Master Thesis in Finance
MSc Program in Business Administration
An empirical examination of the capital asset
pricing model and asset pricing theory
Using Chinese data
Author: Dandan Deng
Student Number: 1748300
Supervisor: Prof. Dr. Auke Plantinga
An empirical examination of the
capital asset pricing model and
asset pricing theory
Using Chinese data
Faculty of Economics and Business, University of Groningen Dandan Deng
Abstract
After examining the data of Shanghai Stock Exchange from 1999 to 2007, we find that a relationship between firm size and average stock returns as well as book to market value and average stock returns. However, several results in this paper contradict previous results. First, the average returns of large firms are much higher than those of small firms. Second, it seems that the Fama and French three factor model does not add additional explanation power to the capital asset pricing model in the Chinese stock market. That is, the beta factor seems to be an important determinant of security returns in the Chinese stock market.Table of Content
1. Introduction...4
2. Literature review...6
2.1 literature of the capital asset pricing model...6
2.2 literature of the arbitrage pricing theory...7
2.3 literature of Fama and French three factors model...8
2.4 hypotheses ...10
3 Backgrounds and Data Description...10
3.1 A brief introduction of Chinese stock market...10
3.2 Data Description ...13
3.3 Methodology ...16
4 Data Analysis and Results...18
5 Conclusion and Discuss...25
1. Introduction
The standard form of the capital asset pricing model was formulated independently by William Sharpe, John Lintner and Jan Mossin, building on the earlier work of Markowitz (1959) on diversification and modern portfolio theory. Hence, it is often referred to as the Sharpe-Lintner-Mossin form of the capital asset pricing model. In the development of the asset pricing model it is assumed that (1) all investors are single period risk-averse utility- of-terminal-wealth maximizers and make decisions solely in terms of excepted values and standard deviations of the returns on their portfolios, (2) there are no personal income taxes or transactions costs, (3) all investors have homogeneous views regarding the parameters of the joint probability distribution of all security returns, and (4) all investors can borrow and lend at a given riskless rate of interest unlimitedly. The main result of the model is a linear statement of the relation between the expected risk premiums on individual assets and their “systematic risk.”
“The attraction of the capital asset pricing model (CAPM) is its powerfully simple logic and intuitively pleasing predictions about how to measure risk and about the relation between expected return and risk. Unfortunately, perhaps because of its simplicity, the empirical record of the model is poor – poor enough to invalidate the way it is used in applications.” (Fama and French (2003))
The arbitrage pricing theory (APT), originally introduced by Ross (1976) and extended by Huberman (1982) and Connor (1982), is an asset pricing model that identifies significantly priced common risk factors influencing asset returns. It is built on the twin assumptions of no arbitrage opportunities in the capital market and a linear relationship between actual returns and K common factors. Many economists are engaged in research various APT models. Of these, the three factor model proposed by Fama and French (1992) is considered to be one of the most influential APT models.
as the United States, Japan and so on. However, one would like to know if the models perform well in emerging markets and are the empirical test results obtained in the well-studied US markets transferable to an emerging market like China? Having such knowledge may allow investors who are interested in emerging markets to make investment decision more effectively. The second limitation of literature is the minority of studies that compare CAPM and APT in the same stock market.
I will compare CAPM and APT, and test whether they can explain the empirical results in the stock market of China. When testing APT, I choose the Fama and French (1992) three factor model to investigate the relation between the cross-section average stock returns and size (ME), book-to-market equity (BE/ME), and market beta. The difference between this study and previous ones is that it utilizes a more current sample.
Based on the results of this paper, we find that a relationship between firm size and average stock returns as well as book to market value and average stock returns in the overall Shanghai Stock Exchange. However, several results contradict previous results. First, average returns of large firms are much higher than those of small firms. Second, when comparing the results of Wald Test, it seems that the Fama and French three factor model does not add additional explanation power to the capital asset pricing model in the Chinese stock market for the period January 1999 to December 2007. In other words, the beta factor seems to be a dominical determinant of security returns in Chinese stock market.
