Download Fama EF and French KR (1996) Multifactor explanations of asset

Chapter I
INTRODUCTION
This research gave an overview of the most widely used theories in asset pricing and
some more recent developments. The aim of these theories was to determine the fundamental
value of an asset. As in the first section there was a close relation between fundamental and
market variables and an appropriate return. The main focus of asset pricing theories was to
determine this appropriate return. This chapter provides empirical investigations presented in
very short, citing the results of the most prominent works. This chapter is divided into
following sub sections:1.1 Asset Pricing Model
1.2 Single Factor Model
1.3 Multifactor Model
1.4 Benefits of Multifactor Model
1.5 Types of Multifactor Model
1.6 Application of Multifactor Model
1.7 Three Factor Model
1.1 Asset Pricing Model
Asset pricing models are models for the pricing of financial assets. It is interesting in
itself to be able to model and understand the pricing mechanisms in the seemingly complex
financial markets, but it is also important for a number of financial problems faced by
individuals and corporations such as:
Asset allocation: How individual and institutional investors combine various financial
assets into portfolios;

The measurement and management of financial risks, e.g. in banks and other financial
institutions;

Capital budgeting decision in firms;

Capital structure decisions in firms;

The identification and possible resolution of potential conflicts of interest between the
stakeholders of a firm, e.g. shareholders vs. creditors, shareholders vs. managers.
The Capital Asset Pricing Model (CAPM) is the best known asset pricing model. The
key message of the model is that the expected excess return on a risky financial asset is given
by the product of the market-beta of the asset and the expected excess return on the market
portfolio.
Elements of asset pricing models are:-
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1. Assets
For potential investors the important characteristics of a financial asset or any other
investment opportunity are its current price and its future payments which the investor will be
entitled to if they buy the asset. Stocks deliver dividends to owners. The dividends will surely
depend on the well being of the company.
2. Investors
In reality, only a small part of the trading in financial markets is executed directly by
individuals while the majority of trades are executed by corporations and financial institutions
such as pension funds, insurance companies, banks, broker firms, etc. However, these
institutional investors trade on behalf of individuals, either customers or shareholders. In our
basic models we will assume that all investors are individuals and ignore the many good
reasons for the existence of various intermediaries.
3. Equilibrium
For any given asset, i.e. any given dividend process, the aim is to characterize the
reasonable price or the set of reasonable prices. A price is considered reasonable if the price is
an equilibrium price. An equilibrium is characterized by two conditions: (1) supply equals
demand for any asset, i.e. markets clear, (2) any investor is satisfied with her current position
in the assets given her personal situation and the asset prices.
4. The time span of the model
As discussed above, the important ingredients of all basic asset pricing models are the
dividends of the assets available for trade and the utility functions, current wealth, and future
incomes of the individuals that can trade the assets. There are three types of asset pricing
models:
One-period model: All action takes place at two points in time, the beginning of the
period and the end of the period. Assets pay dividends only at the end of the period
and are traded only at the beginning of the period. The aim of the model is to
characterize the prices of the assets at the beginning of the period.

Discrete-time model: All action takes place at a finite number of points in time.

Continuous-time model: The continuous-time model is a multi-period model and can
potentially capture the dynamics of asset prices.
One thing that even advanced investors tend to overlook in their asset pricing model
is the inherent limitations in using valuation to forecast future prices. This lack of awareness
has led to the proliferation of a wide array of different valuation models that while might be
good at assessing intrinsic value, are the most part worthless in projecting actual future value.
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1.2 Single Factor Model
Capital Asset Pricing Model is a relationship explaining how assets should be priced
in the capital markets. CAPM postulates that in a perfect market, where shares are correctly
priced, every security will give a return commensurate with its risk. Rational investors
demand compensation for taking higher risks. So, higher risk securities should be priced to
yield higher expected returns. The CAPM has two components of the capital market return,
which are:
Reward for waiting or riskless return.

