Fama French Three Factor Model: A Study of Nifty Fifty Companies

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1 Proceedings of International Conference on Strategies in Volatile and Uncertain Environment for Emerging Markets July 14-15, 2017 Indian Institute of Technology Delhi, New Delhi pp Fama French Three Factor Model: A Study of Nifty Fifty Companies Deeksha Arora 1 and Divya Verma Gakhar 2 Abstract The study aims to explore the applicability of the widely used asset pricing models, namely, Capital Asset Pricing Model (CAPM) and the Fama French Three Factor Model in the Indian equity market. The study has been conducted on the companies that form part of the Nifty fifty index for a period of five years 2011 to The asset pricing model is examined by forming portfolios on the basis of two variables market capitalization (size effect) and book-to-market equity ratio (value effect).the results suggest that Fama French three factor model performs better when compared with CAPM in explaining average stock returns. Thus, the study provides a substantiation of the presence of the Fama French three-factor model in elucidation of the variations in the stock returns. This study may provide a basis for future research in the generalized asset pricing model comprising of multiple risk factors. Keywords: Book-to-market equity, Fama French three factor Model, Market Capitalization, Size effect, Value effect. 1. Introduction The risk and return relationship is explained by the Asset Pricing Models. Sharpe (1964) developed the Single Index Model which explains that market return is the only and sufficient factor to explain differences in returns of the stocks. The model also suggests that the security or portfolio risk can be segregated into two parts, namely, systematic risk and unsystematic risk. These two risks are also called non-diversifiable risk and diversifiable risk respectively. Unsystematic risk is the security specific risk and can be reduced by diversification whereas Systematic risk is associated with overall movements in the general market and thus cannot be eliminated. Sharpe (1964), Lintner (1965) and Mossin (1966) autonomously developed a model known as the Capital Asset Pricing Model (CAPM) which is based on Single Index Model. The Capital Asset Pricing Model (CAPM) explains the association between the expected rate of return of a security and its systematic risk which is measured through beta. Following the development of Single Index Model and CAPM, many empirical researchers have found that there are influences beyond the market that cause stocks prices to move together and this laid to the development of multifactor models. 1. PhD Research Scholar, University School of Management Studies, Guru Gobind Singh Indraprastha University deeksha.arora18@gmail.com 2. Assistant Professor, University School of Management Studies Guru Gobind Singh Indraprastha University divya.ipu@gmail.com

2 Fama French Three Factor Model: A Study of Nifty Fifty Companies 2. Literature Review Fama and French (1992) explained the role of the two variables, namely, size and book tomarket equity in explanation of the stock returns. Both the variables were found to be significant. Hence, Fama and French (1993) developed a three factor asset pricing model by including these two variables along with the systematic risk component (i.e. CAPM beta). They used a time-series regression approach. It was found that the excess market return contains some information about the average stock returns and the amalgamation of size (market capitalization) and book-to-market (BE/ME) imbibes the role of leverage and earning yield in average stock returns. Yang and Xu (2006) conducted a study on Chinese stock market and tested the applicability of CAPM. It was found that the expected returns and beta hold a linear relationship. But the slope and intercept terms were found to be insignificant. Thus, there was no evidence of the applicability of CAPM in the Chinese Stock market. Michailidis et al. (2006) conducted the applicability of CAPM in Greek Securities Market and they found evidence against the applicability of CAPM. Kumar and Gupta (2009) studied the effectiveness of Fama and French Three Factor Model in Indian Stock market. It was found that the Indian equity market bears size and value effect strongly. Cakici et al. (2013) undertook the study of few of the economies that are emerging. Their study revealed that the ratio of the book-to-market equity is an extremely vital factor in explaining the stock returns and thus, cannot be ignored in the area of asset pricing. However, there are evidences that the three factor model does not completely elucidate the deviations in returns with respect to the two variables, namely, investment and profitability. Novy (2013) revealed that not only book-to-market ratio but the gross profitability also had the similar strength in elucidation of the variation in average stock returns. Hou et al. (2015) suggested that apart from the two variables -market capitalization and book to market ratio, investment and profitability also play a vital role in explaining stock return variation. Singh and Yadav (2015) did a comparative study of the three asset pricing models, namely, Capital Asset Pricing Model (CAPM), the Fama and French three factor model (1993) and the Fama and French five factor model (2015) in the Indian stock market. The sample size of their research are the companies that are listed in the CNX Nifty 500 index. The three factor model was found to be better than the Capital Asset Pricing Model. However, the five factor model performed better than the other models when investment was also considered for portfolio formation. 3. Objective/s The study aims to test whether there is a considerable size effect and value effect in Indian stock returns. The study also analyses whether Fama-French three-factor model is a better model in the Indian context as compared to Single Factor Model. 4. Data and Research Methodology The study has been done on the companies that form part of the on the Nifty Fifty Index as on 31st March However complete data of only thirty seven companies could be obtained. The study covers a time period of 5 years ( ). We have considered only those companies whose March closing data was available. The adjusted closing price data for the sample companies is obtained from the Prowess (database of Center for Monitoring Indian Economy). 91 day Treasury bills rate is obtained from the central bank, Reserve Bank of India, website which is a proxy for the risk free rate. The time series data of share prices was used to construct monthly return series. The CNX Nifty 500 index returns has been used as the proxy for return on market. 673

