Validation of Fama French Model in Indian Capital Market

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1 Validation of Fama French Model in Indian Capital Market Validation of Fama French Model in Indian Capital Market Asheesh Pandey 1 and Amiya Kumar Mohapatra 2 1 Professor of Finance, Fortune Institute of International Business, New Delhi, India, asheeshpandey@rediffmail.com 2 Associate Professor - Economics, Fortune Institute of International Business, New Delhi, India, amiyaeco125@gmail.com Abstract: In this paper, we evaluate the efficacy of three factor Fama French Model for Indian capital market. Using data of BSE 500 companies from July 2001 to January 2015 from CMIE Prowess we test the validity of Fama French model for Indian capital market. We check the robustness of the model in two ways: 1) by using alternative measures of size viz. market capitalization, enterprise value and total assets and 2) by dividing the total period into two sub periods, i.e. pre subprime crisis and post sub prime crisis. Controlling for size effect, we find that the three factor Fama French model totally explains the extra normal returns for the study period. Further, we find that the findings are robust for alternative size based portfolio constructions as well as for both the sub periods. Thus, we confirm that in the Indian context, both size and value factors, along with market factor have strong return explanatory power as compared to standalone Market factor. Key Words: Size Effect, Value Efect, CAPM Anomaly, Missing Factor, Fama French JEL Code: C13, C22, G11, G12 Introduction SECTION 1 Till mid-nineties, Capital Asset Pricing Model (CAPM) as developed by Sharpe (1964), Lintener (1965) and Blacket.al. (1972) was considered to be a robust model, used by both practitioners as well as academic, for finding out the relationship between equity risk and return. CAPM is used as a tool to find out prices of assets in equilibrium and is built on the tenet that market is the only relevant factor for pricing assets. However, it started losing its ground, due to researches being done to find out anomalies in the model, popularly known as CAPM Anomalies. One of the first anomaly was provided by Banz (1981) who came out with Size as a relevant risk factor to be considered apart from the market while pricing assets. Similarly, value effect was recorded by Chan et.al. (1991) and Price to Earnings effect was given by Basu (1977). 263 International Journal of Economic Research

2 Asheesh Pandey and Amiya Kumar Mohapatra Stattman (1980) and Rosenberg et.al. (1985) came out with Book Equity to Market Equity as a factor which is positively related to stock returns. Bhandari (1988) finds a positive relationship between leverage and average returns of stocks. Fama and French (1992) find a significant positive relationship between the book to market ration and stock returns and a significantly negative relationship between size and stock returns. A powerful model was introduced by Fama and French (1993) known as Three Factor Fama French Model which comprises of CAPM based market factor and two other risk factors, namely size (measured by market capitalization) and value (measured by book equity to market equity). In subsequent work, Fama French (1996) find out that through their three factor model, all the major CAPM anomalies have been explained. They also find that by using alternative definitions of size their results remain robust. Since, then a lot of empirical work has been produced both internationally as well as in India to test the Fama French three Factor model. In Indian context Connor and Sehgal (2001), Bahl(2006), Taneja (2010),Tripathi (2008), Sehgal and Balkrishnan (2013) have tested three factor Fama French Model and found it has performed better than a single factor CAPM in pricing equity. Since, sub-prime crisis, market fundamentals of both developed as well as developing economies have changed. There has been no study conducted to find out the relevance of Fama French model pre and post sub prime crisis. Further, we try to use the alternative definitions of size to test the Fama French Model. We conduct this study over a period of 14 years, i.e. from July 2001 to January 2015 with the following objectives: 1)To test the relevance of Fama French model in the Indian context over the study period 2) To check the robustness of model by using alternative measures of size; and 3) to check the strength of Fama French Model in Pre and post Sub Prime Crisis. The paper is divided into 5 sections including the present one. Data and their sources are discussed in section 2. In section 3 we describe the research methodology and the estimation procedure. The empirical results are provided in section 4 and summary and concluding remarks are given in the last section. Data and Their Sources SECTION 2 The sample consists of NSE 500 companies for a period of July 2001 to January The National Stock Exchange 500 (CNX 500) index has been used as a market proxy. It is a broad based benchmark index and represents about 96% of the free float of market capitalization of stocks listed on the National Stock Exchange (NSE) and the 500 companies are disaggregated into 73 industry indices. Monthly share prices, adjusted for stock dividends, right issues and stock splits, have been used to compute the percentage returns which are employed for further estimations. The data source is CMIE Prowess, popularly used financial software in India. In order to take risk free return we have taken implicit yields on 91 day treasury bills from the Reserve Bank of India (RBI) monthly handbook of statistics published at RBI website. The yearly information regarding market capitalization and total assets, used as a proxy for size, to form portfolios has been taken at the end of June every year for the sample period. A third proxy for size, i.e. Enterprise Value has been created by adding debt and deducting cash outstanding from the market capitalization for the sample period. In order to create Fama French value factor the information regarding yearly Price to Book Value (P/BV) has been taken at the end of March for the sample period. International Journal of Economic Research 264