The reward per unit of risk borne as measured by the slope of the CML line.
The capital asset pricing model (CAPM) postulates that the variation in stock returns
is solely determined by the market beta. However, several empirical studies show that the
CAPM market beta has very little relation to stock returns (Reinganum 1981; Breeden et al
1989; Fama and French 1992) while a number of studies document relationships between
returns and variables such as size (market capitalization), book to market (BM) ratio, and past
returns. The size effect was first documented by Banz (1981) and Reinganum (1981), who
found a return premium on small stocks in the USA. The BM effect was first documented by
Rosenberg et al (1985), who found a return premium to stocks with high ratios of book value
to market value of equity.
Assumptions of CAPM are:
Aim to maximize economic utilities.

Are rational and risk-averse.

Are broadly diversified across a range of investments.

Are price takers, i.e., they cannot influence prices.

Can lend and borrow unlimited amounts under the risk free rate of interest.

Trade without transaction or taxation costs.

Deal with securities that are all highly divisible into small parcels.

Assume all information is available at the same time to all investors.
The CAPM is a single-index model that defines systematic risk in relation to a broad-
based market portfolio (i.e., the market index). Systematic (market or macroeconomic) risk is
the risk that affects all firms to some degree: external events such as recessions, expansion,
interest rates, world events, etc. Systematic (market or macroeconomic) risk usually accounts
for about 25% of a typical stock’s total risk. The CAPM is used to estimate a stock’s risk
premium and required rate of return. This single factor (“beta”) is unchanging:
Rj = Rf + Risk Premium
or
Rj = Rf + Bj (Rm – Rf)
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where, Rj = expected return on an asset or portfolio
Rf = risk-free rate of return
Rm = expected return on the market
Bj = volatility of the asset or portfolio to that of the market m.
The CAPM has several advantages over other methods of calculating required return,
explaining why it has remained popular for more than 40 years:
It considers only systematic risk, reflecting a reality in which most investors have
diversified portfolios from which unsystematic risk has been essentially eliminated.

It generates a theoretically-derived relationship between required return and
systematic risk which has been subject to frequent empirical research and testing.

It is generally seen as a much better method of calculating the cost of equity than the
dividend growth model (DGM) in that it explicitly takes into account a company’s
level of systematic risk relative to the stock market as a whole.

It is clearly superior to the WACC in providing discount rates for use in investment
appraisal.
The model does not appear to adequately explain the variation in stock returns.
Empirical studies show that low beta stocks may offer higher returns than the model would
predict. The model assumes that investors demand higher returns in exchange for higher risk.
It does not allow for investors who will accept lower returns for higher risk. The model
assumes that all investors agree about the risk and expected return of all assets. The model
assumes that there are no taxes or transaction costs, although this assumption may be relaxed
with more complicated versions of the model. The market portfolio consists of all assets in all
markets, where each asset is weighted by its market capitalization. This assumes no
preference between markets and assets for individual investors, and that investors choose
assets solely as a function of their risk-return profile. The market portfolio should in theory
include all types of assets that are held by anyone as an investment (including works of art,
real estate, human capital, etc). In practice, such a market portfolio is unobservable and
people usually substitute a stock index as a proxy for the true market portfolio.
1.3 Multifactor Model
Multiple factor models (MFMs) which attempt to describe asset returns and their
covariance matrix as a function of a limited number of risk attributes, stand out in the modern
portfolio theory (MPT). The cornerstone of MPT, developed by Harry Markowitz (1952), is
mean–variance portfolio theory. Multi-factor model is a financial model that employs
multiple factors in its computations to explain market phenomena. The multi-factor model can
be used to explain either an individual security or a portfolio of securities. It will do this by
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comparing two or more factors to analyze relationships between variables and the security’s
resulting performance. A multi-factor model is a modeling tool that is used to identify the
underlying reasons for shifts in pricing and other market events. A capital asset pricing model
of this type can be applied to an individual security or utilized in relation to an entire
portfolio. This is accomplished by analyzing the relationships between applicable variables
that result in the performance of that security or group of securities, and will always involve
no less than two specific factors. Understanding the relationship between these variables is
understood to provide valuable clues that can aid investors in making sound decisions
regarding the future disposition of those securities.
1.4 Benefits of Multifactor Model
One of the chief benefits of a multi-factor model is the ability to help an investor
select securities that are ideally suited for the type of portfolio that he or she wishes to
develop. For example, if the investor wants to target investment opportunities that provide a
particular range of monetary return while carrying a risk that is no more than a specified level,
this model can make it easier to identify those securities. Investors that wish to vary
investments in terms of risk level applying this approach can aid in creating the desired
balance within the portfolio. Multi-factor models are advantageous because they allow the
reduction of the variance-covariance matrix needed to analyze large portfolios and they allow
the identification of each factor`s contribution to the portfolio performance.
1.5 Types of Multifactor Model
While there are multiple classifications for a multi-factor model, many investment
professionals identify three basic kinds or classes:
A macroeconomic model often considers factors such as current rates of interest,
the rate of inflation or recession, and the current level of unemployment.

