. The variable SMB and HML use the size and market-to-book portfolios in table 3. The variable RMW make use of size and profitability (OP) portfolios and the variable CMA make use of size and investment (INV) portfolios. To create the 2x3 size and OP portfolios, the same method is used as the size and M/B portfolios. For size, the market capitalization is used to allocate the stocks to small or big stocks. The Shanghai Stock Exchange median is used as a breakpoint. The stocks that are allocated within the 50th percentile are called small stock, and the stocks that are allocated above the 50th percentile are called big stocks. To allocated the stock to different profitability levels, the profitability is sort from low to high profitability. The Shanghai Stock Exchange 30th and 70th percentiles are used. The stocks who lie within the 30th percentile low profitably are called weak stocks. The stocks who lie between the 30th and the 70th percentile are called neutral stocks. And the stocks who lie outside the 70th percentile are called robust stocks. This allocation leads to 6 different portfolios, which are shown in table 6. Table 6: Formation of 2x3 portfolio’s on size and OP

Weak Neutral Robust

Small SW SN SR

Big BW BN BR

The same method is used to create the 2x3 size and INV portfolios. However, investment is allocated in three groups, namely conservative, neutral and aggressive. The Shanghai Stock Exchange 30th and 70th percentiles are used. Stocks which are allocated to the 30th percentile lowest investment are called conservative. Stocks which lie between the 30th percentile and 70th percentile are called neutral stocks. And stocks which lie outside the 70th percentile are called aggressive stocks. This create 6 portfolio’s shown in table 6.

Table 7: Formation of 2x3 portfolio’s on size and INV

Conservative Neutral Aggressive

Small SC SN SA

Big BC BN BA

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The portfolios are used to create the SMB, HML, RMW and CMA variables in the three- and five-factor model. In table 8 the calculation is shown for the SMB and HML for the three-factor model. In table 9 the calculation is shown for the SMB, HML, RMW and CMA for the five-factor model. Table 8: Formulas for the SMB and HML variable for the three-factor model SMB (SV+SN+SG)/3 – (BV+BN+BG)/3 HML (SV+BV)/2 – (SG+BG)/2 Table 9: Formulas for the SMB, HML, RMW and CMA variables for the five-factor model SMB=/? SMB@A SMBBCD SMB HML RMW (SV+SN+SG)/3 – (BV+BN+BG)/3 (SW+SN+SR)/3 – (BW+BN+BR)/3 (SC+SN+SA)/3 – (BC+BN+BA)/3 SMB=/?+SMB@A+SMBBCD (SV+BV)/2 – (SG+BG)/2 (SR+BR)/2 – (SW-BW)/2 CMA (SC+BC)/2 – (SA+BA)/2

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3.3 GRS-test If average excess return is completely explained by the variables of the model, then the intercept of the model is zero. To test the hypothesis of table 2, the GRS-test is used. The GRS-test is founded by Gibbons, Ross and Shanken (1989), and is a test for the efficiency of a given portfolio. The test will be used to test whether the expected value of the 6 intercepts are jointly equal to zero. The GRS-test is common used by Fama & French to test asset pricing models. As well as Fama & French (2015), this study used the GRS test to test the performance of the three-factor model and the-five factor model. The formula for the GRS-test is given in table 10. Table 10: Formula GRS-test 𝐺𝑅𝑆 = 𝑇 𝑁 𝑇 − 𝑁 − 𝐿 𝑇 − 𝐿 − 1 [ 𝛼K LM𝛼 1 + 𝜇OKLM𝜇 O]~𝐹(𝑁, 𝑇 − 𝑁 − 𝐿) The GRS test isn’t directly available in STATA. STATA is used to run the regressions, and Excel is used for the matrix-algebra. In the appendix 2 the steps to calculate the GRS-statistic are explained.

