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Fama French

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ABSTRACT

With growing number of stocks and options to invest there is always the need of finding out new ways to efficiently allocate assets in our portfolio. This paper tries to study the financial performance of the 43 stocks of the national stock exchange using nifty 50 has the benchmark index. Monthly data over the past 5 financial years have allowed us to measure returns closely over this short duration. We use the Fama-French three factor model to compute returns for
Indian equity stocks. We also use regression techniques to estimate the coefficients of the three risk parameters in the model. We have tried to find the optimum betas through solver and also bring out the contrast between traditional CAPM and fama French. In the process we have tried to understand the model and its limitations and have tried to come up with further scope of this model and recommendations.
LITERATURE REVIEWThe main objective of portfolio managers is to select stocks efficiently that can give higher returns given the risk. Markowitz (1952). Portfolio theory used stock return variance as a measure of risk and a deciding factor for stock selection
Jack treynor(1962), william sharpe(1964), John Lintner(1965) and Jan Mossin(1966) gave the
CAPM model which was proposed to quantify the relationship between beta of an asset to its respective return, given the appropriate assumptions.
Over the years many researchers have tried to contribute to the CAPM equation for evaluating the performance of stocks. Eugene Fama and Kenneth French developed the Fama-French three factor model that described value and sized to be the most important factors outside of market risk to explain the return of publicly traded stock.
Bhavna Bahl(2006) studies the Fama-French model of stock returns along with its variants for 79 stocks on BSE100 for India. She concluded that factor portfolios SMB and HML are better in explaining the asset returns than one factor CAPM.
Vanita tripathi(2008) and Yash pal Taneja(2010) also studied various Indian companies and concluded that the size and value variables do improve the traditional CAPM. Even internationally, Palo Rogers(2007) conducted tests on portfolios for the Sao Paulo stock exchange. Veysel Eraslan(2013) have also validated the model for the Istanbul Stock Exchange. Faff(2001) tests the model in the Australian stock exchange using sheff Index. Results support the three factor model.

S.A.P.M 1

The use of OLS to find the betas of the three factors in the model has been used to calculate the return of stocks. To make the model more robust quantile regression can be used to estimate the coefficients.(Abhay Kumar, David Allen,2010).

Background
2.1 Fama-French Three Factor Model
After the Markowitz model many attempts have been made to successfully define the relation between risk factors and returns. CAPM was a popular model which used one factor or risk premium to calculate the returns. However, an empirical study done by Fama and French showed that there was no relation between the covariance of market returns and excess portfolio returns. The three factor model is based on the fact that average excess portfolio returns can be estimated by three factors



Excess market return
The difference between the excess return on small and big stock portfolios
The difference between excess return on a portfolio of high book to market stocks and the xcess return on a portfolio.

The formula is given as r=Rf +β3(Km −Rf )+βs *SMB+βv *HML+α

Where, rA is the return of the asset rM is the return of the market rF is the risk free rate of return α is the intercept of regression
SMB is the size portfolio return
HML is value portfolio return
The model aims to cure the anomalies of the CAPM model.
This paper tries to test the three factor model on the National Stocl Exchange India(NSE). The aim is to test the validity of the model with india equity. We aim to study whether these additional factors are good indicators to predict rate of return or construct portfolios.

2

Auro University

3.Research Methodology
The study is an empirical investigation on the stocks of India exchange for the period between
2011-2015.
Al l calculations are based on monthly data. The prices have been taken from the national stock exchange using Nifty has a benchmark index. The Nifty 50 consists of 50 companies listed belowWe have analyzed the data for 43 stocks except –Vedanta, Infosys, Hindustan Unilever, Acc,
The methodology can be summarized in the following steps







Collect monthly prices for 43 stocks from april 1 2011 to march31st 2015.
Find growth rates.
Arrange the stocks in ascending order of their market capitalization and book-to-market ratios.(see table 2)
Create 6 portfolios to calculate the SMB and HML
Use linear regression to get coefficients and calculate the excess return from portfolios using fama French equation.
Optimize the betas to validate the three factor model hypothesis.
Contrast with traditional model

Table 3 summarizes the calculated returns ( column 6)and actual returns(column 7- calculated by historical data) and their difference( column 8) .

4. Discussion of results







21 stocks out of 50 have done fairly well and have performed as per the expectation that is the difference between the actual and calculated values of excess return are less than
5%. In these also there are 7 stocks who have given less than 1% difference between actual and calculated.
Banking and energy sector have performed as expected.
Stocks like sun pharma have performed beyond the calculated expectation and can be said to be most volatile as it gives 8% higher return. On the other hand ICICI has given a negative 30% return than expected.
The difference between actual and calculated are more in Traditional CAPM model than in fama French
When optimized, the weights given to the smb and hml variables increase.
S.A.P.M 3

5. Scope




4

The study can go on to include Momentum factors and make it a 4 factor model.
Techniques can be made more robust by using quantile regression, classification of small large companies according to Indian Economy.
Use more filters like liquidity of a company to select the initial companies in a more efficient way.

