The Current

Global Trends

Vol. 2; Issue 1; Year 2013; Page 7-13 ISSN: 2329-0102 DOI: http://dx.doi.org/10.1111%2Fcgt.v2i1.40 Available at http://sci-edit.net/journal/index.php/cgt/index

Fama-French Three Factor Model in Indian Stock Market Sahil Jain Department of Mathematics, Indian Institute of Technology, Roorkee, INDIA __________________________________________________________________________________________________ ABSTRACT This paper studies the financial performance of Indian Stocks by implementing the Fama French Three Factor model to 27 stocks of the Bombay Stock Exchange using daily Stock (closing) data with SENSEX as the benchmark Index. Daily data allow us to reliably evaluate a stock’s performance over shorter time horizons. This is important for two reasons: performance persistence is often a short-lived phenomenon and a stock’s risk exposures can change over time. The results suggest that Banking and Automotive Company Stocks have outperformed every other stock. On the other side, the stocks belonging to the Oil and Gas, Power, Real Estate, Steel, Steel and Power and Telecommunication have performed terribly. This suggests that besides the three factors suggested by the Fama and French, there must be factors that account for the Sector performance. Keywords: Fama-French Three Factor Model, Capital Asset Pricing Model, SENSEX, Performance, Risk Return. ___________________________________________________________________________________________________ INTRODCUTION Study of Stocks through various financial models value factor (HML). The study concluded that the Fama has always been a topic of interest to Analysts. Several and French fairs better in explaining the cross-section of Researchers have immensely contributed in evaluating returns in the portfolios than its variants and the CAPM. Yash Pal Taneja (2010) examined the CAPM and the performance of Stocks from time to time. Pablo Rogers and José Roberto Securato (2007) con- the Fama French Three factor model by taking a sample ducted tests on portfolios, in accordance with the Fama of 187 companies for a study period of five years, rangand French’s (1993) and Bornholt’s (2007) methodology, ing from June 2004 to June 2009. The study concluded and applied in two sub-samples of stocks with available that efficiency of Fama French Model, for being a good data in the São Paulo Stock Exchange (BOVESPA). They predictor, can not be ignored in India but either of the concluded that the results tend to support the Fama and two factors (size and value) might improve the model. Vanita Tripathi (2008) examined the relationship French Three-Factor model to explain future returns. between four company fundamental variables (viz. Jan Bartholdy and Paula Peare (2002) compared the performance using CAPM and Fama French Three market capitalization, book equity to market equity ratio, Factor Model for individual stocks.   First, they esti- price earnings ratio and debt equity ratio) and equity mated individual stock returns based on CAPM using returns in Indian stock market using monthly price different time frames, data frequencies, and indexes. data of a sample of 455 companies forming part of S&P Then, they obtained individual stock returns based on CNX 500 Index over the period June 1997 to June 2007. the Fama and French model using five years of monthly The results concluded that the Fama-French three factor model ( based on market risk premium, size premium data. Bhavna Bahl (2006) studied the Fama and French and value premium) explains cross sectional variations three-factor model of stock returns along with its vari- in equity returns in India in a much better way than the ants, including the one-factor Capital Asset Pricing Mod- single factor CAPM. The objective of this study is to measure and el for 79 stocks listed on the BSE-100 stock market index for India and found that factor portfolios that explain analyze the performance of Indian Stocks listed on the the returns are the market factor, size factor (SMB) and benchmark Index- SENSEX by using Fama French Three Factor Model. Before starting to perform this study, a _________________________________________ huge body of financial articles and books concerning the *Corresponding author subject of Fama French Model have been studied. More email [email protected] details are discussed in the ‘Methodology’ part of the Tel.: + 91 955 710 8385, Fax: + NA study. This work does an empirical investigation to the Accepted on 25th July, 2013