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Chapter 4: Data

This chapter discus details of the sample and data observed from two databases, namely Datastream and COMPUSTAT. 4.1 Sample In this research, the Chinese stock market is represented by the Shanghai stock exchange. Only the ‘A’ shares from the Shanghai stock exchange are used. The complete company list is available at the site of the Shanghai Stock exchange. Excel is used to create a random sample. The sample consist of 108 stocks, which are mentioned in appendix 1. The Shanghai stock exchange ‘A’ share index is used as the market proxy for this research. Wong, Tan and Lui (2006) also use ‘A’ share index as the market proxy for the Shanghai stock exchange, and state that the correlation between the ‘A’ share index and Shanghai stock exchange is very high (0,9996). Fama & French (1993, 2015) used the one-month treasury bill rate as a proxy for the risk-free rate. For the Chinese market, the three-month deposit rate is used. This deposit rate is set by the People’s Bank of China. 4.2 Data from Datastream The databases Datastream is used to receive data of return on equity, return on the market, the risk-free rate, market capitalization and the market-to-book ratio. The data is obtained at a monthly basis from 2005 to 2015. The return on equity is calculated with the official closing price. The formula to calculated the return is given in table 11. Market capitalization is share price times shares outstanding. For this variable, the market value (MV) is used. Fama and French (1993,2015) use the book-to-market ratio. However, there was limited data available of the book-to-market ratio for the Chinese stock market. Instead, the market-to-book ratio is used. As stated above, for the return on the market, the ‘A’ share index is obtained. And for the risk-free rate, the three-month deposit rate set by the People’s bank of china is downloaded.

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Table 11: Equation return on equity 𝑹𝒊= 𝑷𝒕− 𝑷𝒕L𝟏 𝑷𝒕L𝟏 ∗ 𝟏𝟎𝟎 4.3 Data from COMPUSTAT The database COMPUSTAT is used to get annually accounting data for the fiscal year from 2004 till 2015. The accounting data contains of total revenue, cost of goods sold, interest expense, selling, general and administrative expense, total assets and shareholders equity. Profitability is calculated with data of the fiscal year t-1. It is calculated as follow, total revenue minus cost of goods sold, interest expense, selling, general and administrative expense. The results of the subtraction are divided by shareholder’s equity of the fiscal year t-1. Investment is the difference in total asset. It is calculated as the total asset of fiscal year t-1 minus the total asset of fiscal year t-2, divided by the total assets of t-2.

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Chapter 5: Results

This chapter shows the results of the CAPM, the three-factor model and the five-factor model regressions. 5.1 CAPM In table 11 the results of the CAPM regression on the six portfolios are shown. The average adjusted R-square is 0.0256, which means that 2.56% of the variation in average excess portfolio return is explained by excess market return. This results state that the CAPM can not capture the variation in average excess portfolio return. This result is in line with the literature review. Historical studies found that the empirical results of CAPM are poor. Moreover, all b parameters are statistically significant. Table 11: Results of the CAPM regression This table shows the results of the CAPM regression on six portfolio’s formed on size and market to book ratio. The dependent variables are the average excess portfolio returns of the portfolio’s SV, SN, SG, BV, BN and BG. The CAPM equation is: 𝑅$ = 𝑎'+ 𝑏' 𝑅*− 𝑅, + 𝑒' 𝑎' 𝑏' 𝐴𝑑𝑗 − 𝑅# 𝑆𝐸𝑅 SV 1.0505 (1.0159) 0.2067* (0.1088) 0.0218 10.97 SN 1.3291 (1.0412) 0.2981*** (0.1116) 0.0499 11.244 SG 0.7505 (1.0240) 0.2005* (0.1097) 0.0196 11.057 BV 1.1976 (0.9473) 0.2029** (0.1015) 0.0250 10.23 BN 1.2548 (1.0225) 0.2567** (0.1095) 0.0370 11.041 BG 0.9888 (0.9011) 0.2479** (0.0965) 0.0456 9.7303

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5.3 Three-factor model In table 12 the results of the three-factor model for all six portfolios are shown. The average adjusted R-square is 0.1178, which means that 11.78% of the average excess portfolio return is explained by the variables excess market return, SMB and HML. This results is not what would expected from historical studies. Most of the historical research on the Chinese stock market found that the three-factor model is good in predicting the average excess portfolio return. For example, Xie & Qu (2016) found evidence that the three-factor model can explain the average excess portfolio return, with a mean R-square of 87.36%, for the period 2005 to 2012. Also, Xu & Zhang (2014) found that the three-factor model explains 93% of the variation in average excess portfolio return on the Chinese stock market for the period 1996 to 2013. However, they provide evidence that construction of the portfolios can have a large effect on the results. In their study they used the 5x5 portfolio formation and they used the book-to-price ratio instead of the book-to-market ratio. The difference between the adjusted R-square may be caused by the difference in formation of the portfolios. The b parameters are statically significant. The s parameters are statically significant for the small portfolio’s (SV,SN,SG) , and not statistically significant for big portfolio’s (BV,BN,BG). This means that the factor SMB only has explanatory power for small firms. The factor HML is statistically significant for the two value portfolio’s, SV and BV. More details are shown in table 12 on the next page.