Auro University

Table 2 book to market ratio. stock cairn hindalco vedanta pnb tat steel bob sbi ongc tata power bharat heavy
GAIL
NTPC
RELIANCE
GRASIM tata motors icici bharti airtel idea yes bank axis bank infosys l&t bharat petrol acc ambuja wipro indus ind tech mahindra hdfc ultratech cements kotak hdfc bank coal adani cipla hcl reddy maruti bajaj hero

ratio

b/m
0.4
0.41
0.49
0.64
0.68
0.92
1.01
1.03
1.16
1.19
1.27
1.31
1.32
1.42
1.44
1.79
1.91
1.97
2.36
2.43
2.49
2.93
2.93
2.97
3
3.24
3.42
3.73
3.75
3.89
3.95
4.19
4.33
4.39
4.4
4.64
4.67
5.64
6.42
6.45

2.5
2.43902439
2.04081633
1.5625
1.47058824
1.08695652
0.99009901
0.97087379
0.86206897
0.84033613
0.78740157
0.76335878
0.75757576
0.70422535
0.69444444
0.55865922
0.52356021
0.50761421
0.42372881
0.41152263
0.40160643
0.34129693
0.34129693
0.33670034
0.33333333
0.30864198
0.29239766
0.26809651
0.26666667
0.25706941
0.25316456
0.23866348
0.23094688
0.22779043
0.22727273
0.21551724
0.21413276
0.17730496
0.15576324
0.15503876

HIGH

MEDIUM

sun pahrma itc bosch tcs lupin zee asian painta hindustan unil

6.6
7.12
7.25
7.55
8.22
9.41
15.4
44.91

0.15151515
0.14044944
0.13793103
0.13245033
0.1216545
0.10626993
0.06493506
0.02226676

LOW

S/L
S/H
S/M
B/L
REDDY
CAIRN
GRASIM
MARUTI
HINDALCO IDEA
BAJAJ
VEDANTA
YES BANK
SUN
TATA STEEL L&T
ITC
TATA POWER BHARAT
TCS
BHARAT
WIPRO
ZEE
GAIL
INDUS IND
BOSCH
TECH MAHINDRA
LUPIN
ULTRATECH
ASIAN PAINTS
KOTAK
CIPLA
ADANI
COAL
HCL

B/M
B/H
0 RELIANCE
SBI
TATA MOTORS OB
B
ICICI
PNB
BHARTI AIRTEL NGC
O
AXIS BANK NTPC
HDFC
HDFC BANK

Company
State Bank of India
ICICI Bank Ltd
Bank of Baroda
PNB
HDFC Bank
Reliance Industries Ltd
Axis Bank
HDFC Ltd
ONGC
Tata Motors Ltd
NTPC Ltd
Bharti Airtel Ltd
L&T
Vedanta Ltd
Power Grid Corp Ind Ltd
Tata Steel Ltd
Kotak Mahindra Bank Ltd
Hindalco Industries
Yes Bank Ltd
Coal India Ltd
IndusInd Bank
Bharat Petroleum Corp Ltd
Tata Power Co Ltd
TCS
Bharat Heavy Electricals Ltd
GAIL Ind Ltd
Cairn Ind Ltd
Idea Cellular
Wipro Ltd
Grasim Ltd
Sun Pharma
ITC Ltd
Ultra Tech
Maruti Suzuki Ltd
Tech Mahindra
Dr Reddy Lab
Bajaj Auto
Cipla Ltd
Lupin Ltd
Bosch Ltd
Asian Paints
Zee Ent Ltd
HCL Tech Ltd

Assets
27,001,100,000
8,260,792,000
7,339,774,000
6,360,112,000
6,070,965,000
5,044,860,000
4,672,430,000
3,495,252,000
3,376,827,000
2,386,580,000
2,195,762,000
1,957,818,000
1,941,841,000
1,902,824,000
1,607,643,000
1,589,455,000
1,485,758,000
1,431,389,000
1,361,430,000
1,105,415,000
1,091,159,000
869,569,000
754,429,000
736,609,000
708,887,000
696,453,000
668,343,000
604,668,000
600,033,000
540,536,000
490,279,000
459,908,000
380,631,000
344,786,000
198,481,000
194,762,000
159,656,000
157,175,000
131,377,000
104,308,000
89,125,000
70,058,000
5,371,000