A fundamental multi-factor model looks closely at the amount of return generated
by a given security and the value of its underlying assets.

With a statistical model, the focus is typically on the returns of each security that
is being considered, comparing and contrasting the performance of each.
1.6 Application of Multifactor Model
Applications of multifactor model include:
Risk measurement and estimation.

Risk management and hedging.

Factor-neutral strategies.
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
Trading and arbitrage.

Portfolio optimization.

Tailoring risk exposures.

Style analysis.

Performance evaluation.
1.7 Three Factor Model
It is apparent that the single-factor CAPM is no longer suitable to explain the
relationship between risk and return, but so far there is no universally accepted model to
replace it. The most ubiquitous model in the current finance literature is the Fama-French
three-factor model, henceforth the Fama French model which posits that the cross-section of
average returns can be explained by three factors:
1. The excess market return;
2. A size factor; and
3. A book-to-market equity factor.
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-tomarket ratio. They then added two factors to CAPM to reflect a portfolio's exposure to these
two classes:-
r = Rf + β3 ( Km – Rf ) + bs . SMB + bv . 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" β is analogous to the classical β 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.
Earlier research in empirical finance had shown that variables like dividend yields,
price-to-earnings (P/E) ratios, book-to-market ratios as well as past returns had significant
explanatory power for the variation in cross section of expected returns even after
controlling for market risk (Fama and French, 1992).
Blieberg [1994] employs aggregate data for future stock returns and average P/E ratio
to develop a market timing and asset allocation strategy. To this end, he grouped historical
average P/E ratios into quintiles and related them with future returns using S&P 500 index. In
this paper, he initially adopted a similar approach by grouping observed average P/E and
book-to-market ratios (PBV) into quintiles in 19 emerging equity markets and associating
them with 3-month, 6-month and 12-month ahead future returns. He also performed
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econometric tests on the panel data of emerging equity markets for the period between 1986
to 1999. The results indicated that both P/E and book-to-market ratios had predictive power of
future return, especially over longer time periods.
Dimson et al (2002) reported the best and worst realized real returns for each country
and asset class over the period covered. For the German stock market the minimum return of 89.6% in1948 was immediately followed by the maximum return of 155.9% in 1949.
If asset returns had systematic skewness, expected returns should include rewards for
accepting this risk. Harvey and Siddique (2002) formalized this intuition with an asset pricing
model that incorporated conditional skewness. Their results showed that conditional skewness
helped to explain the cross-sectional variation of expected returns across assets and was
significant even when factors based on size and book-to-market were included.
What can be concluded is that the returns from stock investments can be explained
with the help of both market factors as well as the accounting based fundamentals related to
the stocks, the relative importance of these factors however has been inconclusive. Moreover,
most of the research is confined to the US or other developed markets with emerging and
developing markets largely devoid of research inputs. In the light of these arguments, an
attempt is required to evaluate the contribution of accounting based fundamentals as well as
the market related factors in explaining the stock returns with a special reference to Indian
Stock Market. Specifically, the following objectives will be focused on:
1. To study the relationship between stock returns and selected accounting based
fundamental variables.
2. To study the relationship between stock returns and selected market variables.
The rest of this research is organized as follows. Section 2 relates the research to
previous literature. Section 3 introduces the construction of the stock returns, the data, and the
summary statistics, followed by evidence about the relationship between stock returns with
both market and fundamental variables. Section 4 shows results obtained to achieve the
objectives. Various statistical tools had been used for this purpose and section 5 concludes.
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Chapter II
REVIEW OF LITERATURE
A brief review of the relevant studies has been presented in this section:
