comp.fundamental and equity returns indian markets
TRANSCRIPT
Electronic copy available at: http://ssrn.com/abstract=1247717
1
Submission Cover 21st Australasian Finance and Banking Conference
1. Title
Company Fundamentals and Equity Returns in India 2. Primary Author Dr. Vanita Tripathi
3. Co-Authors (separate with comma) 4. Prizes Select the prizes for which you would like to be considered (you may pick more than one). (For more information about prizes please see the conference web site: www.banking.unsw.edu.au/afbc) Prize Yes/No
Barclay's Global Investors Australia Prize Yes
BankScope Prize No
Sirca Research Prize No Australian Securities Exchange Prize No
5. Journals Select the journals for which you would like to be considered (you may pick more than one). Journal Yes/No Journal of Banking and Finance Yes Journal of Financial Stability No 6. Conference Proceedings
Yes/No Would you like your paper (if accepted) to be published by World Scientific Publishing Co Ltd as a review volume compiling selected papers?
Yes
Electronic copy available at: http://ssrn.com/abstract=1247717
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Company Fundamentals and Equity Returns in India
Author:
Dr. Vanita Tripathi
Senior Lecturer
Department of commerce
Delhi School of Economics
University of Delhi
Delhi-110007
Telephone: 91-011-27667891
9213269951
Email: [email protected]
Date of submission: May 13,2008
JEL Classification Number: G12, G14
Keywords: Size Effect, Value effect, P/E effect, Leverage effect, CAPM, Asset
pricing.
Acknowledgements:
The author is thankful to Indian Council of Social Science Research (ICSSR)
New Delhi for providing financial support to carry out this study
Abstract
This paper examines the relationship between four company fundamental variables (viz.
market capitalization, book equity to market equity ratio, price earnings ratio and debt
equity ratio) and equity returns in Indian stock market using monthly price data of a
Electronic copy available at: http://ssrn.com/abstract=1247717
3
sample of 455 companies forming part of S&P CNX 500 Index over the period June 1997
to June 2007. We also investigate whether the inclusion of any one or more of these
fundamental variables can better explain cross sectional variations in equity returns in
India than the single factor CAPM. We find that market capitalization and price earnings
ratio have statistically significant negative relationship with equity returns while book
equity to market equity ratio and debt equity ratio have statistically significant positive
relationship with equity returns in India. The investment strategies based on these
variables produced extra risk adjusted returns over the study period. Using Davis Fama
and French(2000) methodology we find that Fama-French three factor model ( based on
market risk premium, size premium and value premium) explains cross sectional
variations in equity returns in India in a much better way than the single factor CAPM.
These results have important implications for market efficiency, asset pricing and market
microstructure issues in Indian stock market.
.
4
Company Fundamentals and Equity Returns in India
Abstract
This paper examines the relationship between four company fundamental variables (viz.
market capitalization, book equity to market equity ratio, price earnings ratio and debt
equity ratio) and equity returns in Indian stock market using monthly price data of a
sample of 455 companies forming part of S&P CNX 500 Index over the period June 1997
to June 2007. We also investigate whether the inclusion of any one or more of these
fundamental variables can better explain cross sectional variations in equity returns in
India than the single factor CAPM. We find that market capitalization and price earnings
ratio have statistically significant negative relationship with equity returns while book
equity to market equity ratio and debt equity ratio have statistically significant positive
relationship with equity returns in India. The investment strategies based on these
variables produced extra risk adjusted returns over the study period. Using Davis Fama
and French(2000) methodology we find that Fama-French three factor model ( based on
market risk premium, size premium and value premium) explains cross sectional
variations in equity returns in India in a much better way than the single factor CAPM.
These results have important implications for market efficiency, asset pricing and market
microstructure issues in Indian stock market.
5
Company Fundamentals and Equity Returns in India
I INTRODUCTION
In an emerging stock market like India, investment analysts and market participants are
continuously in search for investment strategies that can outperform the market. Efficient
Market Hypothesis (EMH) rules out the possibility by anybody to consistently earn extra
normal return in an efficient stock market. According to this hypothesis securities are
correctly priced and return is solely determined by the amount of risk one assumes (as per
the standard Capital asset Pricing Model – CAPM). However a plethora of empirical
studies doubts such a phenomenon and documents the availability of extra normal returns
by using investment strategies based on firm specific variables such as size (Banz
(1981)), leverage (Bhandari (1988)), price earnings ratio (Basu (1977)), book equity to
market equity ratio (Stattman (1980), Rosenberg, Reid and Lanstein (1985)) etc. These
empirical evidences have been commonly cited as anomalies to CAPM based on
company fundamentals and popularly known as the size effect (small capitalization
stocks outperform large capitalization-stocks), leverage effect (high debt-equity stocks
outperform low debt-equity stocks), Price Earnings Effect (low P/E stocks outperform
high P/E stocks) and value effect (high book equity to market equity stocks outperform
low book to market equity stocks).
Two schools of thought have emerged in search for possible explanation of persistent
departure from the standard CAPM. One argument is that CAPM is mis specified; there
is/are some missing risk factor(s) which beta fails to capture. Hence there is a move
towards multifactor asset pricing framework as specified by Fama and French (1996).
The other school blames the investors' irrationality for the existence of the phenomenon.
Whatever be the cause, the presence of these CAPM anomalies provide gainful
investment opportunities to the investing community. The robustness of size and value
effects in US stock market motivated Fama and French (1992, 1993, 1996) to suggest the
inclusion of a size and value factor in asset pricing model. A number of research studies
have explored the economic feasibility of investment strategies based on fundamental
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variables, but most of these studies relate to US and other mature markets. Similar
evidence for emerging markets including India is limited and more recent in origin.
As a result of financial sector reforms initiated since early 1990s the Indian stock market
has witnessed metamorphic changes as regards to the size, structure and turnover. With
more than 4700 listed companies, 20 millions shareowners and a market capitalization of
Rs.30,257,720 million (in 2005-06) developments in Indian stock markets are now
comparable to those in other mature markets. Hence there is a felt need for a study which
can examine the relationship between various company fundamentals and equity returns
in Indian stock market in this changed regime and test for the economic feasibility of
fundamentals based investment strategies in the advent of technological up gradation.
The results of the study are of pertinent use by investment analysts, mutual fund
managers as well as marginal investors in devising fundamentals based investment
strategies to earn extra-normal returns in Indian stock market.
II RESEARCH OBJECTIVES
The primary objectives of the study are :
� to examine the relationship between four company fundamentals (size, leverage,
P/E ratio and Book to market equity ratio) and equity returns in India.
� to test whether the investment strategies based on these company fundamentals
yield any extra risk adjusted returns in Indian stock market.
� to check whether the inclusion of any or more of these fundamental variables can
better explain cross sectional variations in average equity returns in India. In
other words whether a multifactor model can better explain cross-sectional
variations in equity returns in India or not.
The study also attempts to examine the following research issues :
� Whether arbitrage opportunities are available in Indian stock market.
� Whether company fundamentals can explain variation in average stock return in a
better way than market factor in Indian context.
III RESEARCH HYPOTHESES
Following hypotheses have been tested in the study –
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I. Regarding company fundamentals and equity returns in India.
(i) There is a statistically significant relationship between various company
fundamentals and equity returns in India.
(ii) Stocks of small companies outperform the stocks of large companies in
Indian stock market.
(iii) Low P/E stocks outperform the stocks of high P/E stocks.