2. Literature review
2.1 literature of the capital asset pricing model
The publication of the seminal article on capital asset pricing by Sharpe (1964), revolutionized the theory as well as the applicability of modern techniques in finance. As we know, there are numerous articles that study the capital asset pricing model. Of these, perhaps the most influential is the mean-variance formulation originally developed by Sharpe (1964) and Treynor (1961), and extended and clarified by Lintner (1965a; 1965b), Mossin (1966), Fama (1968a; 1968b), and Long (1972). In addition Treynor (1965), Sharpe (1966), and Jensen (1968; 1969) have developed portfolio evaluation models which are either based on this asset pricing model or bear a close relation to it.
Capital asset pricing model (CAPM) dominates the academic literature for a long time. The use of beta in portfolio construction, use of CAPM in computing the cost of capital for capital budgeting etc. is known to all the students of finance. However, the empirical validity of this model has been questioned by several studies. The empirical findings by Friend and Blume (1970), Black et al. (1972), Miller and Scholes (1972) and Blume and Friend (1973), etc. show that the CAPM overestimate (underestimate) the real returns for low (high) beta stocks.
Based on the theory of the “two-parameter” (that is, mean-variance) portfolio model and the market equilibrium model derived from the “two-parameter” model, Fama and MacBeth (1973) find that there is a positive linear relationship between the Beta and return in the common stocks of the New York Stock Exchange during the period January 1926 through June 1968. This indicates that risk-averse investors expect a higher return of efficient portfolios associated with higher risk in a perfect market. Furthermore, they argue that there is no other risk affects the average stock returns. More specifically, they propose an equation which is Rit = γ0t + γ1tβi + γ2tβi2 + γ3tsi + eit. The subscript t refers to
period t, so that Rit is the one-period percentage return on security i from t-1 to t. No
systematic effects of non-β risk means that E(γ3t) =0. Finally, they also examine that the
consistent with an efficient capital market in which prices of securities completely reflect all the available information.
2.2 literature of the arbitrage pricing theory
Roll and Ross (1980) were first to empirically test the APT. Using data for individual equities, they find that there are three or four factors priced in the US stock market during the 1962-1972 period. Factor loading techniques are applied to determine the common systematic risk factors in this paper. Ross’s theory states that the expected return vector should be equal to a linear combination of the loading vectors and a unit vector conditional that a set of asset returns conforms to a factor model. Shanken (1982) criticize it is essentially require that all securities have the same expected return based on a two-step procedure. Ross and Dybvig (1985), however, show the testability of empirical tests of the APT. They argue that Shanken’s analysis of the APT has no relevance for actual empirical tests. What is more, the way Shanken chosen portfolios is the opposite of diversification. That is the reason applying the APT to these portfolios gives a paradox.
Hughes (1982) and Lam (1988) investigate the Canadian stock market and find that three to four factors significantly explain stock returns. Hamao (1988) uses the Japanese stock data from 1975 to 1984 and argues that three factors appear to have a significant effect on the Japanese stock market. Antoniou et al. (1998) analyses the UK stock market and find three factors are priced. Similar to other tests, the empirical evidence from the APT tests indicate that there are at least two factors explaining returns in stock market. What is more, there are numerous empirical study focusing on the relationship between firm size (ME), book to market ratio (BE/ME), earnings-price ratio (E/P) and stock returns.
shares outstanding), adds to the explanation of the average returns. These important results have been referred to as the ‘size effect’. Keim (1983) and Reinganum (1983) find the abnormal return to small firms (measured relative to the CAPM) occurs during the first two weeks in January which became known as the “turn-of-the-year effect.” Bhandari (1988) finds that there is a positive relation between leverage and average stock returns in tests that include both size (ME) as well as beta.
Stattman (1980) and Rosenberg et al. (1985) document that average returns in the US stock markets are positively related to the ratio of a firm’s book value of common stock to its market value, BE/ME. Chan et al. (1991) and Daniel et al. (1997) also find that book-to-market equity, BE/ME, has a positively strong power in explaining average returns in Japan stock market.
Heston et al. (1999) studies the ability of beta and size in explaining the cross-section of average stock returns in an international sample of twelve European countries during the period of 1980-1995. They find that average stock returns are positively related to beta and negatively related to firm size. Rouwenhorst (1999) examines more than 1700 firms in 20 emerging stock markets. This paper documents a strong positive cross-sectional correlation between the return factors and share turnover in emerging markets.