Earlier evidence concerning the relation between stock returns and the effects of size
and earnings to price ratio (E/P) was not clear-cut. This paper re-examined these two effects
with a substantially longer sample period, 1951-1986, data that was reasonably free of
survivor biases, both portfolio and seemingly unrelated regression tests, and an emphasis on
the important differences between January and other months. Over the entire period, the
earnings yield effect was significant in both January and the other eleven months. Conversely,
the size effect was significantly negative only in January. Jaffe et al (1989) also found
evidence of consistently high returns for firms of all sizes with negative earnings.
Restoy and Rockinger (1994) presented general conditions under which it was
possible to obtain asset pricing relations from the intertemporal optimal investment decision
of the firm. Under the assumption of linear homogeneous production and adjustment cost
functions, it was possible to establish, state by state, the equality between the return on
investment and the market return of the financial claims issued by the firm. The result proved
to be, in essence, robust to the consideration of very general constraints on investment and the
inclusion of taxes.
Fama and French (1996) concluded that average returns on common stocks were
related to firm characteristics like size, earnings/price, cash flow/price, book-to-market equity,
past sales growth, long-term past return, and short-term past return. As these patterns in
average returns were not explained by the CAPM, they were known as anomalies. They found
that, except for the continuation of short-term returns, the anomalies largely disappeared in a
three-factor model. Their results were consistent with rational ICAPM or APT asset pricing,
but they also considered irrational pricing and data problems as possible explanations.
Ansari (2000) reviewed the content and scope of CAPM model, examined the issues
in the controversy and provided an empirical assessment of the model in India. He used data
relating to 96 stocks listed in the Bombay Stock Exchange over the period January 1990 –
December 1996. It was inferred that Beta leaves returns unexplained in India during the study
period. But the author concluded that it seemed too early to take a stand on the performance
of CAPM as an asset pricing model in India. More rigorous tests were warranted in this
regard. Only then the applicability of this model in the Indian context can be assured.
Bagella et al (2000) found that portfolio strategies based on low values of earning per
share (EPS), market to book value (MTBV), market value (MV) and return on equity (ROE)
significantly outperformed the index. They found that the significance of cross-sectional
determinants of these strategies was not absorbed by ex post betas. They were not riskier in
terms of monthly return standard deviations, covariation with GDP growth and their premia
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did not disappear when survivorship bias was taken into account. Portfolio mean monthly
returns (MMRs), regressed on several risk factors in 3-CAPM models, confirmed that S&V
strategy premia persist when risk adjusted. Empirical results also mark the difference between
ROE and MTBV portfolios, on the one side, and MV and EPS portfolios, on the other.
Descriptive statistics on preformation and postformation returns, average balance sheet values
and preformation standard deviations clearly showed that ROE and MTBV portfolios had a
common financial distress factor and were then more exposed to systematic risk.
Trecartin (2001) examined whether the book-to-market ratio consistently explained
the cross-section of stock returns through time. The results revealed that the book-to-market
ratio was positively and significantly related to return. Other value/growth variables such as
Cash Flow, Sales Growth and Size performed even more erratically than the book-to-market
ratio, and were thus less likely to be viewed as legitimate risk proxies.
Keith (2002) investigated the relation between stock returns and β, size (ME),
leverage, book-to-market equity ratio, and earning-to-price ratio (E/P) in Hong Kong stock
market using the Fama and French (FF) approach. Size, book-to-market equity, and earningto-price ratios, seemed able to capture the cross-sectional variation in average monthly returns
over the period. The other two variables, book leverage and market, were able to capture the
cross-sectional variation in average monthly returns. But their effects seemed to be dominated
by size, book-to-market equity, and earning-to-price ratios, and considered to be redundant in
explaining average returns when size, book-to-market equity, and earning-to-price ratios were
also considered. The results were consistent across sub periods, across months, and across