(iv) High BE/ME stocks outperform low BE/ME stocks.
(v) Stocks of companies with high D/E ratio outperform the stocks of low
D/E ratio companies.
(vi) The investment strategy based on company size yields extra normal
returns in Indian stock market.
(vii) The investment strategy based on P/E ratio of companies yields extra
normal returns in Indian stock market.
(viii) The investment strategy based on BE/ME ratio of companies yields extra
normal returns in Indian stock market.
(ix) The investment strategy based on D/E ratio of companies yields extra
normal returns in Indian equity market.
II. Regarding cross sectional variations in equity returns in Indian stock market.
(x) Company size can better explain cross sectional variations in equity
returns in Indian stock market than market factor.
(xi) P/E ratio can better explain cross sectional variations in equity returns in
Indian stock market than market factor.
(xii) BE/ME ratio can better explain cross sectional variations in equity returns
in Indian stock market than market factor.
(xiii) D/E ratio can better explain cross sectional variations in equity returns in
Indian stock market than market factor.
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(xiv) A two factor model can better explain cross sectional variations in equity
returns in Indian stock market than the single factor CAPM.
(xv) A three factor model can better explain cross sectional variations in equity
returns in India than single factor CAPM or two factor model.
(xvi) A four factor model can better explain cross sectional variations in equity
returns in Indian stock market than any of the single factor, two or three
factors model.
(xvii) A five factor model (based on excess market return, size premium, P/E
risk premium value premium and leverage risk premium) can better
explain cross sectional variations in equity returns in Indian stock market
than any of the single factor, two factors, three factors or four factors
model.
IV DATA AND THEIR SOURCES
The data comprises of monthly closing adjusted share prices of 455 listed
companies/stocks in India (as included in S&P CNX 500 index) over the most recent 10
years period June 1997 to June 2007 (See Annexure I for List of Sample Companies).
The monthly price data have then been converted into monthly return data using the
following equation :
( )
( )1ti
1tiit
itP
PPR
−
−−=
for i = 1 to 455 for t = 1 to 120 (1)
where
Rit = Return on stock i in the month t
Pit = Closing adjusted share price of stock i in month t
Pi(t-1) = Closing adjusted share price of stock i in month t-1.
This gives us a monthly return series of 120 observations for every stock (or company).
Monthly return on market portfolio (proxied by S&P CNX Nifty) have also been
calculated using equation (1) except that in place of closing adjusted share prices we have
used closing Index Values.
9
Rate of returns on 91-days Treasury Bills has been used as a proxy for risk free return
and S&P CNX NIFTY, a broad based market index has been used as a proxy for the
market portfolio. The study also uses various accounting and financial information
regarding the sample companies such as market capitalization, P/E ratio, BE/ME ratio
and D/E ratio. The data have been primarily collected from PROWESS (a financial
database of Centre for Monitoring Indian Economy) and web sources such as rbi.org,
sebindia.com and nseindia.com.
It is important to mention here that the entire data set (regarding four company
fundamentals as well as closing adjusted share prices) was not available for all sample
companies throughout the sample period of 10 years. Hence effective number of
companies used in the analysis ranges from 295 to 455.
V OPERATIONAL DEFINITIONS OF VARIOUS COMPANY
FUNDAMENTALS USED IN THE STUDY
As mentioned earlier we have used four company fundamentals in the study. The
selection of these fundamentals is based on the fact that robust CAPM anomalies have
already been detected in developed countries using these variables.
Table 1 provides operational definitions of various company fundamentals used in the
study.
VI RESEARCH METHODOLOGY
Internationally accepted methodology as used by Davis Fama and French (2000) and
Chan, Hamao and Lakonishok (1991) has been used to test various research hypotheses
regarding relationship between company fundamentals and equity returns.
(i) Construction of Portfolios
In June-end of year T all the sample companies are ranked on the basis of size (measured
by market capitalization : MC). The ranked sample companies are then divided into 5
equally weighted portfolios namely P1MC, P2MC, P3MC, P4MC and P5MC. P1MC is
the smallest sized portfolio consisting of 20 percent of companies with lowest size while
P5MC consists of top 20 percent companies with largest size. The process is repeated
10
using P/E ratio, BE/ME ratio and D/E ratio as the sorting variable. Since the study uses
four company fundamental variables (MC, P/E, BE/ME and D/E) there are four sets of 5
portfolios each or in total 20 portfolios. Portfolios sorted on the basis of P/E ratio have
been specified as P1PE (lowest), P2PE, P3PE, P4P3 and P5PE (highest). Portfolios sorted
on the basis of BE/ME ratio are named as P1BEME (lowest), P2BEME, P3BEME,
P4BEME and P5BEME (highest), while those sorted on the basis of D/E ratio are
specified as P1DE (lowest), P2DE, P3DE, P4DE and P5DE (highest).
Portfolios are rebalanced on annual basis. Then monthly equally weighted returns on all
portfolios including market portfolio (proxied by S&P CNX NIFTY) have been
calculated from July 1997 till June 2007 giving a total of 120 monthly observations. The
relationship between company fundamentals and stock returns has been tested using time
series regression as implied in the famous market model equation i.e.
( ) tftmtppftpt eRRbaRR +−+=− (for t = 1 to 120) (2)
(for p = 1 to 20)
where
ftpt RR − = Excess return on portfolio i.e. return on portfolio P minus risk for return in
month t.
ftmt RR − = Excess return on market portfolio in month t.
ap = Intercept term
bp = Slope coefficient (or beta coefficient) of the market factor.
et = error term
It must be mentioned here that if ap = 0 then equation (2) reduces to Black Jensen Scholas
(1972) version of single factor CAPM. The null hypothesis is that there are no extra
normal returns earned on portfolios sorted on the basis of various company fundamentals
which is equivalent to testing ap = 0 for all sorted portfolios. The alternate hypothesis is
ap ≠ 0. The hypothesis is tested at 5 percent level of significance.
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In order to test whether the investment strategy based on company fundamentals yields
any extra normal returns in Indian equity market, equation (2) is estimated for the
following portfolios.
(i) Portfolio consisting of long position in P1MC and a short position in P5MC
which is SMB (small minus big) i.e. size based investment strategy.
(ii) Portfolio consisting of long position in P1PE and short position in P5PE and
which is LMH (low minus high) i.e. the P/E ratio based investment strategy.
(iii) Portfolio consisting of long position in P5BEME and short position in P1BEME
which is HML (high minus low) i.e. BE/ME ratio based investment strategy.
(iv) Portfolio consisting of long position in P5DE and short position in P1DE which is
LEVG (high leverage minus low leverage) i.e. leverage or D/E ratio based
investment strategy.
In order to test whether inclusion of any one or more of the four company fundamentals
(viz. Market capitalization : MC, Price Earnings ratio : P/E, Book equity to market
equity ratio : BE/ME and Financial Leverage : D/E ratio) can better explain cross
sectional variations in average equity returns in Indian stock market we have used the
methodology followed by [Davis, Fama and French (DFF) : 2000] with the following
modifications.
(i) DFF (2000) constructed and used only nine portfolios based on size and book to
market equity. We have constructed, and used 20 portfolios based on size, P/E
ratio, book to market equity ratio and D/E ratio.
(ii) DFF (2000) used the following 3 factors and tested Fama-French three factor
asset pricing model equation :
Factors used by DFF (2000)
(a) Market Risk Premium = (RM – RF)
(b) Size Premium = SMB = Return differential between small & large firms
portfolios.
