BACHELOR THESIS
BSc Economics and Business
Bachelor Specialization Finance and Organization
APPLICABILITY OF THE FAMA-FRENCH
THREE-FACTOR MODEL IN EMERGING
MARKETS
Author: J. Kok
Student Number: 10721754
Thesis Supervisor: Mr R.C. Sperna Weiland MSc Date of Publication: June 2018
ABSTRACT
This thesis analyzes the applicability of the Fama and French Three-Factor Model on emerging markets for the 2011 – 2017 period. The hypothesis is that the model is less applicable due to absence of perfect market integration. This hypothesis will be tested with the Fama and Macbeth double-pass method, consisting of a time-series regression and a cross-section regression. The result is that it cannot be concluded that the Three-Factor model is applicable in emerging markets, because every sample has an invalidity on a certain point in the analysis.
JEL classification: G12; G15
Keywords: Asset pricing; Factor models, Emerging Markets
STATEMENT OF ORIGINALITY
This document is written by Student Joey Kok, 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.
TABLE OF CONTENTS
ABSTRACT ... 2
TABLE OF CONTENTS ... 3
LIST OF TABLES ... 4
CHAPTER 1 Introduction ... 5
1.1 Background ... 5
1.2 Methodology ... 5
1.3 Main Results ... 5
1.4 Contribution ... 5
1.5 Thesis Composition ... 6
CHAPTER 2 Theoretical Framework ... 7
2.1 Capital Asset Pricing Model ... 7
2.1.1 Introducing the Capital Asset Pricing Model ... 7
2.2 Multifactor Model ... 7
2.3 Asset Pricing in Emerging Markets... 8
CHAPTER 3 Data and Variables ... 10
3.1 Data ... 10
3.2 Explanatory Variables ... 10
3.2.1 Summary Statistics Variables ... 10
3.3 Portfolios ... 11
CHAPTER 4 Methodology ... 14
Chapter 5 Results ... 15
5.1 Summary statistics 25 size-B/M portfolios. ... 15
5.2 Time-series results ... 15
5.3 Cross-sectional Results ... 23
Chapter 6 Summary and Conclusion ... 24
Chapter 7 Discussion and Future Research ... 25
LIST OF TABLES
TABLE 1: Summary statistics for explanatory returns 10
TABLE 2: Descriptive statistics stock portfolios formed on size and B/M ratio
TABLE 2a China 11
TABLE 2b South Korea 12
TABLE 2c Taiwan 12
TABLE 2d India 12
TABLE 3: Summary statistics for the 25 size-B/M portfolios
TABLE 3a China 15
TABLE 3b South Korea 15
TABLE 3c Taiwan 16
TABLE 3d India 16
TABLE 4: Results from time-series regressions of the 5x5 portfolios per country.
TABLE 2a China 17
TABLE 2b South Korea 18
TABLE 2c Taiwan 19
TABLE 2d India 20
CHAPTER 1 Introduction
1.1 Background
The Fama and French three-factor model is a fundamental model in asset pricing. Asset pricing models are widely tested in developed markets (Black, Jensen and Scholes, 1972; Fama and Macbeth, 1973; Harvey, 1991; Fama and French, 1998). However, the applicability of the models is not widely tested in emerging markets (Harvey, 1995). These emerging markets are still developing and not yet integrated. The lack of integration may affect the applicability of asset pricing models (Bekaert, 1995). The following research question is formed to check this statement:
Is the Fama and French three-factor model applicable in emerging stock markets for the 2011 – 2017 period?
1.2 Methodology
In this thesis an empirical method is used to test whether the Fama and French three-factor model (1992) is applicable in emerging markets over the 2011 – 2017 period. The four biggest emerging markets are tested; China, South Korea, Taiwan, and India. The data is obtained through DataStream. Using the returns, market capitalizations, and book-to-market ratios, the Fama and French factors and 25 portfolios are constructed following their original research (1992).
To test the applicability the double-pass method proposed by Fama and Macbeth (1972). First, a time-series regression will be conducted, followed by a cross-sectional regression.