Table 1. List of Companies Industry wise # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Company Housing Development Finance Corporation Cipla Bharat Heavy Electricals State Bank Of India HDFC Bank Hero Motocorp Infosys Oil and Natural Gas Corporation Reliance Industries Tata Power Hindalco Industries Tata Steel Larsen & Toubro Mahindra & Mahindra Tata Motors Hindustan Unilever ITC Sterlite Industries Wipro Sun Pharmaceutical GAIL ICICI Bank Jindal Steel & Power Bharti Airtel Maruti Suzuki Tata Consultancy Services NTPC DLF Bajaj Auto Coal India

Curr. Global Trends 2:1 (2013) 7-13

Industry Consumer finance Pharmaceuticals Electrical equipment Banking Banking Automotive Information Technology Oil and gas Oil and gas Power Metals and Mining Steel Conglomerate Automotive Automotive Consumer goods Conglomerate Metals and Mining Information Technology Pharmaceuticals Oil and gas Banking Steel and power Telecommunication Automotive Information Technology Power Real estate Automotive Metals and Mining

performance of Indian Stocks for the period between May 2008 and May 2013. materials and methods This section gives an overview of the data used in this study. All calculations are based on the daily returns. The data used for calculations in this report cover the period from May 2008 through May 2013. Though there are a number of Stock Exchanges in India, the data for this study has been taken from the Bombay Stock Exchange, and SENSEX has been considered as the Benchmark Index for the study. The S&P BSE SENSEX (S&P Bombay Stock Exchange Sensitive Index), also-called the BSE 30 or

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simply the SENSEX, is a free-float market capitalization-weighted stock market index of 30 well-established and financially sound companies listed on BSE Ltd. The 30 component companies which are some of the largest and most actively traded stocks are representative of various industrial sectors of the Indian economy. Published since 1 January 1986, the S&P BSE SENSEX is regarded as the pulse of the domestic stock markets in India. The base value of the S&P BSE SENSEX is taken as 100 on 1 April 1979, and its base year as 1978–79. On 25 July 2001 BSE launched DOLLEX-30, a dollar-linked version of S&P BSE SENSEX. As of 21 April 2011, the market capitalization of S&P BSE SENSEX was about 29,733 billion (US$511 billion) (47.68% of market capitalization of BSE), while its free-float market capitalization was 15,690 billion (US$270 billion). The BSE Sensex currently consists of the following 30 major Indian companies, as listed below: In this study we have analyzed the data for all of the above stocks except Hero Motocorp, Housing Development Finance Corporation and Tata Power, with SENSEX as the Benchmark Index. The historical data for these stocks and the Index has been taken from the website: www.finance.yahoo.com In asset pricing and portfolio management the Fama-French three factor model is a model designed by Eugene Fama and Kenneth French to describe stock returns The traditional asset pricing model, known formally as the Capital Asset Pricing Model (CAPM) uses only one variable, beta, to describe the returns of a portfolio or stock with the returns of the market as a whole. In contrast, the Fama–French model uses three variables. Fama and French started with the observation that two classes of stocks have tended to do better than the market as a whole: (i) small caps and (ii) stocks with a high book-to-market ratio. They then added two factors to CAPM to reflect a portfolio’s exposure to these two classes:

r = R f + β 3 ( K m − R f ) + β s * SMB + β v * HML + α Here, r is the portfolio’s expected rate of return, Rf is the risk-free return rate, and Km is the return of the whole stock market. The “three factor” is analogous to the classical but not equal to it, since there are now two additional factors to do some of the work. SMB stands for “small (market capitalization) minus big” and HML for “high (book-to-market ratio) minus low”. They measure the historic excess returns of small caps over big caps and of value stocks over growth stocks. These factors are calculated with combinations of portfolios composed by ranked stocks (BtM ranking, Cap ranking) and available historical market data. “Moreover, once SMB and HML are defined, the corresponding coefficients are determined by linear

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Table 2. Total Assets of Companies #

Company

Assets INR (Cr) 3512 6138 7562 8149 15279 16266 18871 20738 20954 25218 25496 26472 26971 29596 30067 30379 32725 35119 36059 46604 63559 75910 115001