(c) Value Premium = HML (High Minus Low) = Return differential between high
BE/ME stocks portfolio and low BE/ME stocks portfolio.
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Instead we have used the following five factors :
Factors used in the present study
(a) Market Risk Premium = FM RR −
(b) Size Premium = SMB (Small Minus Big) = Monthly Return differential between
PIMC (Smallest Stocks Portfolio) and P5MC (Largest Stocks Portoflio).
(c) P/E risk premium = LMH (Low Minus High) = Monthly return differential
between PIPE (lowest P/E stocks portfolio) and P5PE (highest P/E stocks
portfolio).
(d) Value risk premium = HML (High Minus Low) = Monthly return differential
between P5BEME (Highest BE/ME stocks portfolio) and P1BEME (Lowest
BE/ME stocks portfolio)
(e) Leverage risk premium = LEVG = Monthly Return differential between P5DE
(Highest D/E stocks portfolio) and PIDE (Lowest D/E stocks portfolio).
Then we have estimated the following first pass time series regression equations for each
portfolio over the 120 months between July 1997 – June 2007. The standard notations
used in equations (3 to 33) are given below :
ptR = Portfolio return in month t
ftR = Risk free return in month t
mtR = Return on market portfolio in month t
SMBt = Size risk premium in month t
LMHt = P/E risk premium in month t
HMLt = Value premium in month t
LEVGt= Leverage risk premium in month t
a = Intercept
b = slope coefficient of market risk premium i.e. beta
s = Slope coefficient or factor loading of size risk premium
p = Slope coefficient or factor loading of P/E risk premium
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h = Slope coefficient or factor loading of value risk premium
λ = Slope coefficient or factor loading of leverage risk premium
et = error term
Statistically significant values of slope coefficient of various factors would indicate that
those factors are important in explaining cross sectional variations in portfolio returns
otherwise not. Moreover whether independent variable(s) in a particular model
significantly explain cross sectional variations in equity portfolio returns or not can be
detected by looking at its adjusted R2 value. The higher the value of adjusted R
2 the
greater is the explanatory power of the independent variable(s) included in the model.
I. Single Factor Model
Here one independent factor is used to estimate portfolio excess returns i.e. the dependent
variable. We have used all four company fundamentals separately for this purpose and
compared the results with the results of the single factor market model.
(i) Market alone
( ) tftmtftpt eRRbaRR +−+=− for t = 1 … 120 (3)
p = 1 … 20
(ii) Size alone
( ) ttftpt eSMBsaRR ++=− (4)
(iii) P/E risk premium alone
( ) ttftpt eLMHpaRR ++=−
(5)
(iv) Value premium alone
( ) ttftpt eHMLhaRR ++=−
(6)
(v) Leverage risk premium alone
( ) ttftpt eLEVGaRR ++=− λ (7)
II. Two Factor Model :
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Here we have used two independent variables to estimate portfolio excess returns i.e. the
dependent variable.
(i) Market and Size
( ) ( ) ttftmtftPt eSMBsRRbaRR ++−+=− (8)
(ii) Market and P/E risk premium
( ) ( ) ttftmtftPt eLMHpRRbaRR ++−+=− (9)
(iii) Market and Value Premium
( ) [ ] tftmtftpt eHMLthRRbaRR ++−+=− (10)
(iv) Market and Leverage (D/E ratio) risk premium
( ) ( ) ttftmftpt eLEVGRRbaRR ++−+=− λ (11)
(v) Size and P/E risk premium
[ ] [ ] tttftpt eLMHpSMBsaRR +++=− (12)
(vi) Size and value premium
[ ] [ ] tttftpt eHMLhSMBsaRR +++=− (13)
(vii) Size and Leverage risk premium
[ ] [ ] tttftpt eLEVGSMBsaRR +++=− λ (14)
(viii) P/E risk premium and value premium
[ ] [ ] tttftpt eHMLhLMHpaRR +++=− (15)
(ix) P/E risk premium and leverage premium
[ ] [ ] tttftpt eLEVGLMHpaRR +++=− λ (16)
(x) Value premium and leverage risk premium
[ ] [ ] tttftpt eLEVGHMLhaRR +++=− λ (17)
III. Three Factor Model
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Here we have included three independent factors to explain portfolio excess returns (i.e.
the dependent factor).
(i) Market, Size and P/E risk premium
[ ] [ ] [ ] tttftmtftpt eLMHpSMBsRRbaRR +++−+=− (18)
(ii) Market, Size and value premium
[ ] [ ] [ ] tttftmtftpt eHMLhSMBsRRbaRR +++−+=− (19)
This is the famous Fama-French three factor asset pricing model equation.
(iii) Market, Size and Leverage
[ ] [ ] [ ] tttftmtftpt eLEVGSMBsRRbaRR +++−+=− λ (20)
(iv) Market, P/E and value premium
( ) ( ) ( ) tttftmtftpt eHMLhLMHpRRbaRR +++−+=− (21)
(v) Market, P/E and Leverage premium
( ) ( ) ( ) tttftmtftpt eLEVGLMHpRRbaRR +++−+=− λ (22)
(vi) Market, Value and Leverage Premium
( ) ( ) ( ) tttftmtftpt eLEVGHMLhRRbaRR +++−+=− λ (23)
(vii) Size, P/E and value premium
( ) ( ) ( ) ttttftpt eHMLhLMHpBMBsaRR ++++=− (24)
(viii) Size, P/E and Leverage premium
( ) ( ) ( ) ttttftpt eLEVGLMHpSMBsaRR ++++=− λ (25)
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(ix) Size, Value and Leverage premium
( ) ( ) ( ) ttttftpt eLEVGHMLhSMBsaRR ++++=− λ (26)
(x) P/E, Value and Leverage Premium
( ) ( ) ( ) ttttftpt eLEVGHMLhLMHpaRR ++++=− λ (27)
IV. Four Factor Model
Here we have included four independent variables to explain the dependent variable i.e.
portfolio excess returns.
(i) Market, Size, P/E and Value Premium
( ) ( ) ( ) ( ) ttttftmtftpt eHMLhLMHpSMTsRRbaRR ++++−+=− (28)
(ii) Market, Size, Value and Leverage Premium
( ) ( ) ( ) ( ) ttttftmtftpt eLEVGHMLhSMBsRRbaRR ++++−+=− λ (29)
(iii) Market, Size, P/E and Leverage
( ) ( ) ( ) ( ) ttttftmtftpt eLEVGLMHpSMBsRRbaRR ++++−+=− λ (30)
(iv) Market, P/E, Value and Leverage Premium
( ) ( ) ( ) ( ) ttttftmtftpt eLEVGHMLhLMHpRRbaRR ++++−+=− λ (31)
(v) Size, P/E, Value and Leverage
( ) ( ) ( ) tttttftpt eLEVGHMLhLMHp)SMB(saRR +++++=− λ (32)
V. Five Factor Model
Here we have included all five factors under study as independent variables to estimate
the portfolio excess returns (i.e. dependent variable).
The estimated regression equation is
( ) ( ) ( ) ( ) ( ) tttttftmtftpt eLEVGHMLhLMHpSMBsRRbaRR +++++−+=− λ (33)
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We have used Statistical Package for Social Sciences (SPSS) and Excel for the purpose
of data analysis.
VII EMPIRICAL RESULTS
Table 2 presents cross correlation matrix of fundamental variables used in the study. As
is evident there is positive but low relationship between size and P/E ratio.