1.3 Main Results
This thesis finds that there is not enough evidence regarding the applicability of the Fama and French Three-Factor model in emerging markets. Every analyzed market has an invalidity on a certain point in the analysis. Thus, it cannot be concluded that the model is applicable in emerging markets.
1.4 Contribution
This thesis contributes to the existing literature in the following way. First, relevant literature about the Fama and French three-factor model and its applicability in different markets is summarized. Second, this thesis extends the existing knowledge on its applicability by applying the model on more recent periods and different markets. Most of the literature covers outdated periods and developed markets. Therefore, it would be interesting to see whether the Fama and French three factor model is applicable in more recent periods, and increasingly important, emerging markets.
1.5 Thesis Composition
The structure of the thesis is as follows. The next chapter reviews the theoretical background of this thesis. In chapter three, the data, and the formation of the variables and portfolios are discussed. Chapter 4 is the methodology section, where the research method is given. In chapter five the results are discussed, followed by a conclusion in chapter 6. This thesis ends with providing its limitations and giving recommendations for future research.
CHAPTER 2 Theoretical Framework
2.1 Capital Asset Pricing Model
2.1.1 Introducing the Capital Asset Pricing Model
The foundation of asset pricing models was laid by Markowitz (1952). He introduced the Modern Portfolio Theory, which describes how investors can select an optimal portfolio given their
preferences for risk and return. This portfolio 1) maximizes the expected return at a given variance, and 2) minimizes the variance at a given expected return. An investor can create an optimal portfolio by selecting assets which are not perfectly correlated; thereby eliminating the idiosyncratic risk. Tobin (1958) build on the theory by considering the combination of risky securities with risk-free investment. He states that a second stage could be added to the portfolio selection. After constructing a portfolio, investors could choose their ideal exposure to risk by investing a certain ratio in the portfolio and the risk-free asset.
In the 1960’s a new model was developed by Sharpe (1964) and Lintner (1965). They expanded the Modern Portfolio Theory by adding two key assumptions:
1) Investors have the same expectations regarding the volatilities, correlations, and expected returns of assets.
2) Investors can borrow and lend at the risk-free interest rate, regardless of the amount borrowed or lend.
Their model, called the Capital Asset Pricing Model (CAPM), describes a linear relation between risk and expected return. The CAPM calculates the expected return based upon the risk-free rate and a risk premium, which is the asset’s correlation with the market (beta) times the market risk premium. The general formula of the CAPM is as follows:
𝐸𝐸(𝑅𝑅𝑖𝑖) = 𝑅𝑅𝑓𝑓+ 𝛽𝛽𝑖𝑖�𝐸𝐸(𝑅𝑅𝑚𝑚) − 𝑅𝑅𝑓𝑓� + 𝜀𝜀𝑖𝑖 (1)
Where 𝐸𝐸(𝑅𝑅𝑖𝑖) is the expected return of an individual asset, 𝑅𝑅𝑓𝑓 is the risk-free rate of return, 𝛽𝛽𝑖𝑖 is the beta coefficient of an individual stock, and 𝐸𝐸(𝑅𝑅𝑚𝑚) is the expected return of the market portfolio.
2.2 Multifactor Model
Several researchers found other factors to be significant in explaining the expected returns. Banz (1981) identified a size effect. He analyzed the relationship between the expected return and the market capitalization at the New York Stock Exchange. He came to the conclusion that smaller firms,
earned significant higher returns than bigger companies. Another effect found to be significant is the value effect. Stattman (1980) and Rosenberg, Reid, and Lanstein (1985) found a positive relation between expected returns and a firms’ book-to-market ratio for U.S. stocks. Meaning that value stocks have a higher expected return than growth stocks. Chan, Hamao, and Lakonishok (1991) found that the value effect to be significant in the Japanese market as well.