3 Deeksha Arora and Divya Verma Gakhar The variables are described as follows (Fama and French (1993)): Market capitalization: this is calculated by multiplying the outstanding shares (number) and the market value (adjusted closing price per share). Both the vlues to be taken as on September end each year, say year t. Book to market equity: this is calculated by dividing book equity by market equity (Book value and market value per equity share). Both the values to be taken as on March end each year, say year t. Market factor: Market factor refers to the coefficient of risk premium that is (Rm- Rf). It is obtained by regressing assets excess return with Risk Premium. Return: Return as been calculated using the formula [P(t)/ P(t-1)] -1 Where-, R (t): Return of security at time t, P(t) : Month (t) end price of security P(t-1): Month (t-1) end price of security The methodology includes calculating monthly returns which are equally weighted for each portfolio from October (year t) to September (year t+1). In this way, a time series of 60 (5 years X 12 months) monthly returns for each portfolio is obtained. We have taken a time interval of two quarters from the accounting year end (March) to the date of creation of the portfolio (September). We took a lag of two quarters because the firms have a time period of six months to publish their accounting data from the end of accounting year. Thus, the accounting figures are expected to be known by September end. 4.1 Methodology used to Create Size Portfolios Size portfolios have been created on the basis of the market capitalization at September end each year from 2011 to The sample companies are arranged in descending order of their size. After that, the sample is divided into two groups based on the median value as breakpoint. The bottom 50% is called Small and the top 50% is termed as Big. This leads to the creation of two size portfolios of stocks falling under each group namely Small and Big named as Sand B respectively. 4.2 Methodology used to Create Value Portfolios Value portfolios have been calculated in March end depending upon the BE/ME ratio. The sample companies stock are filtered in descending order based on their value. Then, three value portfolios are created in the following manner- Low (bottom 30%), Medium (middle 40%) and High (top 30%).. Thus, three value portfolios are obtained falling under three groups namely Low, Medium, and High named as L, M, and H. 4.3 Calculate Size and Value Portfolio Return Six portfolios are created from the combination of two groups based on size and three groups based on BE/ME ratio and are named as S/L, S/M, S/H, B/L, B/M, and B/H. After calculating these portfolios, equally weighted returns are calculated for the six portfolios for each month starting from October 2011 till September The portfolios are formed again every year in September end. 4.4 Size and Value Factors Return After calculating the portfolio returns, the next step is to calculate the size and value factor returns namely SMB and HML as stated by the Fama- French Model. The market factor has been calculated as (Rm Rf). The SMB factor return is the arithmetic mean of the return on 674