3 Methodology Validation of Fama French Model in Indian Capital Market SECTION 3 We test the relevance of Fama French model for a total period, i.e. from July 2001 to January 2015 by creating double sorted portfolios based on ranking of sample securities on two company characteristics namely, size (market capitalization) and value. We further check the robustness of the model in two ways: a) by using two alternative measures of size viz. Total Assets and Enterprise Value. Stock classifications based on total assets and enterprise value were used only to check the robustness of size effect i.e by employing market as well as non- market based measures of firm size. (see Berk 1995,1996) and b) by dividing the total period into two sub periods, i.e. from July 2001 to June 2007 and July 2007 to January 2015 as demarcated by Sub Prime Crisis. The robustness check has been done in order to be sure that by using alternate definitions of size, we get the same result as well as to check the relevance of Fama French model over time. The portfolios are formed based on following procedure. Before forming portfolios, we remove penny stocks from our list. We eliminate the return observations of penny or tiny stocks which may contain data errors. Such stocks are often called as fallen angels (see Chan and Chen, 1991) which are highly speculative and have limited liquidity which can lead to price manipulations. Further, such stocks also tend to exhibit extremely large positive/negative return value. For example a movement of Rs.2 to Rs. 10 owing to a speculative pressure may result in a monthly return of 500%. Such outliers shall distort our analysis. For the reasons mentioned above, we eliminate all the stocks from the sample period with a market price of less than Rs.10. After removing the Penny stocks, in June of year (t) the sample stocks are ranked on the basis of size measure (measured as market cap()). They are then classified into two groups, i.e., small (S) bottom 50 per cent and big (B) top 50 per cent. The sample stocks are also classified into three equal groups, i.e., low (L) bottom percent, medium (M) per cent to per cent and high (H) above per cent based on Price to Book Value (PB) ratio in March of year (t). Subsequently, the ranked stocks are divided into six portfolios (S/L, S/M, S/H, B/L, B/M and B/H) from the intersection (-PB) of two market capitalization and three price to book groups. The S/L portfolio contains small and relatively more distressed stock, while B/H consists of big and relatively less distressed stock. Equally monthly returns are estimated for these portfolios for the next twelve months (July of year t to June of year t+1). The process is repeated for the total period, i.e. from July 2001 to January We call them unadjusted returns. We further check the robustness of our results by taking two more proxies for size viz. Enterprise value and Total Assets. Portfolios are ranked and constructed in a similar manner as that for market capitalization, except that the stocks are ranked in March (instead of June) each year for Total Assets measure. Further, we also test the robustness of the model by forming portfolios (in a similar manner as explained above) for two sub periods, i.e. from July 2001 to June 2007 and July 2007 to January 2015 as demarcated by the subprime crisis. Next, we evaluate if the multi-factor models as depicted by various combinations of market factor and size/ Value factor or the three factor Fama Frecnh Model provide better results in terms of asset pricing as compared to Single Factor CAPM. Tests are performed for all the three classifications of size viz. Market Capitalization, Total Assets and Enterprise Value as well as for all the periods that is Total Period, Sub Period1 and Sub Period International Journal of Economic Research