The size- and value effect have been tested by Fama and French (1992). They concluded that the size- and value factor helped explaining the average returns. They found a negative relation between the firms’ size and its average return, and a strong positive relation between the book-to-market ratio and the average return. Fama and French added the two factors to the CAPM and proposed a three-factor model to explain the U.S. average returns:
𝑅𝑅𝑖𝑖 = 𝛼𝛼 + 𝑅𝑅𝑓𝑓+ 𝛽𝛽𝑖𝑖�𝑅𝑅𝑚𝑚− 𝑅𝑅𝑓𝑓� + 𝑏𝑏𝑠𝑠∗ 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝑏𝑏𝑣𝑣∗ 𝐻𝐻𝑆𝑆𝐻𝐻 + 𝜀𝜀𝑖𝑖
Where 𝐸𝐸(𝑅𝑅𝑖𝑖) is the expected return of an individual asset, 𝑅𝑅𝑓𝑓 is the risk-free rate of return, 𝛽𝛽𝑖𝑖 is the beta coefficient of an individual stock, 𝐸𝐸(𝑅𝑅𝑚𝑚) is the expected return of the market portfolio, 𝑆𝑆𝑆𝑆𝑆𝑆 is the difference between the returns of diversified portfolios of small stocks and big stocks, and HML is the difference between the returns of diversified portfolios of value stocks and growth stocks.
2.3 Asset Pricing in Emerging Markets
One of the assumptions of asset pricing models is the assumption of perfect capital markets. This implies that markets are completely integrated. However, markets are not completely integrated according to Bekaert (1995). He mentions that investors face three kind of barriers when investing in emerging markets. First, there are direct barriers. For example, restrictions on foreign ownership. This means that foreign investors have a different legal status, and for example, are excluded from owning stocks in certain sectors. Other examples of direct barriers are taxes on dividends and capital gains, or minimum investment periods. Second, there are indirect barriers, arising from differences in regulatory and accounting environment. Third, barriers consisting of emerging-market-specific risks (EMSRS). These risks discourage foreign investment and result in de facto segmentation. Examples of EMSRS are liquidity risk, political risk, economic policy risk, macro-economic instability, and currency risk.
The lack of market integration might result in less applicability of the asset pricing models. Harvey (1991, 1995) has tested the CAPM in both developed and emerging markets. He found that CAPM is able to predict returns in developed markets, but not in emerging markets. However, Harvey (1995) used world factors in his estimations, while Griffin (2002) found that domestic models
perform better than world models. This is contrary to Fama and French (1998) who argue that a global model result in lower intercepts and higher 𝑅𝑅2. Therefore, it would be interesting to analyze whether the Fama and French three-factor model is applicable in emerging markets using domestic factors. Resulting in the following research question:
Is the Fama and French three-factor model applicable in emerging stock markets for the 2011 – 2017 period?
CHAPTER 3 Data and Variables
3.1 Data
In this research the four biggest emerging markets were analyzed. These markets were chosen based on their weight in the Morgan Stanley Capital International (MSCI) indices. MSCI constructs multiple indices based on its classification of countries. It classifies countries in three markets: developed markets, emerging markets, and frontier markets. The chosen emerging markets are China (31.74%), South Korea (15.36%), Taiwan (11.65%) and India (8.48%) (MSCI, 2018). The data consists of monthly data covering prices of the indices and stocks, market capitalization of the companies, and their market-to-book values obtained from DataStream. The sample spans the period from July 2010 – December 2017. Stocks with missing values or negative B/M ratios were removed from the sample in the respective year. All returns are in local currency to prevent currency risk, one of the barriers mentioned by Bekaert (1995). The monthly excess returns are returns in excess of the one-month Treasury bill rates of the respective country.
3.2 Explanatory Variables
For the construction of the variables the method described in Fama and French (1992) was closely followed.