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Table 12: Results of the three-factor model regression This table shows the results of the three factor model regression on six portfolio’s formed on size and market to book ratio. The dependent variables are the average excess portfolio returns of the portfolio’s SV, SN, SG, BV, BN and BG. The three-factor equation is: 𝑅$ = 𝑎'+ 𝑏' 𝑅*− 𝑅, + 𝑠'𝑆𝑀𝐵 + ℎ'𝐻𝑀𝐿 + 𝑒' 𝑎' 𝑏' 𝑠'' 𝐴𝑑𝑗 − 𝑅# 𝑆𝐸𝑅 SV 0.9180 (0.9223) 0.2269** (0.0986) 1.1724*** (0.2606) 0.9987*** (0.2990) 0.1993 9.9243 SN 1.3277 (0.9809) 0.3080*** (0.1049) 1.1365*** (0.2772) 0.4686 (0.3179) 0.1627 10.555 SG 0.9187 (0.9329) 0.1992** (0.0998) 1.3318*** (0.2636) -0.1181 (0.3024) 0.1920 10.038 BV 1.0082 (0.9253) 0.2196** (0.0990) 0.2638 (0.2615) 0.8518*** (0.2999) 0.0763 9.9566 BN 1.1486 (1.0213) 0.2672** (0.1092) 0.2725 (0.2886) 0.5289 (0.3311) 0.0459 10.99 BG 1.0076 (0.9114) 0.2474** (0.0975) 0.1044 (0.2576) -0.0314 (0.2954) 0.0305 9.8071 *,** and *** indicate 10, 5% and 1% significance levels 5.4 Five-factor model In table 13 the results of the five-factor model for all six portfolios are shown. The average adjusted R-square is 0.2201, which means that 22.01% of the variation in average portfolio excess return is explained by the factors excess market return, SMB, HML, CMA and RMW. As well as the three-factor model, this result is lower than expected. There is much variation in the average portfolio excess return that can be explained by other factors. The results of the five-factor model regressions show that not all b parameters are statistically significant. For two of the six portfolios, excess market return has no explanatory power. As well as the three-factor model, the s parameters are statically significant for the small portfolio’s, and not statistically significant for big portfolio’s. The h parameter is now statistically significant for the portfolio’s SV and SG, despite that Fama and French (2015)

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suggest that the HML factor is redundant. Another interesting finding is that the c parameter is only statistically significant for the portfolio SN. It could be the case that investment don’t have explanatory power on the Chinese stock exchange. However, this is inconsistent with the conclusions from historical research. In contrast, the parameter r is statistically significant for all portfolios. So, profitability has explanatory power for the Chinese stock market. Table 13: Results of the five-factor model regression This table shows the results of the five factor model regression on six portfolio’s formed on size and market to book ratio. The dependent variables are the average excess portfolio returns of the portfolio’s SV, SN, SG, BV, BN and BG. The five-factor equation is: 𝑅$ = 𝑎'+ 𝑏' 𝑅*− 𝑅, + 𝑠'𝑆𝑀𝐵 + ℎ'𝐻𝑀𝐿 + 𝑐'𝐶𝑀𝐴 + 𝑟'𝑅𝑀𝑊 + +𝑒' 𝑎' 𝑏' 𝑠' ℎ' 𝑐' 𝑟' 𝐴𝑑𝑗 − 𝑅# 𝑆𝐸𝑅 SV 0.8885 (0.8730) 0.1719* (0.0973) 1.0329*** (0.2895) 0.5593* (0.3011) -0.1918 (0.3002) -0.8627*** (0.2386) 0.2867 9.3671 SN 1.2401 (0.9154) 0.2435** (0.1020) 0.9000*** (0.3035) -0.0327 (0.3157) -0.5422* (0.3147) -1.1025*** (0.2501) 0.2750 9.8219 SG 0.8706 (0.8632) 0.1348 (0.0962) 1.1471*** (0.2862) -0.6317** (0.2977) -0.3007 (0.2968) -1.0344*** (0.2358) 0.3122 9.2615 BV 1.0221 (0.8689) 0.1324 (0.0968) 0.0086 (0.2881) 0.4181 (0.2997) -0.2936 (0.2988) -0.9776*** (0.2374) 0.1900 9.3235 BN 1.1086 (0.9687) 0.1887* (0.1079) 0.0266 (0.3212) 0.1109 (0.3341) -0.5331 (0.3331) -1.0246*** (0.2647) 0.1466 10.394 BG 1.0399 (0.8757) 0.1695* (0.0976) -0.1055 (0.2903) -0.3910 (0.3020) -0.1847 (0.3011) -0.8060*** (0.2392) 0.1101 9.3957 *,** and *** indicate 10, 5% and 1% significance levels