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hindustan Unilever Bajaj Auto Cipla Sun Pharmaceutical Mahindra & Mahindra Maruti Suzuki ITC Coal India Tata Power Jindal Steel & Power Bharat Heavy Electricals DLF GAIL Wipro Sterlite Industries Tata Motors Tata Consultancy Services Larsen & Toubro Infosys Hindalco Industries Bharti Airtel Tata Steel Housing Development Finance Corporation Oil and Natural Gas Corporation

117456

25 26 27 28 29

NTPC Reliance Industries HDFC Bank ICICI Bank State Bank Of India

120630 234543 400332 536795 1335519

regressions and can take negative values as well as positive values. The Fama-French three factor model explains over 90% of the diversified portfolios returns, compared with the average 70% given by the CAPM (within sample). The signs of the coefficients suggested that small cap and value portfolios have higher expected returns—and arguably higher expected risk—than those of large cap and growth portfolios.” –w2 In our study we will calculate the SMB and HML on daily basis for the companies listed in the SENSEX, and then we carry out a regression between the (Ri-Rf) and Rm-Rf, SMB and HML to obtain the corresponding coefficients. These results are discussed in more detail in the next section. RESULTS Calculating SMB

Table 3. Book to Market Ratio of Companies # Company 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Housing Development Finance Corporation Cipla Bharat Heavy Electricals State Bank Of India HDFC Bank Hero Motocorp Infosys Oil and Natural Gas Corporation Reliance Industries Tata Power Hindalco Industries Tata Steel Larsen & Toubro Mahindra & Mahindra Tata Motors Hindustan Unilever

17 18 19 20 21 22 23 24 25 26 27 28 29 30

ITC Sterlite Industries Wipro Sun Pharmaceutical GAIL ICICI Bank Jindal Steel & Power Bharti Airtel Maruti Suzuki Tata Consultancy Services NTPC DLF Bajaj Auto Coal India

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B/M Ratio 0.16 0.24 0.58 0.62 0.23 0.13 0.26 0.43 0.70 0.62 1.78 1.96 0.29 0.22 0.21 0.03 0.07 0.88 0.29 0.08 0.56 0.53 0.49 0.47 0.36 0.11 0.59 0.45 0.12 0.10

We begin our study by arranging the list of companies in the increasing order of their Assets. Through this we shall determine five companies that have least and most assets. As shown in Table 2, the five companies with least assets are- Hindustan Unilever, Bajaj Auto, Cipla, Sun Pharmaceuticals and Mahindra & Mahindra. Similarly, five companies that have the greatest assets are- NTPC, Reliance Industries, HDFC Bank, ICICI Bank and State Bank of India. Next, we list the stock value (Closing) of these companies on daily basis and calculate the SMB. Calculating HML Now, we calculate the Book to Market Ratio for these companies. First we list the Book value per share for these companies, which is easily available on the websites such as www.moneycontrol.com and then we

Curr. Global Trends 2:1 (2013) 7-13

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Table 4. Coefficients, Actual Rate of Return and Expected Rate of Return of the Companies S.No

Name of Stock

1 2 3 4

Bajaj Auto Sun Pharmaceutical ITC Tata Consultancy Services Mahindra & Mahindra HDFC Bank

Coefficients Rm-Rf SMB HML

Actual Rate of Return

Difference

1.0480 0.6814 0.7868 0.9220

0.7274 0.5975 0.0177 0.0456

-0.0264 -0.0782 -0.3793 -0.1186

0.1796 0.1769 0.1210 0.0854

0.4315 0.2984 0.2876 0.2538

0.2518 0.1215 0.1666 0.1684

1.3795 0.7421

0.9347 -0.2992

0.1355 -0.0495

0.1808 0.0254

0.2423 0.2184

0.0615 0.1930

0.7420 1.2656 -0.2797 0.7243 0.6917 1.3445 0.8257 0.8714 0.6707

0.5297 0.3155 2.0823 0.2841 0.5595 -0.4831 -0.4739 0.0937 0.0082

-0.0737 0.1329 3.9481 0.1018 0.0300 -0.0506 0.0789 -0.0862 0.0669

0.1634 0.0841 -0.1073 0.0999 0.1555 -0.0228 -0.0232 0.0903 0.0615

0.2067 0.1872 0.1714 0.1676 0.1506 0.0845 0.0797 0.0477 0.0424

0.0432 0.1032 0.2786 0.0677 -0.0049 0.1073 0.1029 -0.0427 -0.0191

16 17 18

Hindustan Unilever Tata Motors Sterlite Industries Maruti Suzuki Cipla ICICI Bank State Bank Of India Infosys Oil and Natural Gas Corporation Larsen & Toubro Wipro Coal India