First, six portfolios of stocks were sorted on size (market capitalization) and value (book-to-market ratio). For each year t, the (book-to-market cap of December of t-1 was used to split the sample in half. Stocks above the median form the big portfolio (B) and the stocks below the median form the small portfolio (S). Subsequently, the stocks in those portfolios were sorted by B/M ratio using the value in July of t. Next, the portfolios were split in three, creating 2x3 portfolios. This was done in a 30%, 40%, 30% ratio. The stocks in the lowest 30% form the low group (L), those in the middle 40% form the medium group (M), and finally, those in the highest 30% form the high group (H). This results in six portfolios ordered by size and value – SL, SM, SH, BL, BM, and BH. Secondly, the value-weighted returns of these portfolios are calculated for year t. The previous explained steps were followed for all years t in the sample period. Finally, the returns of the small companies are averaged, as well as the returns of the big companies. The average returns for the big companies were subtracted from the small companies to construct the Small-Minus-Big (SMB) explanatory variable. The High-Minus-Low (HML) explanatory variable was formed using the same method. The average returns of the low book-to-market firms were subtracted from the average returns of the high book-to-market firms.
3.2.1 Summary Statistics Variables
The equity premiums, the average difference between the market returns and risk-free rate, are small to medium (Table 1). However, the estimates are imprecise, as mentioned in previous research
(Fama and French, 2012). A size premium can be observed in Taiwan, 1.39% per month (t=1.06), and India, 0,89% per month (t=2,56). In addition, there are value premiums in all nations except China. The average HML in these countries range from 0,73% per month (t=3,96) in Taiwan to 1,76% per month (t=1,80).
Table 1
Summary statistics for explanatory returns: July 2010 – December 2017.
National portfolios are examined. Portfolios are formed at the start of July of each year at t by sorting stocks into two market cap and three book-to-market equity (B/M) groups. The median market cap is used as breakpoint for the market cap, resulting in an 50% split. The B/M breakpoints are the 30th and 70th percentile. The independent 2x3 sorts on size and B/M produces six value-weight portfolios; SL, SM, SH, BL, BM, BH, where S and B stand for small or big and L, M, and H stand for low, medium, or high. Returns are in local currency. Market is the return on a nation’s value-weight market portfolio minus the national one-month T-bill rate. Mean and Std. Dev are the mean and standard deviation of return, and t-mean is the ratio of mean to its standard error.
3.3 Portfolios
For the construction of the portfolios the method described in Fama and French (1992) was closely followed.
At the start of July of each year, 5x5 portfolios are constructed on size and B/M-ratio for each country. The size breakpoints for each country are the 3rd, 7th, 13th, and 25th percentiles of the
regions aggregate market capitalization. The B/M breakpoints are at the quintiles. The 25 value-weight size-B/M portfolios per country are formed at the intersections
.
Table 2 shows that the portfolios in the smallest quintiles have the most stocks for all countries except China. Although the portfolios with the smallest stocks consist of the most stocks, they account for just between 0,26% and 0,77%. Contrasting, the portfolios with the biggest stocks account for between 66% and 82%.
Table 2 also shows a decrease in the average number of firms in a portfolio and in the average of market value as the B/M ratio increases, for all countries except China. For the biggest Chinese portfolios the inverse is true; as the B/M ratio increases, the average number of firms in the portfolio increases as well as the average annual market value.
Table 2
Descriptive statistics for 25 stock portfolios formed on size and B/M ratio. The tables are ordered in the following way: (2a) China; (2b) South Korea; (2c) Taiwan; and (2d) India.
The 25 size-B/M stock portfolios are formed as follows. Each year t quintile breakpoints for size, measured at July, are used to allocate the stocks to size quintiles. Simultaneously, quintile breakpoints for B/M ratio are used to allocate the stocks to B/M quintiles. The breakpoints are the 3rd, 7th, 13th and 25th percentile of the market cap, as well as the 20th, 40th , 60th, and 80th percentile of the B/M-ratioThe 25 portfolios are formed at the intersections of these quintiles.
The descriptive statistics are computed every year t when the portfolios are formed, and are then averaged across all years t.
2b South Korea
2c Taiwan 2d India
CHAPTER 4 Methodology
The methodology chapter explains the method that is used to test the applicability of the Fama and French Factors (1992). In this thesis the Fama and Macbeth (1973) double-pass method will be used. The steps of this method will be discussed below.