There is negative but low relationship between size and D/E ratio; and size and BE/ME
ratio.
However a statistically significant positive relationship exists between D/E ratio and
BE/ME ratio; and a statistically significant negative relationship exists between D/E ratio
and P/E ratio and BE/ME ratio and P/E ratio. Thus it may be said that in Indian context
BE/ME ratio, P/E ratio and D/E ratio tend to capture almost similar firm characteristics.
VIIa Relationship Between Company Fundamentals and Equity Returns in Indian
Stock Market
First of all the relationship between four company fundamentals ((viz. market
capitalization, P/E ratio, BE/ME ratio and debt equity ratio) and average stock returns are
analysed using correlation coefficients. The results are presented in Table 2. It can be
observed that there exists a
(i) statistically significant negative relationship between company size and average
stock returns over the study period.
(ii) Statistically significant negative relationship between P/E ratio and average stock
returns over the study period.
(iii) Statistically significant positive relationship between BE/ME ratio and average
stock returns over the study period.
(iv) Statistically significant positive relationship between Debt Equity ratio and
average stock returns over the study period.
These results are further substantiated by constructing various portfolios on the basis of
these four company fundamentals and then analyzing the pattern of mean monthly
returns.
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Table 3 provides summary statistics of monthly excess returns of all 20 portfolios sorted
on the basis of four company fundamentals, while Table 4 provides results of the market
factor model.
(i) Regarding Company Size and Equity Returns
The results regarding size sorted portfolios are presented in Panel A of Table 3 and Panel
A of Table 4. It is clearly visible that mean monthly excess returns of smallest size
portfolio (PIMC) is much higher than that of largest sized portfolio (P5MC). The mean
excess return of PIMC was found to be 3.34 percent per month as against 1.02 percent
per month for P5MC. This clearly provides a size premium (the return differential
between PIMC and P5MC) of 2.32 percent per month (t-value 5.800) or about 24 percent
per annum which is quite robust. However the standard deviation of PIMC is also higher
than that of P5MC pointing towards the intuitive fact that small firms are more risky than
their large counterparts.
Panel A of Table 4 presents the results of the market model equation used to check for
the relationship between company size and equity returns in Indian stock market. It is
clear that intercept value (i.e. a) decline monotonically as one moves from PIMC to
P5MC. The smallest sized portfolio has provided an extra normal return of 3.06 percent
per month over the study period as revealed by its "a" value which is statistically
significant (t-value 2.573 as against its critical value of 1.96). Thus we can reject null
hypothesis (i.e. ap = 0) as intercept value for this portfolio is positive and statistically
significant. The same is true for P2MC. However as one moves from P1MC to P5MC
there has been a sharp decline in intercept value and for P3MC, P4MC and P5MC we do
not find any statistically significant extra normal returns. These findings indicate that the
stocks of small firms outperformed those of large firms over the study period. These
results are in line with the results presented earlier by Mohanty (2001) Sehgal &
Muneesh (2002), Sehgal and Tripathi (2005) and Tripathi(2007) for Indian stock market.
A look at the R2 value reveals the fact that market factor is important in capturing a large
amount of variation in equity returns especially for the large stocks portfolios. It is
important to note here that R2 value (coefficient of determination) is low for small stocks
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portfolio (e.g. 50.5 percent for PIMC as against 63.1 percent for P5MC) suggesting that
the portfolio of small stocks have larger unexplained variations in their returns.
The slope coefficient "b" (i.e. commonly known as beta coefficient) of all the portfolios
have been statistically significant but there has been no substantial difference between the
beta coefficient of small and large stocks portfolios. This might indicate that market risk
of small firms is not substantially higher than that of large firms.
(ii) Regarding Price Earnings Ratio (P/E ratio) and Equity Returns
These results are presented in Panel B of Table 3 and Panel B of Table 4. It is clear that
low P/E stocks provided a statistically significant mean monthly excess return of 3.01
percent (t value 3.040) as against 1.33 percent per month by high P/E stocks portfolio
over the study period. The mean monthly excess return declines as one moves from PIPE
to P5PE. However as was the case with size based portfolios, portfolio returns of low P/E
stocks have also shown higher standard deviation (or variability) than those of high P/E
stocks. The LMH (low minus high) risk premium based on P/E ratio has been found to be
a statistically significant 1.68 percent per month (t value 3.111) or about 20 percent per
annum over the study period. If one looks at the intercept values of the market model
results presented in Panel B of Table 4, one finds that the "a" values decline
monotonically as one moves from PIPE to P5PE, showing that low P/E stocks portfolio
provided the investors with statistically significant extra risk adjusted returns over the
study period. The lowest P/E stocks portfolio i.e. PIPE provided an extra risk adjusted
return of 2.17 percent per month (t value 2.879) as against 0.45 percent per month (t
value 1.015) on highest P/E stocks portfolio.
(iii) Regarding Book Equity to Market Equity Ratio (BE/ME Ratio) and Equity
Returns
The summary statistics and market model results of portfolios sorted on the basis of
BE/ME ratio are presented in Panel C of Table 3 and Panel C of Table 4 respectively. As
expected mean monthly excess return of high BE/ME stocks portfolio (P5BEME) is
much larger and statistically significant (3.06 percent per month with t value 3.091) than
that of low BE/ME stocks portfolio (P1BEME : 1.49 percent per month with t value
1.886). Moreover the standard deviation of high BE/ME stocks portfolio is also higher
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than that of low BE/ME stocks portfolio. The intercept value "a" as shown in Panel C of
Table 4 also increases monotonically from 0.67 per cent per month (t value 1.434) for
P1BEME to 2.23 percent per month (t value 2.957) for P5BEME suggesting that high
BE/ME stocks portfolio generated higher risk adjusted extra return during the study
period. The value premium (i.e. the return differential between P5BEME and P1BEME)
is as high as 1.57 percent per month (t value 2.492) which is also statistically significant.
Hence we can conclude that during the study period a strong value effect existed in the
Indian stock market. However the intensity of this effect is slightly lower as found by
Muneesh Kumar and Sehgal (2004) and Sehgal and Tripathi (2007).
(iv) Regarding Debt-Equity Ratio (D/E ratio) and Equity Returns
Bhandari (1988) found leverage effect in equity returns implying that stocks of firms
having high financial leverage provide higher risk adjusted returns than those of firms
having low financial leverage. The results of our analysis regarding financial leverage (as
measured by Debt Equity ratio) and equity returns in India are presented in Panel D of
Table 3 and Panel D of Table 4.
Panel D of Table 3 shows that mean monthly excess return of high D/E stocks portfolio
(P5DE) has been 2.71 percent (t value 2.823) as against 1.40 percent (t value 1.750) on
low D/E stocks portfolio (PIDE). As expected the standard deviation of high D/E stocks
portfolio is also higher than that of low D/E stocks portfolio. The return differential
between high and low D/E stocks portfolio, popularly known as leverage risk premium
(LEVG) has been found to be 1.31 percent per month (t value 2.673) which is also
statistically significant.
Panel D of Table 4 shows that the intercept terms 'a' of P3DE, P4DE and P5DE are
higher and statistically significant than those of PIDE and P2DE. The extra normal return
of P5DE is 1.86 percent per month (t value 2.845) as against 0.61 percent per month (t
value 1.186) for PIDE. This suggests that during the study period stocks of high financial
leverage firms outperformed those of low financial leverage firms implying the presence
of a "leverage effect" in the Indian stock market.