0.9552 0.9753 0.4715

0.0035 0.2503 0.1474

0.1231 -0.0518 0.2197

0.0443 0.1078 0.0692

0.0357 0.0289 -0.0175

-0.0085 -0.0790 -0.0866

19 20 21 22 23 24 25 26 27

NTPC GAIL Jindal Steel & Power Bharti Airtel Reliance Industries Hindalco Industries BHEL Tata Steel DLF

0.6149 0.7591 1.0462 0.7764 1.0075 1.1844 0.8399 1.3311 1.4596

-0.2158 0.1597 -0.0120 0.0106 -0.1763 0.4077 -0.1299 0.2391 0.0231

-0.0577 0.0552 0.0726 -0.0254 0.0687 0.2903 0.0246 0.2104 0.1026

0.0440 0.0850 0.0459 0.0714 0.0209 0.0798 0.0397 0.0589 0.0348

-0.0279 -0.0349 -0.0440 -0.0645 -0.0806 -0.0984 -0.0989 -0.1838 -0.1856

-0.0719 -0.1199 -0.0899 -0.1359 -0.1016 -0.1783 -0.1386 -0.2427 -0.2203

5 6 7 8 9 10 11 12 13 14 15

find the corresponding Book to Market Ratio. Table 2 below summarizes the results: From the above table we find that five companies with least Book to Market Ratio are Hindustan Unilever, ITC, Sun Pharmaceuticals, Tata Consultancy Services and Bajaj Auto. Similarly, five companies with the highest B/M ratio are State Bank of India, Reliance Industries, Sterlite Industries, Hindalco Industries and Tata Steel. Then we list the daily Stock- closing values, for the period May 2008 to May 2013, of these companies and calculate the HML. Calculating Coefficients and Expected Rate of Return After obtaining the SMB and HML, we obtain the coefficient corresponding to Rm-Rf, SMB and HML for individual stocks. We obtain these coefficients by regressing Ri-Rf with SMB, HML and Rm- Rf. The results are summarized in Table 3:

DISCUSSION Performance of Stocks The Table 3 above summarizes the results. The Stocks in the above table have been sorted in the decreasing order of the difference between the Actual rate of return and the expected rate of return- as per the Fama –French Three Factor Model. 3rd, 4th and 5th columns list the coefficients corresponding to the Rm-Rf, SMB and HML. These coefficients have been obtained by regressing Ri-Rf with Rm-Rf, SMB and HML. After obtaining these coefficients, we substitute them in Fama- French three factor model formula to obtain the Expected Rate of Return. Additionally, using the historical values, we also calculate the Actual Rate of Return. Then, we list the difference between the two in the last column. The above results show that 9 out of 27 stocks performed fairly well i.e. the difference between the expected and actual rate of interest is more than 10%.