Basu (1983) examines the relationship between earnings' yield, firm size and returns on the common stock of NYSE firms. The results show that earnings-price ratio (E/P) have additional explanation power of the average returns on U.S stocks. Ball (1978) claims that earnings-price ratio (E/P) can serve as a proxy for unnamed factors in expected returns. This paper indicates that when stocks have relatively higher risks and expected returns, their prices are likely to be lower relative to earnings and therefore the E/P is likely to be higher.
2.3 literature of Fama and French three factors model
documented. First, market Beta does not have power in explaining the cross-section of average stock returns. Second, two variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with leverage and E/P ratios. Obviously, their paper provides empirical evidence against the traditional Sharpe, Lintner, and Black (SLB) model, that average returns are positively related to market Betas.
Since the time of the original publication of the Fama and French, controversy has emerged in the academic circle over the empirical performance of beta and the CAPM. Robert Faff (2004) suggests four main themes that have emerged from this literature:
First, one of the arguments is that ‘it takes a model to beat a model’. More specially, it argues that the alternative Fama and French three factor model needs more time and further empirical confirmation before it can be accepted as an ideally theory-based model to replace the CAPM.
Second, the data selection procedures of Fama and French are criticized by several researchers. For example, Shumway and Warther (1999) argue that there is a substantial delisting bias in CRSPs NASDAQ data due to missing returns. They document that the missing returns are large and negative on average, and that delisted stocks experience a considerable decrease in liquidity. After a correction is made for the bias, the size effect disappears.
Fourth, Loughran (1997) finds that the Fama and French results are driven by two factors, one of them is a January seasonal in the book-to-market effect and the other one is extremely low returns on small, young, growth stocks.
Generally speaking, Fama and French three factor model is one of the most well-known and controversial APT models in the academic literature. One may also take an interest in whether it can be applied to an emerging market. This paper will try to provide some empirical results in Chinese stock market.
2.4 hypotheses
Based on the literature, the following hypotheses can be defined with regard to CAPM and the three factor model.
(I) The relationship between the expected return on a security and the unsystematic risk factors is linear.
(II) Market beta has significant power in explaining the cross-section of average stock returns.
(III) In a market of risk-adverse investors, high risk should be associated with higher expected return, that is E (Rm-E (R0)>0.
(IV) Firm size has explanatory power in the average stock returns.
(V) Book to market equity has significant power in explaining the average stock returns.
3 Backgrounds and Data Description
3.1 A brief introduction of Chinese stock market
These two stock exchanges have the same variety of functions, such as providing marketplace and facilities for the securities trading; formulating business rules; accepting and arranging listings; managing and disseminating market information; organizing and monitoring securities trading; regulating members and listed companies. A qualified company can freely choose to be listed on one of the exchanges, or to be listed on both exchanges. However, each of them has its own strength and focus.
(Internet source: http://www.sse.com.cn/sseportal/en_us/ps/about/bi.shtml)
By comparing the number of listed companies, number of shares listed, total market value, tradable market value, and stock turnover in value, we can easily find that the Shanghai Stock Exchange is lager than the Shenzhen Stock Exchange. Up to now, Shanghai Stock Exchange is the largest stock market in mainland China and fifth largest in the world. As of February 2008, 861 companies were listed on the Shanghai Stock Exchange and the total market capitalization of SSE reached RMB 23,340.9 billion (US$3,241.8 billion; US$1 = RMB 7.20). Most national large board companies, key industries in infrastructure and high technical sectors prefer to list on the Shanghai Stock Exchange. Among them, more than 80% of the total market value is covered by the companies of industrial sector and conglomerates.
Table 1 Trade summary for 2007
Stock listing Market value
(billon Yuan)
Annual turnover value (billion Yuan)
A-shares 850 26,849.7 30,196.0
B-shares 54 134.2 347.4
Total 904 26983.9 30,543.4
all the companies listed on the Shenzhen Stock Exchange. Among them, more than 300 manufacturing companies consist of about 60% of total stocks issued capitalization in the market. (Internet source: http://www.szse.cn/main/en/aboutsse/sseoverview/) So for the size and different strength of these two Stock Exchange, I focus on the stocks traded on the Shanghai Stock Exchange in this paper.