A peculiar feature of all the above results has been that the slope coefficients (or beta
coefficients) of all portfolios have been statistically significant but R2 values have been
lower for PIMC, PIPE, P5BEME and P5DE portfolios and high for P5MC, P5PE,
21
PIBEME and PIDE portfolios suggesting that portfolios of small capitalization stocks,
low P/E stocks, high BE/ME stocks and high D/E stocks have larger unexplained
variations in their returns than those of large capitalization stocks, high P/E stocks, low
BE/ME stocks and low D/E stocks, although market factor has been important in
capturing cross sectional variations in average stock returns of all portfolios.
VIIb Economic Evaluation of Company Fundamentals based Investment Strategy
The statistically significant relationship between company fundamentals and equity
returns in India gives rise to arbitrage opportunities which can be used to earn extra
returns on risk adjusted basis in Indian stock market. Table 5 presents results regarding
the extra returns on a risk adjusted basis which can be generated by investment strategies
based on four company fundamentals viz. Market capitalization, P/E ratio, BE/ME ratio
and D/E ratio. It can be observed that size based investment strategy generated a
statistically significant extra normal return of 2.43 percent per month (t value 2.273), P/E
ratio based investment strategy provided 1.71 percent per month (t value 3.157), BE/ME
based strategy gave 1.56 percent per month (t value 2.474) and D/E ratio based strategy
provided the investors with an extra normal return of 1.25 percent per month (t value
2.502) over the study period.
The fact that all these investment strategies generated statistically significant extra risk
adjusted returns points towards the fact that arbitrage opportunities were present in
Indian stock market during the study period.
VIIc : Cross sectional variations in Equity returns
The empirical results regarding the role of company fundamentals in explaining cross
sectional variations in equity returns in Indian stock returns are presented in Table 4 and
from Table 6 to 10.
It is clearly visible from Table 4 that market factor (excess return on market portfolio)
captures the most part of cross-sectional variations in equity returns in India, but not all.
Moreover Panel A to D of Table 6 shows that no other factor (be it size premium, P/E
risk premium, value premium or leverage premium) can capture any significant portion
of cross sectional variations in average equity returns, in isolation, as all other single
factor models have very low R2 values as compared to the single factor market model.
22
Hence we conclude that the company fundamentals, per se, are not capable of explaining
cross sectional variations in equity returns in India. They must be clubbed with market
factor (or some other independent variable) to check whether a multifactor model can
better explain cross sectional variations in equity returns in India or not.
The results regarding two factor model based on market and size factors are presented in
Table 7. It can be observed that there has been considerable improvement in adjusted R2
value when both excess market return and size premium are used as independent
variables. This can also be confirmed by the fact that the slope coefficient of size
premium i.e. s is statistically significant for all 20 portfolios while all (except six)
intercept values i.e. 'a' values are very low and not statistically significant. Hence we
conclude that size and market factors together can better explain cross sectional
variations in equity returns in India than the market factor alone.
As far as other company fundamentals are concerned we found an improvement in
adjusted R2 value when they are used in addition to the market factor but such an
improvement has not been as large as the one produced by market and size factors. Hence
detailed results are not provided here.
Regarding various three factor models, Fama French three factor model (based on market
, size and value premium) turned out to be the best in explaining cross sectional
variations in equity returns in India. The results of this model are presented in Table 8.
These results are in line with those found by Connor and Sehgal(2003).
In case of various four factor models the one based on market, size, P/E and value
premium provides the best results as shown in Table 9.However here adjusted R2 values
have improved only marginally as compared to the three factor model based on market,
size premium and value premium. This might be due to the overlapping effect of value
and P/E risk premium in Indian context.
Finally, the results of the five factor model have been provided in Table 10. It is clearly
visible that the five factor model does not show any substantial improvement in
explaining cross sectional variations in equity returns in India over three or four factor
models, as adjusted R2
values have improved only marginally with the inclusion of two
additional factors (P/E risk premium and leverage premium).
23
VIII SUMMARY OF THE RESEARCH RESULTS
On the basis of the empirical results presented in this paper, following conclusions may
be drawn.
(i) There existed a statistically significant negative relationship between company
size (Market Capitalisation) and equity returns in India over the study period. The
smallest stocks portfolio (PIMC) outperformed largest stocks portfolio and
provided the investors with an extra risk adjusted return of 3.06 percent per month
(t value 2.573) as against 0.63 percent per month (t value 1.329) on P5MC i.e.
largest stocks portfolio. The size premium (i.e. the return differential between
smallest and largest stocks portfolios) has been found to be 2.32 percent per
month (t value 5.800) over the study period which is quite robust.
(ii) There existed a statistically significant negative relationship between P/E ratio
and equity returns in India over the study period. The lowest P/E ratio stocks
portfolio (PIPE) outperformed the highest P/E stocks portfolio (P5PE) and
provided the investors with an extra risk adjusted return of 2.17 percent per month
(t value 2.879). The P/E risk premium (i.e. the return differential between PIPE
and P5PE) has been found to be statistically significant over the study period
(1.68 percent per month with t value 3.111).
(iii) There existed a statistically significant positive relationship between BE/ME ratio
and equity returns in India over the study period. The highest BE/ME stocks
portfolio outperformed the lowest BE/ME stocks portfolio. The highest BE/ME
stocks portfolio (P5BEME) produced an extra risk adjusted return of 2.23 percent
per month (t value 2.957) as against 0.67 percent per month (t value 1.434) on
P1BEME i.e. the lowest BE/ME stocks portfolio. The HML premium or value
premium (i.e. the return differential between P5BEME and P1BEME) has been
found to be 1.57 percent per month (t value 2.492) which is also statistically
significant.
(iv) There existed a statistically significant positive relationship between D/E ratio and
equity returns in India over the study period. The highest D/E stocks portfolio
(P5DE) outperformed the lowest D/E stocks portfolio (PIDE) and provided an
24
extra risk adjusted return of 1.86 percent per month (t value 2.845) as against 0.61
percent per month (t value 1.186) on lowest D/E stocks portfolio i.e. PIDE. The
leverage risk premium has been found to be statistically significant at 1.31 percent
per month (t value 2.673) over the study period.
(v) The investment strategies based on size, P/E ratio, BE/ME ratio and D/E ratio
would have provided the investors with statistically significant extra risk adjusted
returns of 2.43 percent (t value 2.273), 1.71 percent (t value 3.157), 1.56 percent
(t value 2.474) and 1.25 percent (t value 2.502), respectively over the study
period. It shows that opportunities are available for Indian investors to earn extra
returns on a risk adjusted basis by following investment strategies based on
company fundamentals.
(vi) Excess market return has been found to be an important factor in explaining cross
sectional variations in equity returns in India although it is not capable of
explaining all such variations. However none of the company fundamentals, in
isolation, could explain cross sectional variations in equity returns in India in any
significant way. It implies that other company fundamentals should be added to
the asset pricing model in order to explain cross-sectional variations in equity
returns in India in a better way.
(vii) The three factor model based on market, size premium and value premium
(Popularly known as Fama-French Multifactor asset Pricing Model) explained
cross-sectional variations in equity returns in India in a much better way than the
single factor CAPM or any two factor model. Four factors or five factors models
did not improve the results regarding cross-sectional variations in equity returns
in India in any significant manner and hence we may conclude that the three
factor Fama-French model works well in Indian context.