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Chapter 6: GRS-test

This chapter will test if the five-factor model performs better than the three-factor model for the Chinese stock market. This will be done with the GRS-test stated in 3.3. To calculate the GRS-test, the steps explained in the appendix are taken. The GRS-statistic, the average absolute value of the intercepts and the means of the adjusted R-squares, are shown in table 14. Table 14: GRS-statistics This table contains the results of the GRS-test, average absolute value of the intercepts and the means of the adjusted R-squares of the portfolio’s. GRS 𝐴 𝑎' 𝐴𝑑𝚥 − 𝑅# Three-factor model 53,2369*** 1.0548 0.1178 Five-factor model 43,7499*** 1.0283 0.2201 *,** and *** indicate 10, 5% and 1% significance levels The GRS test rejects the three-factor model and the five-factor model. So, the GRS test confirms that the three-factor model and the five-factor model are incomplete models to explain variation in average return for the Chinese stock market. This results are in line with Fama and French (2015) where they reject all models. In this study, the performance of three three-factor model will be compared with the performance of the five-factor model. To determine which model is best (but imperfect) in explaining variation in average return, the results in table 14 are used. The GRS-statistic of the five-factor model is lower than the GRS-static of the three-factor model. Also, the average absolute value of the intercepts is lower for the five-factor model than for the three-factor model. And the mean of the adjusted R-square of the portfolios is higher for the five-factor model than for the three-factor model. So, the five-factor model outperforms the three-factor model based on these three measures.

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Chapter 7: Limitations

The Chinese stock market is an emerging and turbulence market. In figure 1 the price of ‘A’ share index is shown from the period 1992 till 2015. As the figure makes clear, the ‘A’ shares on the Shanghai Stock exchange is volatile. Especially during the sample of this study, which covers the period between 2006 to 2015. Our sample contains a short time period, with relatively high volatility. This could be an explanation why the three-factor model and five-factor model do not perform as expected. The historical studies stated in the literature review research periods with lower volatility. Like Wong, Tan and Wei (2006) which covers the period between 1993 and 2002. This period has relatively lower volatility. Or Xu and Zhang (2014) which covers the period between 1996 and 2013. This period contains more volatility because they include the financial crisis in 2008. But they have a larger time frame. This could be an explanation why the three-factor model performs well for these two studies. However, Xu and Qu (2016) study the period between 2005 and 2012. This period has a high volatility and a short time period. Nevertheless, they provide evidence that the three-factor model can explain on average 87.36% of the variation in returns. Figure 1: The ‘A’ share index time frame 0 1000 2000 3000 4000 5000 6000 7000 1992 1993 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2014 2015 In de x Year

'A' share index

'A' share index

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Other limitation is regarding the data. It is well known that the data for the Chinese stock market is poor. There consists lack on information in emerging market. However, for this research, all data was available for the companies in the sample. On the other hand, the quality of this data is questionable. Wang & Iorio (2007) found that the quality of listed company’s characteristics is not good. The average listed company had comparative low dividend yield, low earning per share and low book-to-market value. All available data is checked with care. Nevertheless, it is possible that their remains some default in the data set. This may be cause the three-factor and the five-factor model are imperfect for this dataset.

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Chapter 7: conclusion

This chapter contains the conclusion, the limitations and suggestion for future research. 7.1 conclusion This study researches the three-factor model and the five-factor model for the Chinese stock market in the period between 2006 and 2015. The research question is: Does the five-factor model performs better than the three-factor model for the Chinese Stock market? The sample consists 108 ‘A’ shares on the Shanghai Stock exchange. This study provide evidence that the three-factor model and the five-factor model are incomplete models to explain variation in average return for the Chinese stock market in the period between 2006 and 2015. To provide an answers to the research question, this study research which model performs better (but imperfect). The conclusion is that the five-factor model performs better (but imperfect) than the three-factor model.