There are three different types of share in the Chinese stock market. Companies incorporated in mainland China are traded in the mainland A-share markets. The price of A shares is quoted in Chinese currency, the renminbi (RMB), and is listed on the Shanghai or Shenzhen stock exchanges. Currently, only mainlanders and selected foreign institutional investors are allowed to trade A shares. B shares came into existence in 1991. They allow foreign investors to invest in shares issued domestically by People's Republic of China companies. They are subscribed and traded in foreign currencies and are listed and traded in securities exchanges inside China. In the past, only foreigners were allowed to trade B shares. Starting from March 2001, mainlanders can trade B shares as well. H shares are shares in Chinese companies issued in China under Chinese law. They are listed on the Hong Kong Stock Exchange and subject to its stringent listing and disclosure requirements. The shares are denominated in H.K. dollar and trade like any other shares listed on the Hong Kong Exchange.
(Internet source:
http://www.chinadaily.com.cn/bizchina/2006-03/17/content_543430.htm)
3.2 Data Description
Table 2 shows some basic descriptive statistics of the 346 stocks traded on Shanghai stock exchange. The period of data extends from January 1999 to December 2007. As I mentioned above, by the end of 2007, there are more than 800 stocks traded in the Shanghai Stock Exchange. However, only about half of them have been traded for more than eight years. For this paper, stock prices, market values and market-to-book value for each company are required. 376 companies have all those data published for the Shanghai A-shares market. Of these, 30 companies are excluded due to their negative book value of equity in 1999. So our sample constitutes 346 companies with data from Datastream International. Pt-1 is the stock price of preceding month and Pt is the stock price of
subsequent month. Ln (Pt/Pt-1) is used to calculate the stock returns of the whole sample.
In order to simplify the process, the stock dividend is assumed to be zero. The market index used is the Shanghai A share – price index, while the risk free rate of return is proxied by the 1-year monthly deposit interest rate. All of the data is collected from Datastream.
Table 2. Summary Statistic for 346 Stocks traded on ShangHai Stock Exchange
This table reports summary statistics for 346 A-share stocks in the sample from 1999 to 2007.
ME (value of all tradable shares) is denominated in thousands of RMB.
Stock returns (monthly) Book-to-Market ME
Mean 0.7% 0.341 3353.8
Median 0.0% 0.286 2267.6
Maximum 238.7% 2.041 91648.8
Minimum -131.6% 0.002 134.3
Reform1 of Listed Companies from this year. From then on, the Shanghai Exchange index increases slowly and reaches to the highest point in November 2007. So this choice of sub-periods reflects the desire to separate “bull” and “bear” periods. The sub-period of 2002-2004 refers to a down market and the other two sub-periods refer to an up market. The whole research period is divided into three short periods as follow:
1 The Equity Division Reform is a process of eliminating systematic differences of stock transfers in
Table 3 sub-period data of the whole sample
Ln (Pt/Pt-1) is used to calculate the monthly stock returns.Pt-1 is the stock price of preceding month
and Pt is the stock price of subsequent month. ME (value of all tradable shares) is denominated in
thousands of RMB.
1999-2001
Stock returns (monthly) Book-to-Market ME Interest rates
Mean 1.1% 0.25 3,605 2.5% Median 0.2% 0.23 2,608 2.3% Maximum 115.6% 2.04 30,539 3.8% Minimum -60.8% 0.007 260 2.3% Std. Dev. 0.1 0.14 3,491 0.58 Skewness 1.0 3.3 3.5 1.8 Kurtosis 8.8 35.5 19.6 4.2 Jarque-Bera 21,278.5 4,306.2 15,015 21.4
2002-2004
Stock returns (monthly) Book-to-Market ME Interest rates
Mean -1.2% 0.31 3,410 2.0% Median -1.5% 0.29 2,403 2.0% Maximum 80.4% 0.88 38,127 2.3% Minimum -131.6% 0.009 458 2.0% Std. Dev. 0.1 0.16 3,503 0.09 Skewness -0.3 0.73 3.9 2.5 Kurtosis 7.8 3.4 24.4 7.1 Jarque-Bera 13,429.3 92.9 24,097.7 62.3
2005-2007
Stock returns (monthly) Book-to-Market ME Interest rates
3.3 Methodology
The CAPM model can be specified as
Rit - Rf = α + βi (Rmt – Rf) (1)
Where Rit is the expected return on security i in month t, Rmt is the expected return of the market portfolio in month t, Rf is the risk free rate and βi is a measure of risk for security i.