First, Fama and Macbeth calculate individual betas and group stocks in portfolios. However, in this research the portfolios were not grouped based on their betas. Instead, the portfolios will be formed based on the size- and B/M quintiles, as described in the previous chapter.
The second step of the double-pass method is to calculate the coefficients of the factors. A time-series regression is used to obtain the alpha’s, beta’s, s’s and h’s:
𝑅𝑅
𝑖𝑖− 𝑅𝑅
𝑓𝑓= 𝛼𝛼 + 𝑏𝑏
𝑖𝑖�𝑅𝑅
𝑚𝑚− 𝑅𝑅
𝑓𝑓� + 𝑠𝑠
𝑖𝑖∗ 𝑆𝑆𝑆𝑆𝑆𝑆 + ℎ
𝑖𝑖∗ 𝐻𝐻𝑆𝑆𝐻𝐻 + 𝑒𝑒
𝑖𝑖The third step is to use a cross-section regression to calculate the gammas. The excess returns of the portfolios are regressed on the a’s, b’s, s’s and h’s calculated in the previous regressions.
𝑅𝑅�
𝑖𝑖− 𝑅𝑅
𝑓𝑓= 𝛾𝛾
0+ 𝛾𝛾
1𝑏𝑏
� + 𝛾𝛾
𝚤𝚤 2𝑠𝑠
� + 𝛾𝛾
𝚤𝚤 3ℎ�
𝑖𝑖+ 𝑒𝑒
𝑖𝑖If the model is applicable the coefficient for alpha must be close to zero, the beta coefficient should be insignificant and the SMB and HML coefficient should be significantly different from zero. This results in the following hypothesis:
H0: The Fama and French Three-Factor Model does capture cross-sectional differences in expected returns for emerging markets.
H1: The Fama and French Three-Factor Model does not capture cross-sectional differences in expected returns for emerging markets.
Chapter 5 Results
In this chapter first, the summary statistics for the 25 size-B/M portfolios per country will be discussed. Followed by the results of the time-series regressions. Finally, the cross-sectional regression results will be discussed.
5.1 Summary statistics 25 size-B/M portfolios.
Table 3a – 3d show that the average excess monthly returns increase as the B/M-ratio increases. This effect is observable across all size portfolios and across all the countries. Thus, the value effect seems to be present. A decrease in average excess monthly returns as the size increases is only found in India. In contrast, the returns of the portfolios of the other countries seem to increase as the size increases, however this is not evident. This effect is contradictory to previous research (Fama and French, 1992, 1993, 1998). According to Fama and French (1992) small stocks should outperform big stocks due to their higher levels of risk. Higher levels of risk are associated with higher standard deviations. However, the table shows increasing standard deviations for the portfolios as size increases, apart from China, where there is a negative relation between size and the standard deviations.
5.2 Time-series results
Table 4a – 4d show the results of the first-pass time-series regressions. If the models describe the expected returns as expected, the alphas should not be significantly different from zero. However, as the tables show, all the intercepts from China are significantly different from zero. Furthermore, 13 intercepts from South Korean portfolios, 3 intercepts from Taiwanese portfolios, and 4 intercepts from Indian portfolios are significantly different from zero at a 5% significance level. However, significantly different intercepts are also found in the work of Fama and French (1998). Thus, the results do not differ from previous papers.
Nevertheless, there is a result which differs from previous research. The R2 of China, Taiwan,
and India are almost all relatively high, which could be expected after analyzing previous research. However, the R2 of the South Korean portfolios are relatively low, ranging from 0.15 to 0.66. Thus,
the the model does not a good job at capturing the variation in the returns on the Indian portfolios. The betas of the portfolios are almost all below 1, except from China, where they are almost all above 1. This implies that the portfolios react less to changes in the economic environment than the market proxy. For the all the countries the size effect and value effect are evident. The SMB factor declines as the size increases and becomes negative for the last quartiles. This is in line with Fama and French (1996), which found negative SMB factors for the big portfolios. The HML factor changes from negative in the first 1 to 2 quartiles, to almost all positive in the last quartiles. This is in
line with the result of Fama and French (1996). They found that HML coefficient tend to be negative in the first quartile and positive for the other quartiles.