IX POLICY IMPLICATIONS OF THE FINDINGS
The findings of this research paper have important policy implications and are of
pertinent use for equity analysts, fund managers and investing community at large.
25
(i) Implications for Market Efficiency : We have found a statistically significant
relationship between four company fundamentals (viz. market capitalization, P/E
ratio, BE/ME ratio and D/E ratio) and equity returns in India over the study period
of 1997-2007. This implies that a strong size effect, P/E effect, value effect and
leverage effect existed in Indian stock market over the most recent ten years
period. This further implies that Indian stock market is still not semi strong
efficient because publically available financial information can be used to earn
extra risk adjusted return in Indian stock market. Although the intensity or
robustness of these effects have been lower than those detected by earlier studies
during the decade of 1990s. Hence although the efficiency level has been
increasing in Indian stock market, it has still not become fully semi-strong
efficient.
(ii) Implications for Investment Strategies : Presence of strong size effect, P/E
effect, value effect and leverage effect are indicative of the fact that arbitrage
opportunities are available in Indian stock market and gainful investment
strategies can be formulated and used by equity analysts, fund managers and
investing community at large based on these company fundamentals. Since the
research results are of the most recent ten years period their utility gets further
enhanced in this context.
(iii) Implications for Asset Pricing Framework
a. We have found that no single factor asset pricing model (be it based on market
risk premium or any of the company fundamentals) works well in explaining
cross sectional variations in equity returns in India. Hence more factors should
be included in the asset pricing framework. We have found that addition of
two company fundamentals (viz. size premium and value premium) in the
asset pricing model can substantially explain cross-sectional variations in
equity returns in India. This lends further support to the Fama French three
factor asset pricing model in Indian stock market in a recent time period.
b. Contrary to Fama & French (1996) we have found that market risk premium is
still ‘the’ most important independent factor in asset pricing framework
although its relative importance has substantially declined since the decade of
26
1980’s or 1990’s. This implies that company fundamentals are gaining
importance in explaining cross sectional variations in equity returns in India.
(iv) Implications for Market Microstructure : The findings also have important
implications for market microstructure aspects as we have found the presence of
strong size effect, P/E effect, value effect and leverage effect on National Stock
Exchange (i.e. the prominent exchange having much higher turnover than that of
Bombay Stock Exchange). Earlier studies have found the presence of size and
value effect on Bombay Stock Exchange (Sehgal and Tripathi (2005,2007). This
implies that unlike Reinganum (1990) market microstructural aspects do not
affect the relationship between company fundamentals and equity returns in India
in any substantial manner.
27
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Tripathi V, 2007, Size Effect in Indian Stock Market, Serials Publications, New Delhi.
29
Table 1
Operational Definitions of Various Company Fundamentals
used in the Study
S.No. Fundamental
Variable
Measured by
1. Size Market capitalization (MC) as on June end every year
2. Price Earnings
ratio
Price Earnings ratio (P/E ratio) as on June end every year
3. Book Equity to
Market Equity Rate
Book equity to market equity ratio (BE/ME ratio) as on
June end every year. This is calculated as inverse of Price
to Book value ratio (PB ratio) provided by PROWESS
database as on that date.
4. Financial leverage Debt equity ratio (D/E ratio) as on March end every year
Table 2
Cross Correlation-Matrix of Various Fundamental Variables and average Portfolio
Returns
[Pearson's coefficient of correlation]
D/E P/E BE/ME Average Portfolio Return
MC -0.209 .414 -.307 -.716**
D/E - -0.608** +.897** .821**
P/E - - -.764** -0.816**
BE/ME +0.765**
Note : Correlations are calculated across portfolios over the study period.
** Significant at 5% level
30
Table 3
Summary Statistics of monthly excess returns of Portfolios sorted on the basis of
various company fundamentals
(Total Period July 1997- June 2007)
Panel A : Size Based (Firm Size increases as one moves from
P1MC to P1MC)
Portfolio Mean SE (Mean) t(Mean) S.D.
P1MC .0334 .0085 3.929* .0986
P2MC .0245 .0088 2.784* .0967
P3MC .0237 .0088 2.693* .0964
P4MC .0127 .0084 1.512 .0924
P5MC .0102 .0077 1.325 .0848
SMB (P1MC-P5MC) .0232 .0040 5.800* .0442
Panel B : P/E Ratio Based (P/E ratio increases as one moves from P1PE to P5PE)
Portfolio Mean SE (Mean) t(Mean) S.D.
P1PE .0301 .0099 3.040* .1089
P2PE .0241 .0081 2.975* .0883
P3PE .0206 .0082 2.512* .0902
P4PE .0160 .0083 1.927 .0907
P5PE .0133 .0081 1.6419 .0891
LMH (P1PE-P5PE) .0168 .0054 3.111* .0588
*Significant at 5 percent level
Panel C : BEME Ratio Based (BEME ratio increases as one moves from P1BEME
to P5BEME)
Portfolio Mean SE (Mean) t(Mean) S.D.
P1BEME .0149 .0079 1.886 .0868
P2BEME .0195 .0088 2.216* .0908
P3BEME .0171 .0084 2.036* .0924
P4BEME .0243 .0085 2.858* .0930
P5BEME .0306 .0099 3.091* .1084
HML (P1BEME-P5BEME) .0157 .0063 2.492* .0685
*Significant at 5 percent level
Panel D : Financial Leverage or D/E ratio based (D/E ratio increases as one moves
from P1DE to P5DE)
Portfolio Mean SE (Mean) t(Mean) S.D.
P1DE .0140 .0080 1.750 .0877
P2DE .0151 .0080 1.887 .0873
P3DE .0212 .0082 2.585* .0898
P4DE .0240 .0086 2.791* .0943
P5DE .0271 .0096 2.823* .1056
LEVG (P5DE-P5DE) .0131 .0049 2.673* .0543
31
Table 4
Results of the Market Model
Rpt – Rft = a + b (RMt – Rft) + et
Panel A : Portfolios sorted on the basis of Size (MC)
Portfolio a B t(a) t(b) Adj R – Square
P1MC .0306 .932 2.573* 11.068* .505
P2MC .0163 .973 2.643* 11.303* .516
P3MC .0053 1.010 1.600 12.341* .560
P4MC .0082 1.016 1.317 12.904* .618
P5MC .0063 .943 1.329 14.310* .631
Panel B : Portfolios sorted on the basis of P/E Ratio
Portfolio a B t(a) t(b) Adj R – Square
P1PE .0217 1.008 2.879* 9.613* .434
P2PE .0167 .890 2.957* 11.335* .517
P3PE .0127 .948 2.314* 12.439* .563
P4PE .0101 .986 1.925 13.494* .603
P5PE .0045 1.042 1.015 16.675* .700
Panel C : Portfolios sorted on the basis of BE/ME Ratio
Portfolio a B t(a) t(b) Adj R – Square
P1BEME .0067 .9850 1.434 15.153* .658
P2BEME .0110 1.018 1.207 14.639* .642
P3BEME .0091 .958 1.595 12.076* .549
P4BEME .0166 .920 2.74* 10.929* .499
P5BEME .0223 .993 2.957* 9.439* .425
Panel D : Portfolio sorted on the basis of D/E Ratio
Portfolio a B t(a) t(b) Adj R – Square
P1DE .0061 .947 1.186 13.257* .595
P2DE .0123 .942 1.398 13.231* .594
P3DE .0132 .960 2.478* 12.929* .583
P4DE .0156 1.003 2.770* 12.786* .577
P5DE .0186 1.023 2.845* 10.481* .478
*Significant at 5 percent level
32
Table 5
Evaluation of Investment Strategy Based on Various Company Fundamentals
Strategy based on ‘a’ differential t (‘a’ differential)
MC .0243 2.273*
P/E Ratio .0171 3.157*
BE/ME Ratio .0156 2.474*
D/E Ratio .0125 2.502*
* Significant at 5% level.