As mentioned above, I divide the whole period into three sub-periods. The first period is used to estimate betas for each stock using monthly stock returns. In terms of ranking by Betas from low to high, all the stocks are divided into five categories. After that, every category is splite into five smaller groups ranked by market equity from low to high. As a result, the 346 stocks are divided into 25 portfolios; each comprised of 14 stocks equally weighted. That is, the first portfolio has the 14 lowest betas and the last portfolio has the 14 highest betas. Then average returns of these 25 portfolios are calculated. The beta is estimated by regressing each stock’s weekly return against the market index. At last, Ordinary Least Square (OLS) is used to test CAPM. I use the equation proposed by Fama and MacBeth (1973):
Rit = γ0t + γ1tβi + eit (2)
t refers to period t and Rit is the one-period return on stock i from t-1 to t. The disturbance eit is assumed to have zero mean and to be independent of all other variables in (2).
The formula to calculate β is as follow: β= Cov (Rit, R mt)/ σ 2(R
m) (3)
Here, as mentioned above, β is a measure for risk, Rit i is the monthly return for security i
and R mt is the monthly return of the “market” (the ShangHai Market Index). σ 2 (R
m) is the variance of the market index.
Rit = γ0t + γ1tβi + γ2tβi2 + γ3tsi + eit (4)
t refers to period t and Rit is the one-period return on stock i from t-1 to t. βi2 is meant to test linearity. si is included in order to test if there is any risk o stock i which is not deterministically related to βi. The disturbance eit is assumed to have zero mean and to be independent of all other variables in (4).
When testing APT, I decide to choose the three factor model which is proposed by Fama & French (1992a):
Rit=a + b1βit + b2 ln(MEit) + b3ln(BE/MEit) + eit (5)
where Rit is the expected return on stock i , size is measured by market equity (ME),
which is equal to a stock’s price times shares outstanding, BE/MEit is book to market equity, ei is a random error term with mean equal to zero and variance equal to σ2ei. Following the methodology of Fama and French (1993), first, all stocks are ranked on size (prices times shares) and divided into two groups, small and big (S and B). The number of companies is equal in these two groups. Then the sample is split into three book-to-market equity groups based on the breakpoints for the bottom 30% (Low), middle 40% (Medium), and top 30% (High). Fama and French (1993) argue that the reason for sorting firms into three groups on BE/ME and only two on ME is the evidence in Fama and French (1992a) document that the book-to-market ratio has a stronger power in explaining average stock returns than size. Then, six portfolios (S/L, S/M, S/H, B/L, B/M, B/H) are created from the intersections of the two ME and the three BE/ME groups.
on the different return behaviors of high- and low-BE/ME firms which are largely free of the size factor in returns. SMB and HML are calculated as follow:
SMB = （S/L+S/M+S/H）/3-（B/L+B/M+B/H）/3 (6) HML = （S/H+B/H）/2-（S/L+B/L）/2 (7)
After calculating SMB and HML, we need a regression to test the power of the three factors related to returns. That is:
Rpt − Rf = a + b (RMt − Rf ) + s (SMBt ) + h (HMLt ) +εpt (8) SMB and HML are explained above, our proxy for the market factor in stock returns is the excess market return, RMt − Rf. RMt is the return on the value-weighted portfolio of the stocks in the six size-BE/ME portfolios. Rf is the one-month deposit rate. If the three factors are able to completely explain the change of returns, a should be equal to 0.
4 Data Analysis and Results
The major tests of the capital asset pricing model are presented in table 4. For each sub-period, the table shows: γjt , the average of the month-by-month regression coefficient
estimates; S(γjt) the standard deviation of the month-by-month coefficients of
determination; AIC, which refers to Akaike information criterion. Akaike's info criterion is a measure of the goodness of fit of an estimated statistical model which proposed in Akaike (1974). The AIC is a tool for model selection. Given a data set, several competing models may be ranked according to their AIC, with the one having the lowest AIC being the best. So I use AIC as one of the tools to compare which model is perform better in Chinese stock market.