Table 3
Summary statistics for the 25 size-B/M portfolios. The tables are ordered in the following way: (3a) China; (3b) South Korea; (3c) Taiwan; and (3d) India.
The 25 size-B/M stock portfolios are formed as follows. Each year t quintile breakpoints for size, measured at July, are used to allocate the stocks to size quintiles. Simultaneously, quintile breakpoints for B/M ratio are used to allocate the stocks to B/M quintiles. The breakpoints are the 3rd, 7th, 13th and 25th percentile of the market cap, as well as the 20th, 40th , 60th, and 80th percentile of the B/M-ratioThe 25 portfolios are formed at the intersections of these quintiles. The table displays the means of excess returns of the portfolios, their standard deviations, as well as their t-statistic.
Table 3b South Korea
Table3d India
Table 4
Results from time-series regressions of the 5x5 portfolios per country. Portfolio excess returns was chosen as dependent variable. The excess market return, SMB factor, and HML factor were included as the independent variables. The table shows the intercepts, coefficients, and their respective t-statistics, as well as the R2
Table 4a
5.3 Cross-sectional Results
The results of the cross-sectional regression can be found in Table 5.
It can be seen that beta is not significant for China and South Korea. This means that
systematic risk, as predicted by CAPM is not able to explain average returns for these countries. This is in line with previous research. However, the beta is significant for Taiwan and India, contradicting Fama and French theory. The SMB factors are all significant. The size premium of Taiwanese
portfolios and Indian portfolios are positive, indicating that smaller firms indeed earn higher average returns. However, the Chinese SMB factor and South Korean SMB factor are negative. Implying that bigger firms earn higher average returns than smaller firms. Finally, the HML factor is positive and significant for China and South Korean positive but not significant for Taiwan, and significantly negative for India. The alphas of South Korea, Taiwan, and India are significant; thus the model can be improved for those markets.
Table 5
Results from cross-sectional regressions of the portfolio excess returns over the excess market return coefficient, SMB coefficient, and the HML coefficient.
Chapter 6 Summary and Conclusion
This thesis aims at providing evidence whether the Fama and French Three-Factor model is applicable in emerging markets. Bekaert (1995) describes three different barriers which prevent complete integration, thus violating one of the asset pricing assumptions. The absence of complete integration and the findings of Griffin (2002), who found that domestic models perform better than global models, contributed to the decision to analyze the emerging markets using domestic factors and portfolios instead of the global factors of Fama and French (1998).
To test the applicability the Fama and Macbeth double-pass method is used. The time-series regression showed that all intercepts of the Chinese portfolios were significantly different from zero, as well as some portfolios of the other nations. Both the size- and value premiums were present for all countries. However, the model was not able to capture the variation of the South Korean
portfolios, with R2 ranging from 15% to 66%.
Using a cross-section regression an insignificant intercept, but significant Beta, SMB and HML coefficients were found for the Chinese portfolios. Indicating that the model can capture the
variance of the returns of the Chinese portfolios. The value and size effect are also present in the South Korean sample; however, the positive, and significant alpha indicates that the model could be improved. Taiwan and India have significant betas, thus not passing the hypothesis.
Considering the significant alphas of the Chinese portfolios in the time series regression, the low R2 of the South Korean portfolios, and the significant gammas of Taiwan and India in the
cross-section regression, the conclusion cannot be drawn that the Fama and French Three-Factor model is applicable in the emerging stock markets.
Chapter 7 Discussion and Future Research
One of the main limitations is the low number of average firms in some of the big portfolios. This is due high difference between the market caps of the biggest companies in a sample and the rest. However, using different breakpoints might result in more companies per portfolio and probably an increase in the precision of the estimation.
Second, a comparison could be made between global and domestic factors. Griffin found a that domestic factors work better for developed markets, but this might not be true for emerging markets.
Third, the sample period could be increased or using a higher frequency of observations, which likely results in lower standard deviations, and thus more precise estimations.