33
Table 6
Single Factor Model Regression Results
Panel A : Size as Independent Factor
( ) ttftpt eSMBbaRR ++=−
Portfolio a s t(a) t(s) Adj. R2
P1MC .0151 .90 2.904 5.099 .174
P2MC .0184 .662 2.133 3.453 .082
P3MC .0189 .524 2.160 2.687 .050
P4MC .0172 .369 2.029 1.95 .023
P5MC .0151 -.100 1.904 -.569 -.006
P1PE .0242 .643 2.459 2.934 .060
P2PE .0199 .459 2.474 2.563 .045
P3PE .0165 .446 2.003 2.434 .040
P4PE .0147 .401 1.763 2.163 .030
P5PE .0096 .403 1.17 2.22 .032
P1BEME .0105 .480 1.336 2.738 .052
P2BEME .0158 .404 1.899 2.179 .031
P3BEME .0135 .394 1.589 2.087 .027
P4BEME .0200 .458 2.362 2.426 .039
P5BEME .0249 .458 2.362 2.426 .039
P1DE .0094 .497 1.187 2.813 .055
P2DE .0156 .492 1.187 2.813 .055
P3DE .0177 .385 2.144 2.097 .028
P4DE .0196 .475 2.281 2.482 .042
P5DE .5224 .504 2.326 2.344 .036
*all t values above 1.96 statistically significant.
34
Panel B : P/E Risk Premium as Independent Factor
( ) ttftpt eLMHpaRR ++=−
Portfolio a p t(a) t(p) Adj. R2
P1MC .0131 .609 1.590 4.502 .139
P2MC .0150 .561 1.734 3.948 .109
P3MC .0151 .513 1.729 3.579 .090
P4MC .0130 .454 1.545 3.276 .076
P5MC .0062 .474 .811 3.781 .108
P1PE .0121 1.068 1.429 7.671 .327
P2PE .0143 .585 1.84 4.596 .145
P3PE .0122 .496 1.505 3.716 .097
P4PE .0117 .395 1.400 2.880 .058
P5PE .0121 .0683 1.429 .490 -.006
P1BEME .0149 .013 1.801 .010 -.008
P2BEME .0138 .339 1.637 2.444 .040
P3BEME .0075 .568 .919 4.216 .129
P4BEME .0123 .714 1.549 5.496 .197
P5BEME .0139 .990 1.602 6.914 .282
P1DE .0093 .278 1.135 2.059 .027
P2DE .0134 .399 1.675 3.027 .064
P3DE .0126 .512 1.564 3.865 .015
P4DE .0143 .575 1.705 4.179 .122
P5DE .0128 .848 1.445 5.823 .217
*all t values above 1.96 statistically significant.
35
Panel C : Value Premium as Independent Factor
( ) ttftpt eHMLhaRR ++=−
Portfolio a h t(a) t(h) Adj. R2
P1MC .0148 .543 1.836 4.709 .151
P2MC .0171 .469 1.996 3.825 .103
P3MC .0162 .476 1.905 3.904 .107
P4MC .0138 .434 1.684 3.609 .096
P5MC .0065 .485 .893 4.629 .147
P1PE .0167 .856 1.93 6.942 .218
P2PE .0147 .599 2.00 5.708 .210
P3PE .0132 .470 1.670 4.146 .120
P4PE .0127 .357 1.553 3.037 .065
P5PE .0113 .127 1.352 1.070 .001
P1BEME .0157 -0.50 1.928 -.433 -.007
P2BEME .0148 .303 1.777 2.552 .044
P3BEME .0088 .523 1.111 4.573 .143
P4BEME .0135 .683 1.793 6.326 .247
P5BEME .0157 .950 1.928 8.144 .354
P1DE .0102 .243 1.259 2.097 .028
P2DE .0147 .344 1.865 3.040 .065
P3DE .0138 .477 1.748 4.242 .125
P4DE .0149 .573 1.859 4.981 .167
P5DE .0150 .772 1.744 6.280 .244
*all t values above 1.96 statistically significant.
36
Panel D : Leverage as Independent Factor
( ) ttftpt eLEVGaRR +==− l
Portfolio a l t(a) t(l) Adj. R2
P1MC .0157 .584 1.892 3.910 .107
P2MC .0175 .534 2.010 3.412 .082
P3MC .0159 .597 1.858 3.878 .106
P4MC .0129 .592 1.58 4.025 .113
P5MC .0066 .580 .886 4.338 .130
P1PE .0174 .970 1.934 5.994 .227
P2PE .0156 .650 2.043 4.731 .152
P3PE .0143 .480 1.758 3.274 .075
P4PE .0119 .490 1.46 3.328 .078
P5PE .0093 .300 1.132 2.017 .025
P1BEME .0127 .174 1.595 1.188 .003
P2BEME .0146 .378 1.748 2.521 .043
P3BEME .0101 .534 1.222 3.590 .091
P4BEME .0139 .786 1.793 5.612 .204
P5BEME .0173 1.017 1.967 6.420 .253
P1DE .0128 .0875 1.557 .589 -.006
P2DE .0145 .429 1.830 3.03 .063
P3DE .0135 .590 1.707 4.145 .120
P4DE .0148 .695 1.827 4.741 .153
P5DE .0128 1.088 1.557 7.321 .307
*all t values above 1.96 statistically significant.
37
Table 7
Results of Two Factor Model based on Market and Size
( ) ( ) ttftmtftPt eSMBsRRbaRR ++−+=−
Portfolio a b s t(a) t(b) t(s) Adj.R2
P1MC .0070 .942 .926 1.439 14.264 8.652 .691
P2MC .0090 .980 .690 1.76 12.738 5.535 .672
P3MC .0101 1.0160 .553 1.824 13.382 4.49 .694
P4MC .0084 1.021 .398 1.654 14.619 3.520 .732
P5MC .0069 .942 -.073 1.438 14.264 -.688 .815
P1PE .0154 1.015 .671 2.148 10.349 4.224 .721
P2PE .0122 .895 .484 2.248 12.119 4.045 .710
P3PE .0083 .953 .473 1.575 13.294 4.074 .690
P4PE .0061 .991 .429 1.207 14.317 3.825 .670
P5PE .0005 1.046 .433 .128 18.141 4.634 .721
P1BEME .0020 .991 .508 .462 16.931 5.36 .731
P2BEME .0070 1.023 .433 1.462 15.654 4.092 .732
P3BEME .0052 .963 .422 .929 12.670 3.423 .752
P4BEME .0121 .926 .485 2.059 11.580 3.741 .631
P5BEME .0163 1.000 .648 2.249 10.101 4.036 .693
P1DE .0012 .953 .525 .255 14.609 4.963 .726
P2DE .0075 .948 .519 1.560 14.555 4.914 .739
P3DE .0093 .964 .413 1.808 13.629 3.598 .732
P4DE .0109 1.008 .504 2.031 13.746 4.237 .728
P5DE .0136 1.029 .533 1.989 11.038 3.528 .731
*all t values above 1.96 statistically significant.