size groups. These suggested that the results were not driven by extreme observations or
abnormal return behavior in some of the months or by size groups.
Mohanty (2002) documented that it was found that the size (measured by market
capitalization), market leverage, price-to-book value, and earnings-to-price ratio were highly
correlated with stock returns. While size and price-to-book value were negatively correlated
with stock returns, earnings-to-price and market leverage were found to be positively
correlated with stock returns. The study also found a flat relationship between returns and
beta.
Pena and Gilana (2003) studied the suitability of the CAPM to the Spanish Stock
Market Interconnection System (SIBE) for the period 1988-2000, by means of time series and
cross-section multivariate tests. Even though there was no enough empirical evidence to reject
this model, it was shown that the relation between risk beta and stock returns is weak.
Therefore, they looked for several fundamental variables – using Fama and MacBeth OLS
(Ordinary Least Squares) and LTS (Least Trimmed Squares) estimators – which could
explain, with or without beta, the cross-section of stock returns. They concluded that there
was a strong earning-price ratio effect in the Spanish Stock Market and that beta was able to
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explain the cross-section of expected returns, not solely, but jointly with earning price ratio.
On the other hand, there was neither size nor book-to-market ratio effects.
Lewellen (2004) examined whether financial ratios like dividend yield could predict
aggregate stock returns or not. Predictive regressions were subjected to small-sample biases,
but the correction used by prior studies could substantially understate forecasting power. He
showed that dividend yield predicted market returns during the period 1946–2000, as well as
in various subsamples. Book-to-market and the earnings-price ratio predicted returns during
the shorter sample 1963–2000.
Stefanis (2005) showed that the P/E phenomenon also exists in the Athens Stock
Exchange (ASE). In respect to his resulted evidence, the ratio was found to be negatively
related to subsequent equity performance. Furthermore, accounting variables such as market
value and earnings growth play an important role in the explanation of the cross- sectional
variation of stock returns. The resulted evidence presented industry as being an indicative
factor of such accounting variables, as well as, past market returns to be negatively related to
subsequent stock performance.
Weighand and Irons (2005) identified a significant break in the stock return. They
started from market P/E ratios of 21 or greater, 10-year real returns were in line with their
long-term historical average, and real earnings growth was well above average. They modeled
this break in the data and included the effect of several macroeconomic factors which resulted
in forecasts of future returns that were considerably more optimistic than those of previous
studies. They also showed that the way investors use the Fed Model to benchmark the
earnings yield on stocks to the 10-year T-note yield has resulted in these two series becoming
co-integrated over time. The reciprocal of the E/P ratio, the market P/E, becomes nonstationary, which means that the P/E ratio can stay above trend for an indefinite period of
time. The market P/E no longer displays mean-reverting behavior, implying that high P/E
ratios could be with us for the long term.
Rahmani et al (2006) identified the variables affecting stock return and its price in the
emerging markets. According to CAPM, Beta (β) was the only variable capable of predicting
the return. The past studies demonstrated that there existed other variables which
outperformed stock return predictability potential of the Beta. Included among such variables
were the size, debt-to-equity, book-to-market, earnings-to-price and sale-to-price ratios. The
research was aimed at testing the above variables and Beta for the prediction of stock return in
order to recognize the variables which were better capable of predicting the stock return in
Tehran Stock Exchange (TSE).
Choudhary (2007) concluded that low market capitalization, P/E ratio and earnings
per share portfolios respectively earned better than high market capitalization, P/E ratio and
earnings per share portfolios, in terms of absolute and risk-adjusted rate of return.
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Penman et al (2007) demonstrated that enterprise book-to-price ratio was positively
related to
subsequent stock returns but, the leverage component of B/P was negatively associated with
future stock returns (conditional upon the enterprise book-to-price). Their work laid out a
decomposition of book-to-price (B/P) articulating precisely how B/P absorbed leverage. It