4 Asheesh Pandey and Amiya Kumar Mohapatra We start with the standard capital asset pricing model (CAPM) to evaluate if market factor is able to absorb the cross section of average returns for the sample portfolios. The familiar excess return version of market model is used to operationalize CAPM wherein excess returns are regressed on excess market returns as shown below: where, Rp t = Excess Return on sample Portfolio Rm t = Excess Return on the market factor and are the estimated parameters and e t = error term Rp t = + (Rm t ) (1) Next, we create Size and Value factors to employ multi-factor models as follow: Size Factor (SMB): The portfolio small minus big (SMB) is meant to mimic the risk factor in return relating to size. SMB is the difference between the simple average of the returns on the three small-stock portfolios and the simple average of the returns on the three big-stock portfolios. It is expressed in the form of: SMB = (((S/L) + (S/M) + (S/H)) ((B/L) + (B/M) + (B/H)))/3 Value Factor (LMH): The portfolio low minus high (LMH) is meant to mimic the risk factor in return relating to value and LMH is the difference between the simple average of the returns on the two high P/B portfolios (S/H and B/H) and the average returns on the two low P/B portfolios (S/L and B/L). LMH is expressed in the way of: LMH = (((S/L) + (B/L) ((S/H) + (B/H)))/2 Any multicollinearity problem is sorted out before introducing these factors in the F-F framework. After evaluating Single Factor Model, we examined the multi-factor models by using pairwise combinations of markets, Size and value factors and finally the Fama French Three Factor Model. The excess returns on sample portfolios are regressed on various factors as follows: RPt RFt = a + b RMt RFt + s SMBt + et (2) RPt RFt = a + b RMt RFt + l LMHt + et (3) RPt RFt = a + s SMBt + l LMHt + et (4) RPt RFt = a + b RMt RFt + s SMBt + l LMHt + et (5) Equation (5) is a full blown Fama French Equation. And, (RMt RFt), SMB and LMH represent market, size and value factors respectively. Empirical Results SECTION 4 Table 1 Panle A provides results of unadjusted returns on Size (using alternative definitions of size) and value sorted portfolios for Total period. As is evident from the table, all the small size portfolios viz. SH, International Journal of Economic Research 266 (a) (b)

5 Validation of Fama French Model in Indian Capital Market SM and SL have outperformed all the big size portfolios viz. BH, BM and BL in all the alternative portfolio constructions. Within size portfolios, we can see that the portfolio SL i.e. small size and large PB ratio, has given the highest monthly, unadjusted return of 2.9%, 3.0% and 3.46% (translating into a yearly return of 34.4, 36.6% and 41.5%) for market capitalization, Enterprise Value and Total Assets based size sortings respectively for the total period. Moreover, the difference between the SL and BH portfolio for market capitalization based sorting is over 16%. Similar results are found for the other two sorting criteria, namely, enterprise value and total assets. This suggests that there is a strong size effect in the Indian equity market. Our findings are in contrast to the findings of Berk (1996), who did not find strong size effect for U.S. markets. Within Size sorted portfolios, we see that SL portfolio, i.e. small size and low PB portfolio, for all the size based constructions, outperform the SH i.e. small size and high PB portfolio. This suggests the presence of strong value effect in the Indian markets. We find similar results for both the sub periods with the observations that returns in general have sobered down across all portfolios in sub period 2 as compared to sub period 1. Next, we examined if the size and value effect can be explained by using alternative risk adjusted models. We provide the results for a total period Table 2. In order to see if the significant unadjusted returns can be explained by risk models, we first operationalized the single factor CAPM model. We find after adjusting for market risk, the returns of all the small size companies have sobered down (see Table 2- Panel A). The monthly risk adjusted returns for SL, SM and SH for based portfolios are 1.5%, 1.4% and 1.1% respectively as compared to monthly unadjusted returns of 2.9%, 2.7% and 2.4% respectively. The market factor as represented by beta has absorbed a large part of unadjusted returns for small sized companies. We also find that the alphas of all the big size portfolios(for based portfolios), except BM, become insignificant at 5% level of significance under CAPM. The adjusted R 2 of all the portfolios are quite high i.e. above 80%. However, the CAPM could not fully explain the small size portfolios as the alphas of those portfolios are still significant at 5% level. We, find the similar results for the portfolios formed on alternative size based constructions. Next, we test the two factor model, by using pairwise combinations of market, size and value factors (see Table 2: Panel B, C and D), to verify if alphas of small size portfolios get subsumed by additional factors for total period. We first combine the market and size in a multiple regression framework (see Table 2: Panle B) and find that alphas of all the portfolios except SL become insignificant (in all the three size measures) which means that the size factor when added to market factor absorbs the alpha effect of most of the portfolios except small size companies. In contrast, when we add the value factor to in addition to market factor (see Table 2: Panel C) we find that, except BL all other portfolios remain significant at 5% level of significance. It means that value factor plays insignificant role in the Indian capital market in explaining extra normal returns. Finally, when we combine size and value factor without market factor, we find that without market factor both these factors are unable to absorb the alpha effect (see Table 2: Panel D). In nutshell, we find that in all the pairwise combinations of the three factors,alphas remain significant. Finally, we applied three factor Fama French model to examine if the size and value factor alongwith market factor absorb the effect of alphas for small size portfolios. In support of the international evidence we find that (see Table 2 Panel E) for all the alternative size based constructions the t stats of alpha of all the portfolios become insignificant at 5% level. Moreover, the explanatory power of variables is more as compared to single factor model as can be seen by adjusted R 2 values. For almost all the portfolios adjusted 267 International Journal of Economic Research