38
Table 8
Three Factor Model Results based on Market, Size & Value Premium
[ ] [ ] [ ] tttftmtftpt eHMLhSMBsRRbaRR +++−+=−
Portfolio a b s h t(a) t(b) t(s) t(h) Adj.R2
P1MC .000 .938 .859 .486 .001 18.545 10.436 9.148 .822
P2MC .0038 .976 .631 .424 .761 14.445 5.740 5.973 .701
P3MC .0038 1.012 .492 .439 .785 15.419 4.601 6.37 .717
P4MC .0026 1.017 .405 .342 .588 16.874 3.486 6.406 .740
P5MC .000 .938 .486 -.141 .001 18.545 9.148 -1.717 .783
P1PE .0037 1.007 .558 .815 .746 15.016 5.111 11.578 .768
P2PE .0040 .890 .405 .568 .985 16.317 4.564 9.931 .767
P3PE .0020 .949 .412 .438 .441 15.63 4.174 6.864 .723
P4PE .0014 .988 .384 .326 .306 15.619 3.727 4.909 .703
P5PE -.0008 1.046 .420 .0943 -.190 18.238 4.503 1.567 .747
P1BEME .0032 .992 .521 -.089 .747 17.025 5.496 -1.456 .725
P2BEME .0031 1.020 .395 .272 .679 16.709 3.980 4.238 .724
P3BEME -.0019 .95 .353 .459 -.409 15.320 3.465 7.529 .720
P4BEME .0027 .920 .394 .652 .649 16.472 4.336 11.131 .780
P5BEME .0032 .991 .521 .911 .747 17.025 5.495 14.901 .824
P1DE -.0017 .951 .496 .206 -.368 15.113 4.844 3.119 .686
P2DE .0030 .945 .476 .308 .681 15.893 4.917 4.935 .717
P3DE .0029 .960 .35 .448 .667 16.285 3.65 7.247 .737
P4DE .0032 1.00 .428 .540 .757 17.892 4.696 9.177 .784
P5DE .0030 1.022 .43 .7738 .599 15.223 3.938 10.466 .753
*all t values above 1.96 statistically significant.
39
Table 9
Four Factor Model Regression Results based on Market, Size, P/E & Value
( ) ( ) ( ) ( ) ttttftmtftpt eHMLhLMHpSMTsRRbaRR ++++−+=−
Portfolio a b s p h t(a) t(b) t(s) t(p) t(h) Adj.R2
P1MC -.001 .94 .82 .22 .32 -.27 18.85 9.97 1.92 .322 .83
P2MC .002 .99 .57 .40 .13 .41 14.96 5.26 2.56 1.03 .71
P3MC .002 1.02 .45 .23 .26 .56 15.58 4.23 1.5 2.04 .72
P4MC .001 1.02 .31 .21 .25 .36 17.04 3.14 1.54 2.07 .74
P5MC -.001 .95 -.17 .22 .32 -.27 18.85 -2.08 1.92 3.22 .79
P1PE -.0003 1.04 .43 .89 .17 -.07 18.06 4.56 6.58 1.50 .83
P2PE .003 .89 .39 .04 .53 .92 16.22 4.38 .38 4.87 .76
P3PE .001 .96 .38 .21 .28 .23 15.78 3.82 1.47 2.37 .73
P4PE .0002 .99 .34 .26 .13 .05 15.87 3.34 1.80 1.07 .71
P5PE -.003 1.04 .43 -.11 .17 -.07 18.06 4.56 -.79 1.50 .75
P1BEME .0020 1.00 .485 .259 -.276 .476 17.32 5.075 1.91 -2.398 .73
P2BEME .001 1.03 .36 .26 .08 .42 16.96 3.58 1.80 .71 .73
P3BEME .003 .97 .31 .30 .27 -.70 15.65 3.04 2.06 2.25 .73
P4BEME .001 .93 .36 .23 .48 .39 16.72 3.94 1.778 4.38 .78
P5BEME .002 1.00 .48 .25 .72 .47 17.32 5.07 1.91 6.29 .83
P1DE -.002 .96 .46 .21 .05 -.56 15.26 4.49 1.40 .45 .69
P2DE .001 .95 .43 .29 .09 .38 16.25 4.48 2.01 .84 .73
P3DE .001 .97 .31 .26 .26 .39 16.57 3.25 1.90 2.23 .74
P4DE .002 1.00 .41 .13 .45 .61 17.90 4.41 .97 3.99 .78
P5DE .001 1.04 .37 .42 .43 .21 15.82 3.43 2.73 3.32 .77
*all t values above 1.96 statistically significant.
40
Table 10
Five Factor Model Results based on Market, Size Value, P/E and Leverage
( ) ( ) ( ) ( ) ( ) tttttftmtftpt eLEVGHMLhLMHpSMBsRRbaRR +++++−+=− λ
Portfolio a B s h p l t(a) t(b) t(s) t(h) t(p) t(l) Adj.R2
P1MC -.0012 .942 .833 .300 .215 .05779 -.329 18.523 9.962 2.833 1.7780 .637 .825
P2MC .0019 .989 .579 .124 .393 .0315 .379 14.707 5.237 .884 2.479 .262 .713
P3MC .0022 1.01 .472 .213 .209 .140 .452 15.285 4.342 1.5 1.344 1.185 .721
P4MC .0009 1.010 .329 .178 .186 .212 3.324 16.766 1.415 1.257 1.723 .748 .732
P5MC -.0012 .942 -.167 .300 .214 .0579 -.329 18.523 -1.998 2.834 1.790 .636 .787
P1PE -.0009 1.028 .45 .111 .857 .163 -.216 17.767 4.732 .920 6.283 1.571 .833
P2PE .0034 .885 .407 .499 .0306 .0884 .832 15.917 4.448 4.313 .234 .889 .765
P3PE .0012 0.962 .378 .309 .224 -.0601 .277 15.646 3.736 2.41 1.54 -.546 .724
P4PE -.0002 .988 .358 .088 .241 .120 -.046 15.561 3.43 .668 1.609 1.056 .709
P5PE .0001 1.028 .450 .111 -.143 .163 -.216 17.7767 4.732 .919 -1.049 1.571 .749
P1BEME .0013 .987 .502 -.345 .220 .184 .319 17.046 5.278 -2.865 1.614 1.773 .736
P2BEME .0019 1.031 .359 .0902 .260 -0.010 .428 16.731 3.542 .703 1.788 -.698 .727
P3BEME .0031 .975 .306 .301 .313 -.0612 -.650 15.525 2.959 2.302 2.118 -.544 .726
P4BEME .009 .914 .379 .416 .193 .183 .232 16.453 4.151 3.594 1.477 1.836 .7788
P5BEME .0013 .987 .502 .655 .220 .184 .319 17.047 5.278 5.429 1.614 1.773 .831
P1DE -.0010 .993 .426 .220 .3 -.434 -.234 16.649 4.343 1.772 2.134 -.4060 .725
P2DE .0015 .953 .439 .083 .282 .0407 .347 15.969 4.479 .667 2.007 .381 .723
P3DE .0013 .96 .326 .214 .235 .123 .292 16.26 3.35 1.736 1.692 1.159 .743
P4DE .0019 .994 .428 .379 .0899 .180 .453 17.630 4.616 3.232 .678 1.786 .788
P5DE -.0010 .993 .426 .22 .300 .566 -.234 16.649 4.343 1.773 2.135 5.302 .811
*all t values above 1.96 statistically significant.