Curr. Global Trends 2:1 (2013) 7-13 Table 5. Actual Rate of Return of Companies S.No Name of Stock Actual Rate of Return 1 Bajaj Auto 0.4315 2 Sun Pharmaceutical 0.2984 3 ITC 0.2876 4 Tata Consultancy Services 0.2538 5 Mahindra & Mahindra 0.2423 6 HDFC Bank 0.2184 7 Hindustan Unilever 0.2067 8 Tata Motors 0.1872 9 Sterlite Industries 0.1714 10 Maruti Suzuki 0.1676 11 Cipla 0.1506 12 ICICI Bank 0.0845 13 State Bank Of India 0.0797 14 Infosys 0.0477 15 Oil and Natural Gas 0.0424 Corporation 16 Larsen & Toubro 0.0357 17 Wipro 0.0289 18 Coal India -0.0175 19 NTPC -0.0279 20 GAIL -0.0349 21 Jindal Steel & Power -0.0440 22 Bharti Airtel -0.0645 23 Reliance Industries -0.0806 24 Hindalco Industries -0.0984 25 BHEL -0.0989 26 Tata Steel -0.1838 27 DLF -0.1856 These stocks are: Sterlite Industries, Bajaj Auto, HDFC Bank, Tata Consultancy Services, ITC, Sun Pharmaceutical, ICICI Bank, Tata Motors and State Bank of India. Moreover, 5 out of 27 stocks performed as per the expectations i.e. the difference between the Actual and Expected Rate of return is not more than 5%. These stocks are: Hindustan Unilever, Cipla, Larsen & Tourbo, Oil and Natural Gas Corporation and Infosys. On the other hand, 6 stocks performed terribly i.e. the difference between the expected and the actual rate of return was less than -10%. These stocks are: NTPC, Wipro, Coal India, Jindal Steel and Power, Reliance Industries, GAIL, Bharti Airtel, BHEL, Hindalco Industries, DLF and Tata Steel. Now we sort the above Stocks in the order of their actual performance, as listed in Table 4. From the above table we observe that Bajaj Auto has outperformed every other stock on the Index with annual rate of return of 43%. The share price of Bajaj Auto on 26th May 2008 was 302.25, while on 27th may 2013

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it was 1816.50. Other than Bajaj Auto there are 10 stocks that have performed fairly well with an annual rate of return of more than 15%. These stocks are: Sun Pharmaceutical, ITC, Tata Consultancy Services, Mahindra and Mahindra, HDFC Bank, Hindustan Unilever, Tata Motors, Sterlite Industries, Maruti Suzuki and Cipla. Then, there are 6 companies that have given positive annual returns, but less than 10%. These are ICICI Bank, State Bank of India, Infosys, Oil and Natural Gas Corporation, Larsen & Toubro and Wipro. Lastly, there are 10 Stocks that have given a negative annual rate of return. These are: Coal India, NTPC, GAIL, Jindal Steel & Power, Bharti Airtel, Reliance Industries, Hindalco Industries, BHEL, Tata Steel and DLF. Among these Tata Steel and DLF have been the worst performers with an annual rate of return of -18.38% and -18.56% respectively. Sector Wise Performance Table 5 below sorts the stocks by their Industry. Undoubtedly, Banking Sector Companies have performed the best. All the three Banking Sector companiesHDFC Bank, ICICI Bank and State Bank of India- have performed more than expected with an average difference of +13.44 %. After Banking it’s the Automotive Sector companies that have performed the best. Again, all the four Automotive Sector Companies- Bajaj Auto, Mahindra & Mahindra, Tata Motors and Maruti Suzuki have performed more than expected with an average difference of +12.11 %. The performance of companies that belong to the Industries Conglomerate, Consumer Goods, Electrical Equipments, Information Technology, Metals and Mining and Pharmaceuticals has been quite as expected, since the average difference for these industries lie between -5% to +5%. On the other side, the performance of companies (Stocks) belonging to the Oil and Gas, Power, Real Estate, Steel, Steel and Power and Telecommunication has been quite disastrous with an average difference of -10.9%. The result clearly suggests that there has to be some other factor besides those mentioned in the Fama French Three Factor Model that would explain the performance variation among various Industrial Sectors. REFERENCES Research Papers 1. Andreas G. F. Hoepnerab, Hussain G. Rammalc & Michael Rezeca, 2009, Islamic Mutual Funds’ Financial Performance and International Investment Style: Evidence from 20 countries, European Journal of Finance. 2. Antti Petajisto, 2013, Active Share and Mutual Fund

Curr. Global Trends 2:1 (2013) 7-13

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Table 6: Industry wise List of Difference between Actual and Expected Returns S.No