6 Asheesh Pandey and Amiya Kumar Mohapatra R 2 is over 90% for the Fama Frecnh Model versus 80% for the single factor CAPM model. Hence, we empirically find that a three factor model, i.e. Fama French Model is superior as compared to a single factor market model for total period. In order to check the robustness of Fama French model post sub - prime crisis, we further divided our data into two sub periods i.e. pre and post sub prime crisis. The methodology adopted is similar to that for total period. The results are provided in Table 3 and Table 4 respectively, for the two sub periods. As in case of total period, we find that even for sub periods the single factor CAPM is not able to fully explain the portfolio returns. However, as we go into the three factor Fam French model the returns for all the portfolios (in all the size based constructions) are explained for both the periods. Thus, we conclude that the Fama French model is relevant for the total period well as the two sub periods in the Indian context. SECTION 5 Summary and Conclusion: In this paper, we try to evaluate the acceptability of Fama French, three factor model over a single factor, CAPM model. We also check the robustness of the Fama French model in two ways: 1) by using alternative size measures viz. market capitalization, enterprise value and total assets and 2) by dividing the total period into two sub periods viz. pre and post sub prime crisis. Data is employed for BSE 500 companies for a period of July 2001 to January 2015 for Indian capital market. The data source used is CMIE Prowess. After removing penny stocks we, applied double sort criteria on monthly returns of stocks in forming six portfolios based on size and value factor. We used price to book value ratio in order to create the value factor. We, applied single factor CAPM, pairwise combinations of Market, Size and Vlue Facotr and three Factor Fam French Model to test if the excess unadjusted returns are explained by these risk models. We find that single factor CAPM and any pairwise combination of the various risk factors (in all the periods and alternative size based constructions) are unable to fully explain the extra normal returns as depicted by significant alphas. We further, observed that as we applied three factor Fam Frecnh Model, all the extra normal returns are explained for all the periods as well as alternative size based constructions. Hence, we confirm the presence of strong size and value effects in the Indian stock market even after post sub prime crisis. Fama - French three factor model proved to be a better descriptor of returns of company characteristic sorted portfolios compared to one factor CAPM. Table 1 Unadjusted Returns on Alternative Size based Portfolios Panel A: Total Period Portfolios SH SM SL BH BM BL International Journal of Economic Research 268

7 Validation of Fama French Model in Indian Capital Market Panel B: Sub Period 1 Portfolios SH SM SL BH BM BL Panel C: Sub Period 2 Portfolios SH SM SL BH BM BL Panel A: CAPM Results Rp t = + (Rm t ) Table 2 Risk Adjusted Returns on Alternative Size Sorted Portfolios for Total Period Portfolios t á t â SH SM SL BH BM BL SH SM SL BH BM BL SH SM SL BH BM BL International Journal of Economic Research

8 Asheesh Pandey and Amiya Kumar Mohapatra Panel B: Market and Size Based Results = a + b RM t + s SMB t Portfolios SMB t t t SMB SH SM SL BH BM BL SH SM SL BH BM BL SH SM SL BH BM BL Panel C: Market and Value Based Results = a + b RM t + s llmh t Portfolios âsmb t t t SMB SH SM SL BH BM BL SH SM SL International Journal of Economic Research 270

9 Validation of Fama French Model in Indian Capital Market BH BM BL SH SM SL BH BM BL Panel D: Size and Value Based Results for Double Sorted Portfolios = a + s SMB t +llmh t Portfolios LMH t t SMB t LMH SH SM SL BH BM BL SH SM SL BH BM BL SH SM SL BH BM BL International Journal of Economic Research

10 Asheesh Pandey and Amiya Kumar Mohapatra Panel E: Fama - French Results = a + b RM t + s SMB t +llmh t Portfolios SMB LMH t t t SMB t LMH SH SM SL BH BM BL SH SM SL BH BM BL SH SM SL BH BM BL Panel A: CAPM Results Rp t = + (Rm t ) Table 3 Risk Adjusted Returns on Alternative Size Sorted Portfolios for Sub Period 1 Portfolios t t SH SM SL BH BM BL International Journal of Economic Research 272

11 Validation of Fama French Model in Indian Capital Market SH SM SL BH BM BL SH SM SL BH BM BL Panel B: Market and Size Based Results = a + b RM t + s SMB t Portfolios SMB t t t SMB SH SM SL BH BM BL SH SM SL BH BM BL SH SM SL BH BM BL International Journal of Economic Research