4 Fama French Three Factor Model: A Study of Nifty Fifty Companies three small size portfolio i.e. average of (S/L, S/M, & S/H) minus the average of return on three big size portfolios i.e.(average of (B/L, B/M, B/H)).These returns are computed every month over a period of 12 months after the portfolio formation. The process was replicated until the portfolios were reconstructed. Similarly, HML is calculated as: (S/H+ B/H)/2 - (S/L+ B/L)/ Examination of Explanatory Factors of Returns Time series regression is run to examine whether different risk factors, individually and/or collectively, capture variations in returns. For this purpose, the time series regression equations used are listed below in equations: Regression using market factor (Rm Rf) as explanatory variable (the Single Index Model). Rp-Rf= c + b(rm-rf) + e b. Regression using SMB and HML as explanatory factors. Rp-Rf= c + s(smb) + h(hml) + e c. Regression using market and SMB as explanatory factors. Rp-Rf= c + b (Rm-Rf) + s(smb) + e d. Regression using market and HML as explanatory factors. Rp-Rf= c + b(rm-rf) + h(hml) + e e. Regression using market, SMB and HML factors = Rp-Rf= c + b(rm-rf) + s(smb) + h(hml) + e Where: Rp is the monthly return of a portfolio. Rf is the risk free rate (monthly). Rm is the monthly return on market. SMB (Small minus Big) is the size factor. HML (High minus Low) is the BE/ ME (value) factor and b, s and h are the coefficients of the slope. 5. Analysis and Result The analysis has been done using Eviews 8. Table 1 shows the descriptive statistics of the time series data. Table1: Descriptive Statistics of the Sample (60 Observations) Table 1 shows that the mean of the excess return is highest for SH portfolio (1.17%) and lowest for the BM portfolio (0.71%). Also, the maximum excess return is 15.35% which is offered by SH portfolio and the minimum excess return is -2%. 675

5 Deeksha Arora and Divya Verma Gakhar Table 2: Correlations Coefficients MARKET SMB HML MARKET SMB HML 1 Table 2 shows that there exists significant correlation between SMB and HML i.e at 5% significance level. But there is very low degree of correlation between SMB and Market i.e Table 3: Graphs the Excess Returns Portfolio Wise 6. Testing of Significance of Explanatory Variables Before applying regression to the time series data, it is necessary to check the data for Stationarity to avoid spurious results. For this purpose, Augmented Dicky Fuller (ADF) test was applied. ADF test was applied at level and all the variables were found to be stationary. Table 5 reports the results of the regression run in five panels. The coefficients of the market factor is represented by b. The results (see Table 4) show that the market factor coefficient (b) is positive and highly significant for each of the six portfolios. The t statistics of all the beta (b) values, have also been reported and are more than 7, and P-values, as reported in the table, are not different from 0, implying statistical significance of beta in explaining cross section of expected returns. The adjusted R 2 value ranges from 17.5% to 96% for all the models for the sample portfolios. On computing the average adjusted R 2 for all the models, we found that the Fama French three factor model has the highest value (95%) followed by the model having only market and SMB as the explanatory variables (94%). Also, the model without the market factor (having only SMB and HML) has average adjusted R 2 30% reflecting that the market factor cannot ignored for determining returns. 676

6 Fama French Three Factor Model: A Study of Nifty Fifty Companies Table 4: Regression Analysis 677

7 Deeksha Arora and Divya Verma Gakhar 7. Testing of the Intercept Term (c) Table 6 shows the results of the intercept term for all the regression equation. The value of the intercept term is not found to be statistically different from 0, thereby explaining that there are other factors which need to be considered for the explaining the return generating process. Table 6: Intercept Explanatory Variable Portfolio C t(c) P-value t (c) Market, SMB and HML SL SM SH BL BM BH Conclusion and Scope The study tested the applicability of Fama- French three-factor model in elucidation of the differences in portfolio returns for a period ranging October 2011-September It was found that the Fama-French three-factor model explains the cross section of average stock returns that which the single Index model fails to address. The highest value of adjusted R 2 is seen for SH portfolio, that is, 96% for the Fama and French three factor model. We observe that overall the FF three-factor model explains the variation in cross section of stock returns in a meaningful manner. This study can be used as a base for a wider and, rational asset pricing model consisting of multiple risk factors. We have used only five year data spanning from 2011 to 2016 and only the companies that form part of nifty fifty index have been studied. Thus, research can be 678

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