Validity of Fama-French Three Factor Model for Diversified Financial Companies Listed on the Colombo Stock Exchange

This study aims to test the validity of the Fama and French Three-Factor Model (FF3FM) in explaining the cross-sectional variation in stock returns of the diversified financial companies listed on the Colombo Stock Exchange (CSE). It adopted the Fama and French (1992) approach to construct the portfolios. Accordingly, six portfolios were constructed using a 2x3 annual sorting procedure based on market capitalization and book to market equity ratio. The sample period spans for five years, from April 2014 to March 2019 and the sample is included 37 diversified financial companies listed on the CSE. The data analysis is based on both descriptive statistics and inferential statistics which are derived on correlation analysis and multiple regression analysis. The results indicate that FF3FM performs well in explaining cross-sectional variation in stock returns. All three factors of the model market risk premium, size premium, and value premium exhibit significant relations with excess portfolio returns. The study also finds that market risk premium is the most prominent factor of the model, while the other two factors share equal explanatory power. The results further confirm that FF3FM outperforms Capital Assets Pricing Model (CAPM) in explaining cross-sectional variation in stock returns. The study supports the prediction of Fama French (1992) that high BE/ME ratio portfolios outperform the portfolios with low BE/ME ratios. Considering these findings, it is recommended that, in addition to stock beta, size and value information should be made available to stock investors for conducting better assessment of uncertainties associated with investment returns.


Introduction
In general, investors expect to achieve the most appropriate trade-off between risk and returns to improve the financial investment results. Ideally, the most optimal portfolio is the one that generates the highest returns at the lowest risk level. Since the risks and returns are expected to be positively related, reaching such an optimal trading position is dilemmatic for most investors (Brigham & Houston, 2015). One of the most popular empirical models used to resolve this risk-return dilemma is the CAPM which was originally developed by Sharp (1964) and Linter (1965).
The main implication of CAPM is the linear relationship between expected return and systematic risk and it measures systematic risk based on beta (ß). Early empirical studies such as Sharp (1964), Linter (1965, and Fama and MacBeth (1973) provide evidences that support the linear relationship between expected return and systematic risk. However, several empirical studies, after the 1980s, such as Reinganum (1981), Breeden and International Journal of Accounting & Business Finance Vol.7 (Special) pp. 92 -107

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Special -2021 Litzenberger (1989), and Fama and French (1992) found evidence that Beta (ß) has very little explanatory power in explaining the returns.
To enhance the explanatory power of CAPM, Fama and French (1992) introduced FF3FM which incorporates size and value effects of stocks to the existing CAPM model. Accordingly, the model assumes that the crosssectional variation of stock return can be explained by three factors, i.e. market risk premium, size premium and value premium. Fama and French (1992)  Then, Section 6 concludes the paper with the empirical implications.

Evolution of Asset Pricing Models
The evolution of asset pricing theories was started along with the mean-variance portfolio theory introduced by Markowitz (1952). He argued that investors would tend to avoid risks and investing in diversified portfolios will help them to enjoy optimal returns. Based on Markowitz's arguments, Sharp (1964), Linter (1965, and Mossin (1966) developed the first asset pricing theory that was later called the CAPM. The theory assumes that the rate of returns on a financial asset has a linear relationship with the asset market beta. Since its introduction, researchers, such as Black, Jensen, and Scholes (1972), Fama and Macbeth (1973) and Merton (1973) Reinganum (1981), Breeden and Litzenberger (1989) also resulted in negative evidence about the validity of the market risk factor in predicting returns. As a reaction to these arguments, Fama and French (1992) introduced a new extended form of CAPM namely FF3FM.

Context
The testing of Fama and French Three Factors (FF3F) was started in 1981 when Banz (1981) investigated the relationship between firm size and expected return. In addition, Rosenberg, Reid, and Lanstein (1985) found that book-tomarket equity (BE/ME) also has the power to explain the variations in stock return.

Lankan Context
In Sri Lankan context, a very little evidence has been published on FF3FM and the results of these publications have been inconclusive at best. Samarakoon (1997) Fama and French's (1992) that "small-caphigh-value" portfolios will outperform relative "high-cap-small-value" portfolios.
Afterwards, the study conducted by

Data
The sample period covers from April 2014 to  Fama and French (1992)    Source: Fama and French (1992) Consistent with Fama and French (1992), Fama and French (1993) and Fama French (1998), it can be predicted that market return, size factor and value factor relate to excess returns of portfolios, which are hypothesized below.