As we can see in table 4, the probability of γ1t is smaller than the significance level of 1%
We can easily find the R2s of the sub-period A and C are close to 40% and that of the sub-period B is 84% which is much higher. It suggests the explanatory power of the regression is fairly strong in Shanghai Stock Exchange at least from 2002 to 2004. And the values of Akaike info criterion for all these sub-periods are negative.
Table 4 CAPM regression coefficients and tests
This table shows results (coefficients and t values) from regressing on proxies to the beta and the beta square factors that is,Rit = γ0t + γ1tβi + eit for the sample period from 1999 to 2007. R2 is the
adjusted coefficient of determination from this regression. AIC is Akaike information criterion.
Sub-period γ0t γ1t R2 AIC A:1999-2001 Coefficient 0.002*** 0.009*** 46% -8.93 S(γjt) 0.005 0.006 t-Statistic 2.94 (0.000) 17.44 (0.004) B:2002-2004 Coefficient 0.0057*** -0.0223*** 84% -9.08 S(γjt) 0.0006 0.0005 t-Statistic 10.39 (0.000) -42.34 (0.000) C:2005-2007 Coefficient 0.04*** -0.010*** 33% -8.12 S(γjt) 0.0009 0.0008 t-Statistic 43.005 (0.000) -12.92 (0.000)
Notes:* is significant at a level of at least 10%, ** is significant at a level of at least 5% and *** is significant at a level of at least 1%.
The linear tests of the capital asset pricing model are presented in table 5. As we can see from table 5, the values of t(γ3t) are small, and all the signs of the t(γ3t) are positive. So
we can not reject hypothesis (II) of the CAPM, which says that Market β has significant power in explaining the cross-section of average stock returns.
The coefficient of γ2t for the sub-period A and C are significant at the level of 1%.
not reject the hypothesis (I) of the CAPM, which says that the relationship between the expected return on a security and its risk is linear.
Fama and MacBeth (1973) argue that the CAPM can not consider to be standing up well to the data before testing hypothesis (III). That is, investors prefer to a positive tradeoff between risk and return. From the negative sign of beta, we would say that the hypothesis (III) did not seem to be confirmed.
The values of R square and Akaike info criterion do not have much difference compare with those in table 4.
Table 5 the linear test of CAPM regression coefficients and tests
This table shows results (coefficients and t values) from regressing on proxies to the beta and the beta square factors that is,Rit = γ0t + γ1tβi + γ2tβi2 + γ3tsi + eit for the sample period from 1999 to
2007. R2 is the adjusted coefficient of determination from this regression. AIC is Akaike information criterion. Sub-period γ0t γ1t γ2t γ3t R2 AIC A:1999-2001 Coefficient 0.054*** -0.001 0.005*** 0.28 47% -8.95 S(γjt) 0.003 0.004 0.002 0.23 t-Statistic 3.48 (0.001) -0.33 (0.74) 3.05 (0.003) 1.22 (0.22) B:2002-2004 Coefficient -0.0056*** 0.0008 -0.011*** 0.231 86% -9.24 S(γjt) 0.0016 0.0030 0.0014 0.224 t-Statistic -3.60 (0.000) 0.27 (0.785) -7.83 (0.000) 1.03 (0.302) C:2005-2007 Coefficient 0.05*** -0.04*** 0.02*** 0.33 40% -8.24 S(γjt) 0.003 0.005 0.002 0.239 t-Statistic 20.49 (0.000) -8.70 (0.000) 6.53 (0.000) 1.40 (0.163)
Table 6 Average Returns, Post-Ranking betas and Average Size for Portfolios Formed on Size and then betas: July 2000 to July 2007
Portfolios are formed annually based on the 346 stocks. The breakpoints for the size are determined in January of year t (t=2000-2007) with approximately the same number of stocks. Each size decile is equally subdivided into five beta portfolios using pre-ranking betas of individual stocks which estimated with 24 monthly returns ending in June of year t.
The following twelve month returns for the 25 portfolios are then calculated using equal weights. The average return is the time-series average of the monthly equal-weighted portfolio returns, in percent. The average size of a portfolio is the time-series average of monthly average of ln (ME) for stocks in the portfolio. ME (value of all tradable shares) is denominated in millions of
RMB.