Name of Stock

Actual Rate of Return

Difference

Bajaj Auto

Expected Rate of Return 0.180

1

0.431

0.252

Automotive

2

Mahindra & Mahindra

0.181

0.242

0.061

Automotive

3

Tata Motors

0.084

0.187

0.103

Automotive

4

Maruti Suzuki

0.100

0.168

0.068

Automotive

5

HDFC Bank

0.025

0.218

0.193

Banking

6

ICICI Bank

-0.023

0.085

0.107

Banking

7

State Bank Of India

-0.023

0.080

0.103

Banking

8

ITC

0.121

0.288

0.167

Conglomerate

9

Larsen & Toubro

0.044

0.036

-0.009

Conglomerate

10

Hindustan Unilever

0.163

0.207

0.043

Consumer goods

11

BHEL

0.040

-0.099

-0.139

Electrical equipment

12

Tata Consultancy Services

0.085

0.254

0.168

Information Technology

13

Infosys

0.090

0.048

-0.043

Information Technology

14

Wipro

0.108

0.029

-0.079

Information Technology

15

Sterlite Industries

-0.107

0.171

0.279

Metals and Mining

16

Coal India

0.069

-0.017

-0.087

Metals and Mining

17

Hindalco Industries

0.080

-0.098

-0.178

Metals and Mining

18

Oil and Natural Gas Corporation

0.062

0.042

-0.019

Oil and gas

19

GAIL

0.085

-0.035

-0.120

Oil and gas

20

Reliance Industries

0.021

-0.081

-0.102

Oil and gas

21

Sun Pharmaceutical

0.177

0.298

0.121

Pharmaceuticals

22

Cipla

0.156

0.151

-0.005

Pharmaceuticals

23

NTPC

0.044

-0.028

-0.072

Power

24

DLF

0.035

-0.186

-0.220

Real estate

25

Tata Steel

0.059

-0.184

-0.243

Steel

26

Jindal Steel & Power

0.046

-0.044

-0.090

Steel and power

27

Bharti Airtel

0.071

-0.065

-0.136

Telecommunication

Performance, JEL Classification: G10, G14, G20, G23, Working papers series. 3. Ashish Tiwari and Anand M VIJH, 2001, Sector Fund Performance, University of Iowa Working Paper, JEL Classification: G12. 4. Bhavna Bahl, 2006, Testing the Fama and French Three-Factor Model

Industry Sector

and Its Variants for the Indian Stock Returns. 5. Jan Bartholdy and Paula Peare, 2002, Estimation of Expected Return: CAPM vs Fama and French, JEL Classification: G11, G12, G31Working Paper series. 6. K. J. Martijn Cremers and Antti Petajisto, 2009, How Active Is Your Fund Manager? A New Measure That

Curr. Global Trends 2:1 (2013) 7-13

7.

8. 9.

10.

11.

12. 13.

14.

15.

Predicts Performance, AFA 2007 Chicago Meetings Paper, Yale ICF Working Paper No. 06-14, EFA 2007 Ljubljana Meetings Paper. Miranda Lam Detzler, 1999, The Value of Mutual Fund Rankings to the Individual Investor, JEL Classification: G14, working papers series. Richard A. Michelfelder, 2009, Fama-French 3-Factor Model: Theoretical and Conceptual Underpinnings. Rogér Otten and Dennis Bams, 2000, European mutual fund performance, European Financial Management Journal. S.P. Kothari and Jerold B Warner, 1997, Evaluating Mutual Fund Performance, JEL Classification: G12, G14, Working papers series. Thierry Roncalli and Guillaume Weisang, 2008, Tracking Problems, Hedge Fund Replication and Alternative Beta, JEL Classification: G11, C60, working papers series. Tulkin Saidov, 2007, Performance of German Mutual Funds, Working Paper Series. Vanita Tripathi, 2008, Company Fundamentals and Equity Returns in India, SSRN 1134651. Yash Pal Taneja, 2010, Revisiting Fama French Three-Factor Model in Indian Stock Market, The Journal of Business Perspective. Yonggan Zhao, 2005, A Dynamic Model of Active Portfolio Management and Mutual Fund Performance, JEL Classification: B23 C15 C61 G13.

Internet Sources W1. www.moneycontrol.com W2. www.wikipedia.com W3. www.in.finance.yahoo.com W4. www.ssrn.com W5. www.scholar.google.com

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