Conceptualization
H1 : There is a relation between market risk premium and excess returns of portfolios.
H2 : There is a relation between SMB and excess returns of portfolios.
H3 : There is a relation between HML and excess returns of portfolios.

Operationalization of Variables
The FF3FM is specified by the equation (1) (Fama and French, 1992).

 Book-to-Market Equity Ratio
The book-to-market equity ratio (BE/ME) is

Data Analysis
Consistent with many previous studies such as Fama and Macbeth (1973), Nimal (2006), Gregory, and Nimal and Fernando (2013), the "Multiple Regression Framework" is used in this study to estimate coefficients of risk factors. In addition, this study applies a special data analysis and presentation approach adopted by Karp and Vuuren (2017)  during the study period.  Accordingly, the average excess return across the six portfolios during the sample period was 0.08. Fama and French (1992) predict that portfolios with small size and high BE/ME (S/H) stocks have the highest excess return.

Statistical Description of the Portfolios
However, the results of the present study do not confirm this prediction as the highest excess return appears to be in the portfolio with small size and medium BE/ME (S/M).
In general, higher standard deviations of the portfolios are associated with higher average excess returns. Contrary to this argument, this study finds that the portfolio with small size and low BE/ME (S/L) is associated with the highest standard deviation of excess returns (6.11%), which could be due to high volatility of stocks of low-capitalized diversified financial companies. Further, Table   2 highlights that excess returns of the portfolios are approximately normally distributed, as reflected by the average skewness value between 0.5 and 1 (moderately symmetrical) and average kurtosis value closed to one.  were outperforming the portfolios with low BE/ME, which supports the prediction of Fama and French (1992). Further, the same as the data distribution of portfolio excess returns, the distribution of explanatory variables also moderately symmetrical, as reflected by the skewness values in between -1 and +1 and the kurtosis values of around 4.   Table 5 shows the correlation coefficients between the explanatory variables. Accordingly, SMB and market risk premium are negatively correlated (ρ=-0.264). Hence, it is expected that the variation in SMB has a negative impact on the market beta estimation, which however is not consistent with the positive correlation found by Fama and French (1993). On the other hand, consistent with Fama and French (1993), the correlation between HML and SMB is negative (ρ = -0.11). Further, there is a positive correlation between HML and market risk premium (ρ = 0.458).

Regression Results of CAPM
To test the effectiveness of FF3FM over CAPM, the study tests cross-sectional variations of returns explained by market beta alone, as reflected by CAPM. Table 6 reports the regression results of the CAPM for each of the six portfolios.  (1964), Linter (1965), and Limmack and Ward (1990).  Barber and Lyon (1997) and Jackson and Patterson (2003) who documented that FF3FM performs well for financial sector companies. In addition, it is worth noting that coefficient estimates for the market risk premium for all six portfolios are positively significant at 5% level of significance, which made it to be the most prominent factor in FF3FM.  Karp and Vuuren (2017) document that the predictability of HML is low for S/L and S/M.

Removal of Insignificant Variables and Disjoint Tests
In addition to the initial regression test, the regression test was re-run by removing the insignificant variables, the results of which are summarized in Table 8. Then, following the disjoint test procedure suggested by Karp and Vuuren (2017), two additional regressions were run to find which factor of HML and SMB contributes more in explaining cross-sectional variations in stock returns. Tables 9 and 10 present the results of the disjoint tests.   French (1992), it seems that BE/ME ratio is a more powerful predictor than firm size.

Comparison between the CAPM and FF3FM
The results presented in Table 11

Portfolio Performance Evaluation
As suggested by Karp and Vuuren (2017), the performance of the portfolios is evaluated based on the values of the intercept (Jensen's Alpha), which are presented in Table 12.
Accordingly, the intercept estimates of all six portfolios are insignificant at 5 % level of significance, which support the fact that FF3FM captures a significant portion of the cross-sectional variation in stock returns.

Conclusion
As the investors are exposed to high risk when investing in stock markets, especially in frontier and emerging stock markets due to