Table 3- Results
Stock
Rm-Rf
TCS
-0.3536547
Maruti
0.55333948 reddy -1.1118587 sun pharma -0.5006919 itc 0.56728676 zee 0.23926667 bosch 2.20531657 lupin -0.9174692 asian paints 3.12279283 cairn 0.73832537 hindalco 0.58454577 tata steel
1.5208206
tata power
3.05284387
Bhel
-1.5320233
gail
0.78401054
grasim
2.35163895
idea
-1.12765
yes bank
2.15236375
bpcl
1.60039592
whipro
0.56221532
Indusind
1.28303669
Tech mahindra1.47451436
Ultratech
2.51200035
Kotak
0.76325903 cipla 0.12494198 adani 1.95514237 coal 0.96486279
Hcl
0.43140917 reliance 1.09791535 tata motors 1.43532373
ICICI
3.84567834
Bharti Airtel -0.3909248
Axis Bank
2.24006647
HDFC Bank
1.49823227
HDFC Ltd
0.61575407
SBI
-1.1847695
BOB
19.0757074
PNB
-20.260477
ONGC
1.56706324
NTPC
1.80898426

Coefficients
SBM
0.27848489
0.04161072
0.47436449
0.18183669
-0.1465595
0.07135429
-0.382399
0.33456549
-0.7169851
0.08287583
0.45071084
0.38290197
-0.0356334
0.41853539
0.36493445
-0.2511714
0.29466
-0.364193
0.24435375
0.00561684
-0.2597763
-0.1396684
-0.6350952
-0.1329268
0.07919959
-0.409496
-0.0558344
0.05123074
0.12630564
-0.0751296
-11.098641
0.26879817
-0.2933274
-0.2256772
0.05059366
-0.7325478
-2.9828587
2.25031091
0.08848454
-0.043652

calculated Ri-Rf
HML
0.27814442
0.0170084
0.53135434
0.15387547
-0.1353942
0.1092343
-0.2918864
0.34248496
-0.6343924
0.0547145
0.47944995
0.36235655
-0.0563687
0.41872529
0.30969243
-0.265709
0.27273
-0.3862445
0.21744475
0.01297123
-0.270509
-0.1401099
-0.6681684
-0.121249
0.01963855
-0.4274825
-0.0882299
0.04940292
0.11934619
-0.1056889
-11.539838
0.23718877
-0.2880019
-0.2228404
0.05051154
4.47231977
-3.1788515
7.65117129
0.04968184
-0.0834292

-0.050279606
-0.009734854
-0.009770348
-0.003033885
-0.119347559
-0.091987714
-0.147954046
0.030309867
-0.17826348
-0.157816216
-0.133158936
-0.186830044
-0.258180973
0.071350929
-0.116531072
-0.192116724
0.008364747
-0.136072358
-0.121464277
-0.10310263
-0.103228557
-0.134981638
-0.18808594
-0.084479948
-0.024748892
-0.143763597
-0.106103628
-0.07793579
-0.156696233
-0.130883448
0.251388758
-0.039105057
-0.148694399
-0.141208532
-0.085122771
-0.215324228
-0.863534711
0.648210483
-0.167459512
-0.156938417

Actual excess returns. difference
-0.123407935
-0.056903123
-0.01841594
0.082286916
-0.255031356
-0.10332682
-0.126619427
0.073221286
-0.199840713
-0.229003919
-0.251238329
-0.179369574
-0.199530637
0.020161062
-0.122077843
-0.115508983
0.106328829
-0.088846907
0.006727146
-0.121587706
-0.060740296
-0.194462054
-0.162001769
-0.101006374
-0.019097282
-0.192583065
-0.11371838
-0.112959
-0.117231596
-0.126071621
-0.141585137
0.024571987
-0.094955832
-0.112391658
-0.104779586
-0.192228594
-0.179385981
-0.012842612
-0.127194474
-0.15212843

-0.073128329
-0.047168269
-0.008645592
0.085320801
-0.135683798
-0.011339106
0.021334619
0.042911419
-0.021577233
-0.071187702
-0.118079394
0.007460469
0.058650336
-0.051189867
-0.005546771
0.076607741
0.097964082
0.047225451
0.128191423
-0.018485076
0.042488261
-0.059480416
0.026084171
-0.016526426
0.00565161
-0.048819468
-0.007614752
-0.03502321
0.039464637
0.004811827
-0.392973894
0.063677044
0.053738567
0.028816875
-0.019656815
0.023095634
0.684148729
-0.661053095
0.040265039
0.004809987

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