All the columns show statistics for equal-weighted size-decile (ME) portfolios. All the rows show statistics for equal-weighted portfolios of the stocks in each beta group.
Panel A: Average Monthly Return (in Percent)
All Small beta Large beta
All 0.24 0.35 0.39 0.23 0.08 Small-ME -0.04 -0.20 0.04 -0.05 0.06 -0.05 0.04 0.06 0.13 0.21 0.10 -0.30 0.25 0.46 0.36 0.42 0.22 -0.20 0.42 0.35 0.60 0.78 -0.11 0.46 Large-ME 0.62 0.52 0.63 0.59 0.88 0.48
Panel B : Average Size (ln (ME))
All 7.93 7.89 7.97 7.84 7.89 Small-ME 7.06 7.05 7.09 7.02 7.04 7.09 7.53 7.55 7.50 7.55 7.53 7.53 7.82 7.82 7.83 7.79 7.83 7.84 8.19 8.18 8.19 8.23 8.20 8.14 Large-ME 8.92 9.05 8.83 9.27 8.61 8.83
Panel C: Pre-Ranking betas
All 0.54 0.82 1.00 1.22 1.70 Small-ME 1.06 0.61 0.86 1.03 1.20 1.61 1.04 0.56 0.82 1.02 1.21 1.59 1.03 0.46 0.78 1.01 1.24 1.67 1.08 0.62 0.85 0.96 1.23 1.72 Large-ME 1.07 0.46 0.80 0.98 1.21 1.89
returns of big size firm are much higher than those of small size firms which are contradictions of the argument of Fama and French (1992a).
Table 7 this table shows the summary results (mean and std) of average returns of the six portfolios (S/L, S/M, S/H, B/L, B/M, B/H) S/L S/M S/H B/L B/M B/H Mean 0.51% 0.77% 0.85% 0.43% 0.82% 0.91% Median -0.08% 0.31% -0.26% -1.24% 0.04% -0.61% Maximum 27.81% 32.12% 32.55% 23.58% 29.82% 35.72% Minimum -19.57% -18.98% -18.89% -17.15% -16.71% -12.71% Std. Dev. 0.095 0.092 0.088 0.083 0.082 0.084 Skewness 0.49 0.69 0.76 0.76 0.76 1.08 Kurtosis 3.13 3.92 4.13 3.38 3.87 5.08 Jarque-Bera 4.42 12.40 16.04 11.08 13.94 40.51 n 108 108 108 108 108 108
The major tests of the three factor model are documented in table 8. For each period, the table shows: S.D, the standard deviation of the month-by-month coefficients of determination; R2; AIC, which refers to Akaike info criterion. After observing table 8, we can find that all the signs of s are negative. It confirm the conclusion of table 6 that the firm size and average returns are positive related. In addition, the coefficient of SMB of sup-period C is significant at the level of 1%. In that case, we can not reject hypothesis (IV) of the three factor model which says that Firm size has explanatory power in the cross-section of average stock returns.
Meanwhile, the coefficient of HML for the sub-period B is significant at the level of 5% and that of for the sub-period C is almost significant at the level of 10%. So, the hypothesis (V) which says that Book to market equity has significant power in explaining the cross-section of average stock returns can not be rejected.
We can also easily find that the R2s are increasing stability form 13% in sub-period A to
asset pricing model performs better than Fama and French three factor model in Shanghai Stock Exchange.
Table 8 FF model regression coefficients and tests
This table shows results (coefficients and t values) from regressing Rpt − Rf = a + b (RMt − Rf ) + s (SMBt ) + h (HMLt ) +εpt, for the period from 1999 to 2007.
sub-period a b s h R2 AIC A:1999-2001 Coefficient -0.01 0.28 -0.62 -0.43 13% -2.60 S.D 0.01 0.21 0.48 0.32 t-Statistic (Prob.) -1.18 (0.248) 1.38 (0.176) -1.28 (0.210) -1.35 (0.185) B:2002-2004 Coefficient -0.03** 0.03 -0.27 -0.83** 19% -2.49 S.D 0.013 0.2 0.189 0.402 t-Statistic (Prob.) -2.30 (0.03) 0.13 (0.90) -1.44 (0.16) -2.08 (0.05) C:2005-2007 Coefficient -0.002 0.31 -1.16*** 0.94 29% -1.72 S.D 0.03 0.19 0.45 0.60 t-Statistic (Prob.) -0.14 (0.89) 1.65 (0.11) -2.58 (0.01) 1.58 (0.12)
Notes:* is significant at a level of at least 10%, ** is significant at a level of at least 5% and *** is significant at a level of at least 1%.