7.2 Limitations All limitations are briefly discussed in chapter 7. The limitation of that the period covered in this study has high volatility and a short time frame. Another limitation is regarding the data. Generally, that the data for China is poor. For this study, all data was available and is checked with care. However, it is possible that their remains some defaults in the dataset. 7.3 Future Research This study only captures the Shanghai stock exchange. It would be interesting if the five-factor model would be tested for markets across the globe. Fama and French (2015) investigated the American stock market, but it would be interesting to investigate other stock markets, especially the emerging markets.

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References

Banz, R. W. (1981). The Relationship Between Return and Market Value of Common Stocks. Journal of Financial Economics(9), 3-18. Berk, J., & DeMarzo, P. (2014). Corporate Finance. In J. Berk, & P. DeMarzo, Corporate Finance. Edinburgh: Person Education. Black, F., Jensen, M., & Scholes, M. (1972). The Capital Asset Pricing Model: Some Empirical Tests. Studies in the Theory of Capital Markets(1), 79-121. Blume, M., & Friend, I. (1973). A New Look at the Capital Asset Pricing Model. Journal of Finance(28), 19-33. Burton, M., & Derek, J. (2009). The ''value'' effect and the market for Chinse stocks. Emerging Markets Revieuw, 227-241. Cao, Q., Parry, M. E., & Leggio, K. B. (2011). The three-factor model and artificial neural network: predicting stock price movement in China. Annals of Operations Research(185), 25-44. Fama, E. (1996). Multifactor portfolio efficiecy and multifactor asset pricing. Journal of Financial and Quantitative Analysis(31), 441-465. Fama, E., & French, K. (1993). Common risk factors in the return on stocks and bonds. Journal of Financial Economics(33), 3-56. Fama, E., & French, K. (1995). Size and book-to-market factors in earnings and returns. Journal of Finance(50), 131-156. Fama, E., & French, K. (1998). Value versus Growth: The International Evidence. The Journal of Finance(53), 1975-1999. Fama, E., & French, K. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives(18), 25-46. Fama, E., & French, K. (2006). Profitability, investment, and average returns. Journal of Financial Economics(82), 491-518. Fama, E., & French, K. (2008). Dissecting anomalies. Journal of Finance(63), 1653-1678. Fama, E., & French, K. (2012). Size, value, and momentum in international stock returns. Journal of Financial Economics(105), 457-472. Fama, E., & French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116, 1-22. Gibbons, M. R., Ross, S. A., & Shanken, J. (1989). A Test of the Efficiency of a Given Portfolio. Econometrics(57), 1121-1152. Linter, J. (1965). The Valuation of Risk Assets and the Selection of Risky Invesments in Stock Portfolios and Capital Budgets. Review of Economics and Statistics(47), 13-37. Novy-Marx, R. (2013). The other side of value: The gross profitability premium. Journal of Financial Economics(108), 1-28. Roll, R. (1977). A critique of the asset pricing theory's tests. Journal of Financial Economics(4), 129-176. Sharpe, W. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance(19), 425-442. Stambaugh, R. (1982). On The Exclusion of Assets from Tests of the Two-Parameter Model: A Sensitivity Analysis. Journal of Financial Economics(10), 237-268. Stattman, D. (1980). Book Values and Stock Returns. The Chicago MBA: A Journal of Selected Papers(4), 25-45. Titman, S., Wei, J., & Xie, F. (2004). Capital Investments and Stock Returns. Journal of

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Wang, Y., & Iorio, A. (2007). The cross section of expected stock returns in the Chinese A-share market. Global Finance Journal(17), 335-349. Wong, K. A., Tan, R. S., & Lui, W. (2006). The Cross-Section of Stock Return on The Shanghai Stock Exchange. Review of Quantitative Finance and Accounting(26), 23-29. Xie, S., & Qu, Q. (2016). The Three-Factor Model and Size and Value Premiums in China's Stock Market. Emerging Markets Finance & Trade(52), 1092-1105. Xu, J., & Zhang, S. (2014). The Fama-French Three Factors in the Chinese Stock Market. China Accounting and Finance Review(16), 210-227. Zhu, J., & Zhu, X. (2010). Estimating the Equity Risk Premium: the Case of Greater China. SSRN Electronic Jounal, 1-30.