12 Asheesh Pandey and Amiya Kumar Mohapatra Panel C: Market and Value Based Results = a + b RM t + s llmh t Portfolios SMB t t t SMB SH SM SL BH BM BL SH SM SL BH BM BL SH SM SL BH BM BL Panel D: Size and Value Based Results for Double Sorted Portfolios = a + s SMB t +llmh t Portfolios LMH t t SMB t LMH SH SM SL BH BM BL SH SM SL International Journal of Economic Research 274

13 Validation of Fama French Model in Indian Capital Market BH BM BL SH SM SL BH BM BL Panel E: Fama - French Results = a + b RM t + s SMB t +llmh t Portfolios SMB LMH t t t SMB t LMH SH SM SL BH BM BL SH SM SL BH BM BL SH SM SL BH BM BL International Journal of Economic Research

14 Asheesh Pandey and Amiya Kumar Mohapatra Panel A: CAPM Results Rp t = + (Rm t ) Table 4 Risk Adjusted Returns on Alternative Size Sorted Portfolios for Sub Period 2 Portfolios t t SH SM SL BH BM BL SH SM SL BH BM BL SH SM SL BH BM BL Panel B: Market and Size Based Results = a + b RM t + s SMB t Portfolios SMB t t t SMB SH SM SL BH BM BL SH SM SL International Journal of Economic Research 276

15 Validation of Fama French Model in Indian Capital Market BH BM BL SH SM SL BH 8.61E BM BL Panel C: Market and Value Based Results = a + b RM t + s llmh t Portfolios SMB t t t SMB SH SM SL BH BM BL SH SM SL BH BM BL SH SM SL BH BM BL International Journal of Economic Research

16 Asheesh Pandey and Amiya Kumar Mohapatra Panel D: Size and Value Based Results for Double Sorted Portfolios = a + s SMB t +llmh t Portfolios LMH t t SMB t LMH SH SM SL BH BM BL SH SM SL BH BM BL SH SM SL BH BM BL Panel E: Fama - French Results = a + b RM t + s SMB t +llmh t Portfolios SMB LMH t t t SMB t LMH SH SM SL BH BM BL SH SM SL International Journal of Economic Research 278

17 Validation of Fama French Model in Indian Capital Market BH BM BL SH SM SL BH BM BL REFERENCES Banz, Rolf W. (1981), The relation between return and market value of common stocks. Journal of Financial Economics, 9, Basu, S. (1977), The investment performance of common stocks in relation to their prices to earnings ratios: A test of the efficient market hypothesis. Journal of Finance, 32, Bahl, B. (2006), Testing the fama and french three-factor model and its variants for the Indian stock returns, Available at SSRN Berk, J. (1995), A critique of size related anomalies. Review of Financial Studies, 8, Berk, J.B., (1996), An Empirical Re-Examination of the Relation between firm Size and Return. Working Paper, University of Washington. Bhandari, L.C. (1988), Debt-equity ratio and expected common stock returns: Empirical evidence. Journal of Finance, 43, Black, F., Jensen, M., & Scholes, M., (1972), The capital asset pricing model: Some empirical tests. Studies in the Theory of Capital Markets. New York: Praeger. Chan, L.K.C., Hamao, Y., & Lakonishok, J. (1991), Fundamentals and stock returns in Japan. Journal of Finance, 46, Connon, G., & Sehgal, S. (2003), Tests of the Fama-French model in India. Decision, 30(2), July December, Fama, Eugene F., & French, Kenneth R. (1992), The Cross-Section of Expected Stock Returns. Journal of Finance, 47, Fama, Eugene F., & French, Kenneth R. (1993), Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, Fama, Eugene F., & French, Kenneth R. (1996), Multifactor explanations of asset pricing anomalies. Journal of Finance, 51, Lintner, J. (1965), The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economic and Statistics, 47, Rosenberg, B., Reid, K., & Lanstein, R. (1985), Persuasive evidence of market inefficiency. Journal of Portfolio Management, 11, Sehgal,S & Balakrishnan, A. (2013), Robustness of Fama-French Three Factor Model: Further Evidence for Indian Stock Market, Vision: The Journal of Business Perspective 17, Sharpe, W.G. (1964), Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19, International Journal of Economic Research

18 Asheesh Pandey and Amiya Kumar Mohapatra Statman, D. (1987), Book Vlues and Stock Returns. The Chicago MBA: A Journal of Selected Papers, 4, S Taneja, Y. P. (2010), Revisiting fama french three-factor model in Indian stock market. Vision: The Journal of Business Perspective 14, Tripathi, V. (2008), Company fundamentals and equity returns in india. Available at SSRN: http: //ssrn.com/ abstract= orhttp://dx.doi.org/ /ssrn International Journal of Economic Research 280