Wald Test is processed to test hypotheses this conclusion futher. The Wald test is a statistical test, typically used to test whether an effect exists or not. In other words, it tests whether an independent variable has an additional statistically power relative to a model excluding this variable.
Two hypotheses should be defined for Wald Test:
(VII) The two additional factors, SMBt and HMLt, have no significant relationship with average stock returns in regression (8).
The result of Wald Test is showed in table 9. The probabilities for all the Sub-period of CAPM are significant at a level of 1% which indicate that hypothesis (VI) is strongly rejected. The probability of Fama and French three factor model for sub-period A is not significant. However, the probabilities for sub-period B and C are significant. What is more, the value of probabilities are decreasing form sub-period A to C. Even through for the whole period, we can not reject the hypothesis (VII) which says the two additional factors, SMBt and HMLt, have no significant relationship with average stock returns in regression (8). It is obviously that capital asset pricing model performs better than Fama and French three factor model in Shanghai Stock Exchange not only for each sub-period but also for the whole research period.
Table 9 The results of Wald Test
Probability of sub-period
Test Statistic A: 1999-2001 B: 2002-2004 C: 2005-2007
CAPM FF model CAPM FF model CAPM FF model
F-statistic 0.004*** 0.231 0.000*** 0.044** 0.000*** 0.019**
Chi-square 0.003*** 0.215 0.000*** 0.032** 0.000*** 0.011** Notes:* is significant at a level of at least 10%, ** is significant at a level of at least 5% and *** is significant at a level of at least 1%.
5 Conclusion and Discuss
It is important to study what factors determine the Chinese stock returns. Since we usually use the research results found in the mature capital markets such as the U.S. markets, this research also offers a benefit of testing the robustness of the important asset pricing factors using emerging market data.
International. The history of Shanghai Stock Exchange is only 15 years and my research period extends from 1999 to 2007.
I find some relations between firm size and average stock returns as well as book-to- market value and average stock returns in the overall Shanghai Stock Exchange. What is more, the average returns increase significantly as the book to market value increasing. These are consistent with results found in other equity markets. However, there are several results contradictions of pervious empirical results.
First, it appears that the average returns of big firms are much higher than those of small firms in both up and down market which is contradictions of the argument of Fama and French (1992). Second, after comparing the value Akaike info criterion, Wald Test is processed. We can observe a significant increasing trend of the R squares of three factor model. What is more, the values of Akaike info criterion of CAPM regression are much lower than those of three factor model. These findings indicate that Market β has significant power in explaining the cross-section of average stock returns in Shanghai Stock Exchange. Furthermore, according to the results of Wald Test, we can the Fama and French three factor model does not add additional explanation power to the capital asset pricing model in Shanghai Stock Exchange from 1999 to 2007. In other words, the Chinese stock market is strongly captured by systematic risk as measured by beta. The results are consistent across sub-periods, which suggest that the results are not driven by extreme observations or the abnormal return behavior in some of the months.
The history of mainland China’s capital markets is much shorter than many of the developed countries. We can say the markets are still speculative. In this paper, the evidence implies that the book-to-market variable is not very useful in explaining the cross-section of average stock returns. The size effect, however, is very useful for the Chinese stocks.
the Chinese stock market is much sensitive to the government policy especial in the beginning of years. For example, if there is good news for stock market, all the stocks will increase dramatically while if there is bad news, all the stocks will decrease considerably. So it is seemed that the institutional effect is the dominant factor for the Chinese stock market. It is one of a systemic risk which refers to the movements of the whole economy. Even if the investors have a perfectly diversified portfolio there is some risk that they cannot avoid.
In this paper, Shanghai Exchange Stock is the only one stock market I examine. As the market become maturing, futher study is required to test both Shanghai and Shenzhen Exchange Stock and a longer research period can be chosen.
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