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Appendix 1

Appendix 1 contains the list of companies, and the descriptive statistics for the regression factor and for the portfolios.

Table 16: List of companies which are included in the sample

Code Short Name Full Name

600597 BRIGHT DAIRY BRIGHT DAIRY & FOOD CO.,LTD 600962 SDICZL SDIC ZHONGLU FRUIT JUICE CO.,LTD. 600980 BGRIMM TEC BGRIMM Technology Co.,Ltd. 600112 TCKG GUIZHOU CHANGZHENG TIANCHENG HOLDING CO.,LTD. 600191 HZSY BAOTOU HUAZI INDUSTRY CO.,LTD. 600477 HXSS HANGXIAO STEEL STRUCTURE CO.,LTD 600481 SEES Shuangliang Eco-Energy Systems Co.,Ltd 600577 TJSMW TONGLING JINGDA SPECIAL MAGNET WIRE CO.,LTD. 600697 CCEG CHANG CHUN EURASIA GROUP CO., LTD. 600749 TIBET TOURISM TIBET TOURISM CO.,LTD 600984 SCMC SHAANXI CONSTRUCTION MACHINERY CO.,LTD. 600004 baiyunairport Guangzhou Baiyun International Airport Co.,ltd. 600737 Cofco Tunhe Cofco Tunhe Co.,Itd. 600172 HHWW HENAN HUANGHE WHIRLWIND CO.,LTD. 600644 LEP LESHAN ELECTRIC POWER CO.,LTD. 600195 CAHIC China Animal Husbandry Industry Co.,Ltd. 600531 YGGL HENAN YUGUANG GOLD&LEAD CO.£¬LTD 600298 ANGEL ANGEL YEAST CO.,LTD 600167 - Luenmei Quantum Co.,Ltd 600229 QCMC Qingdao Citymedia Co,. Ltd. 600238 HAINAN YEDAO HAINAN YEDAO £¨GROUP£©CO.,LTD 600829 HRPC HPGC Renmintongtai Pharmaceutical Corporation 600470 Liuguo Chemical Anhui Liuguo Chemical Co.,Ltd.

600219 NANSHAN ALUMINIUM SHANDONG NANSHAN ALUMINIUM CO., LTD 600335 Sinomach Auto Sinomach Automobile Co., Ltd. 600406 NARI-TECH NARI Technology Co., Ltd. 600220 JSSS JIANGSU SUNSHINE CO.,LTD. 600337 MIHF Markor International Home Furnishings Co., Ltd. 600425 qscc XINJIANG QINGSONG BUILDING MATERIALS AND CHEMICALS (GROUP) CO., LTD. 600689 SMEG SHANGHAI SANMAO ENTERPRISE (GROUP) CO.£¬LTD. 600973 BAOSHENG SCI BAOSHENG SCIENCE AND TECHNOLOGY INNOVATION CO., LTD. 600686 KLM XIAMEN KING LONG MOTOR GROUP CO.,TLD. 600401 HAREON SOLAR Hareon Solar Technology Co., Ltd. 600236 GGEP GUANGXI GUIGUAN ELECTRIC POWER CO.,LTD.

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600500 SINOCHEM INTERNATIONAL SINOCHEM INTERNATIONAL CORPORATION 600466 BRC SICHUAN LANGUANG DEVELOPMENT CO., LTD. 600680 shpte SHANGHAI POTEVIO CO.,LTD. 600132 CBC CHONG QING BREWERY CO.LTD 600520 Zonfa Technology TongLing Zonfa Trinity Technology Co.£¬Ltd 600415 YIWU CCC ZheJiang China Commodities City Group Co.,Ltd. 600723 BCRG Beijing Capital Retailing Group Co., Ltd. 600305 Hengshun Vinegar JIANGSHU HENGSHUN VINEGAR CO.,LTD 600775 NPEC NANJING PANDA ELECTRONICS COMPANY LIMITED 600783 Luxin Co., Luxin Venture Capital Group Co., Ltd. 600199 AGSW Anhui Golden Seed Winery Co.,Ltd. 600201 JINYUGROUP JINYU BIO-TECHNOLOGY CO.£¬LTD. 600382 GDMZH Guangdong Mingzhu Group Co.,Ltd. 600778 YOUHAO GROUP XINJIANG YOUHAO (GROUP) CO.,LTD 600871 SSC SINOPEC OILFIELD SERVICE CORPORATION 600602 INESA-IT INESA Intelligent Tech Inc. 600055 CR Wandong China Resources Wandong Medical Equipment Co., Ltd. 600054 HSTD Huangshan Tourism Development Co.,Ltd. 600327 CMC WUXI COMMERCIAL MANSION GRAND ORIENT CO.,LTD 600815 XGMA Xiamen XGMA Machinery Company Limited. 600436 PIEN TZE HUANG ZHANGZHOU PIENTZEHUANG PHARMACEUTICAL CO.,LTD. 600889 NCFC NANJING CHEMICAL FIBRE CO.LTD 600861 BURCG BEIJING URBAN-RURAL COMMERCIAL (GROUP) CO., LTD. 600836 J.L.C SHANGHAI JIELONG GROUP INDUSTRY CORPORATION LIMITED 600267 HISUN ZHEJIANG HISUN PHARMACEUTICAL CO.,LTD 600575 Wanjiang Logistics Anhui Wanjiang Logistics (Group) Co.,Ltd 600138 CYTS CHINA CYTS TOURS HOLDING CO.,LTD. 600141 Xingfa group HUBEI XINGFA CHEMICALS GROUP CO.,LTD. 600740 SCC SHAN XI COKING CO.,LTD 600893 AAEC AVIC AVIATION ENGINE CORPORATION PLC 600532 HONGDA MINING SHANDONG HONGDA MINING CO.,LTD 600059 GYLS ZheJiang GuYueLongShan ShaoXing Wine Co.LTD 600550 - BAODING TIANWEI BAOBIAN ELECTRIC CO.,LTD 600256 GUANGHUI ENERGY GUANGHUI ENERGY CO.,LTD. 600557 Kanion Pharmaceutical Jiangsu Kanion Pharmaceutical Co.,Ltd. 600867 THDB TONGHUA DONGBAO PHARMACEUTICAL CO.,LTD. 600202 HAC Harbin Air Conditioning Co.,Ltd. 600275 wcy Hubei Wuchangyu CO.,LTD 600898 SLSS SANLIAN COMMERCIAL CO.,LTD 600588 Yonyou Yonyou Network Technology Co., Ltd. 600375 HUALING XINGMA HUALING XINGMA AUTOMOBILE£¨GROUP£©CO.,LTD. 600491 LYCG LONG YUAN CONSTRUCTION GUOUP CO.,LTD 600739 LNCD LIAONING CHENGDA CO.,LTD.

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600809 Shanxi Fen Wine SHANXI XINGHUACUN FEN WINE FACTORY CO.,LTD 600365 THGW TONGHUA GRAPE WINE CO.,LTD. 600398 HEILAN HOME HEILAN HOME CO.,LTD 600135 LUCKY FILM CO.,LTD LUCKY FILM COMPANY LIMITED 600662 Qiang Sheng Holding Shanghai QiangSheng Holding CO.,Ltd. 600161 BTBP Beijing Tiantan Biological Products Corporation Limited 600487 HTGD Hengtong Optic-Electric Co.,Ltd. 600419 Tianrun Dairy Xinjiang Tianrun Dairy Co., Ltd. 600651 FACS Shanghai Feilo Acoustics Co., ltd 600428 COSCOL COSCO SHIPPING Specialized Carriers Co., Ltd. 600834 shentong metro Shanghai Shentong Metro Co., Ltd.

600701 HGDHTED HARBIN GONG DA HIGH-TECH ENTERPRISE DEVELOPMENT CO.,LTD. 600103 qszy Fujian Qingshan Paper Industry Co.,Ltd. 600655 YYTM SHANGHAI YUYUAN TOURIST MART CO.,LTD 600854 CHUNLAN JIANGSU CHUNLAN REFRIGERATING EQUIPMENT STOCK CO.,LTD 600022 SHANDONG STEEL SHANDONG IRON AND STEEL COMPANY LTD 600789 LKPC SHANDONG LUKANG PHARMACEUTICAL CO.,LTD. 600547 sd-gold SHANDONG GOLD MINING CO.,LTD. 600652 U9 GAME SHANGHAI U9 GAME CO.,LTD. 600598 hacl heilongjiang agriclture company limited 600982 nbtp NINGBO THERMAL POWER CO., LTD 600279 CQGJ CHONGQING GANGJIU CO.,LTD. 600519 KWEICHOW MOUTAI KWEICHOW MOUTAI CO.,LTD. 600203 FFEC FUJIAN FURI ELECTRONICS CO.,LTD. 600717 TIANJIN PORT TIANJIN PORT HOLDINGS CO.,LTD. 600387 HAIYUE ZHEJIANG HAIYUE CO.,LTD 600126 HZIS HangZhou Iron And Steel Co.,Ltd. 600754 JINJIANG SHARES Shanghai Jin Jiang International Hotels Development Co.,Ltd. 600168 WHKG WUHAN SANZHEN INDUSTRY HOLDING CO.,LTD 600449 NXBM NINGXIA BUILDING MATERIALS GROUP Co.,Ltd 600313 NFSI ZHONGNONGFA SEED INDUSTRY GROUP CO., LTD. 600859 Wangfujing WANGFUJING GROUP CO., LTD. Table 17: Descriptive statistic of the regression factors in the Chinese stock market Factor Observations Means Standard Deviation Maximum Minimum

Erm 119 2,2612 0,5986 3,3300 1,1000

SMBT 119 -0,1030 3,5554 9,1085 -10,6778

HMLT 119 0,2741 3,1049 8,6553 -8,4809

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HMLF 119 0,2741 3,1049 8,6553 -8,4809

CMAF 119 -0,1068 3,5138 15,6899 -10,0897

RMWF 119 0,0883 4,4575 17,0758 -15,4514

Table 18: Descriptive statistics of the portfolios

Portfolio Observations Means Standard deviations Maximum Minimum

SV 119 0,8653 11,0474 28,9473 -29,6846 SN 119 1,0595 11,4917 39,5243 -26,9093 SG 119 0,5742 11,1241 28,0626 -34,9757 BV 119 1,0812 10,3620 36,9842 -28,7559 BN 119 1,0449 11,2171 39,5243 -32,9059 BG 119 0,8051 9,9457 31,1563 -28,7559

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Appendix 2

Computing the GRS statistic To compute the GRS statistic STATA and Excel is used. Step 1: run the regressions, three factor model and five factor model, for all portfolio’s. STATA is used to run the regressions. Step 2: estimated intercepts for SV, SN, SG, BV, BN, BG and create a 6x1 vector. 𝛼[ 𝛼bD 𝛼bC 𝛼bc 𝛼?D 𝛼?C 𝛼?c ] Step 3: calculate the residuals for every regression, and create a 118x6 matrix. 𝜀[ 𝜀MbD 𝜀MbC 𝜀Mbc … … … 𝜀MMfbD 𝜀MMfbC 𝜀MMfbc 𝜀M?D 𝜀M?C 𝜀M?c … … … 𝜀MMf?D 𝜀MMf?C 𝜀MMf?c] Step 4: calculate the covariance matrix (6x6) of the residuals. To calculate the covariance matrix Excel is used. Step 5: calculate the sample means of the factor portfolios. For the three factor portfolio it is a 3x1 vector, and for the five factor portfolio it is a 5x1 vector. 𝜇 = 𝐹gh* 𝐹b=? 𝐹i=j & 𝜇 = 𝐹gh* 𝐹b=? 𝐹i=j 𝐹l=m 𝐹n=o Step 6: create a 118x3 or 118x5 matrix of the factor portfolio excess return. 𝐹 𝐹Mgh* 𝜀Mb=? 𝜀Mi=j … … … 𝐹MMfgh* 𝜀MMfb=? 𝜀MMfi=j &𝐹 𝐹Mgh* 𝜀Mb=? 𝜀Mi=j … … … 𝐹MMfgh* 𝜀MMfb=? 𝜀MMfi=j 𝜀Ml=m 𝜀Mn=o … … 𝜀MMfl=m 𝜀MMfn=o Step 7: calculate the covariance matrix (3x3) or (5x5) of the factors. As well as the covariance matrix in step 4, excel is used to calculated the covariance. Step 8: Compute the GRS statistic 𝐺𝑅𝑆 = 𝑇 𝑇 − 𝑁 − 𝐿 𝛼K 𝛼 LM ~𝐹 𝑁, 𝑇 − 𝑁 − 𝐿

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