was found that The B/P ratio could be decomposed into an enterprise book-to-price that
pertained to operations and potentially reflected the operating risk and a leverage component
that reflected the financing risk. The empirical analysis showed that the enterprise book-toprice ratio was positively related to subsequent stock returns but, depending upon the
enterprise book-to-price, the leverage component of B/P was negatively associated with future
stock returns. The finding with respect to the leverage component of B/P survived under
controls for size, estimated beta, return volatility, momentum, and default risk.
Muradoglu and Sivaprasad (2008) investigated the effect of firm’s leverage on stock
returns. They started with the explicit valuation model of Miller and Modigliani (1958) and
expanded the model further to test the relation between stock returns and firms’ leverage.
Miller and Modigliani conducted their empirical tests exclusively in the utilities and oil and
gas industries. They conducted their tests in all risk classes. Miller and Modigliani conducted
their tests in the cross section for one year whereas they employ a rich panel dataset. They
used balance sheet definitions for return to equity while they use stock returns. They first
conducted the analysis at the firm level and then at the portfolio level to include factor
mimicking portfolios for size, book-to market, market risk and momentum. They found that
for utilities, returns increase in leverage and for the other sectors, the relationship was
negative. Results were robust to other risk factors and level of analysis. They concluded that
the contradicting empirical results in literature were mainly due to the restrictions in the
samples used.
Pagas et al (2008) applied a multifactor expected-returns model to estimate security
payoffs against factors related to various characteristics such as risk, price level, liquidity,
growth potential and previous performance. These payoffs were then used to estimate out-ofsample expected returns and to construct a ‘super stock’ portfolio. Their analysis suggested
that compared to the existing risk-factor models, an ‘expected-returns’ factor model exhibited
increased predictive power of expected returns and had consistently higher average realized
returns with lower average risk.
Tripathy (2008) studied 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. The study showed that market
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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.
Elleuch and Trabelsi (2009) examined whether a simple fundamental analysis
strategy based on historical accounting information could predict stock returns. The paper’s
goal was to show that simple screens based on historical financial signals could shift the
distribution of returns earned by an investor by separating eventual winners stocks from
losers. Results showed that historical accounting signals could be used to improve the entire
distribution of future returns earned by an investor. Despite the overall down activity of the
market over the sample period chosen, results revealed that fundamental accounting signals
could be used to discriminate from an overall sample generating future negative returns of a
winner portfolio that provided positive future return from a loser one generating a negative
return. The over-performance of the winner portfolio seemed to be attributable to the ability
of the fundamental signals to predict future earnings. Results showed that fundamental signals
had a positive and significant correlation with future earnings performance and that the
winner portfolio had a future earnings realization that outperformed that of the loser portfolio.
Gilbert et al (2009) aimed to confirm the existence of size, book to market and
momentum effects in the New Zealand stock market. They aimed to compare the performance
of the CAPM, the Fama-French model, and Carhart’s model in explaining the variation of
stock returns. They adapted the Fama and French methodology using a 2 x 3 size - book to
market ratio sort. They also formed three portfolios based on past returns to verify the
momentum effect. They found some improvement in explanatory power provided by the
Fama French model relative to the CAPM but it still leaves a large part of the variation in
stock returns unexplained. The Fama French model was also unable to explain the strong
momentum effect in New Zealand. Their findings implied that cost of capital estimated would
be more accurate using Carhart’s model. Portfolio managers could increase returns by
investing in small and high book to market firms that were recent winners. Performance
evaluation should take into account the size, book to market and momentum effect.
Karani (2009) established the relationship between the debt-equity ratio and the
expected common stock returns while controlling for beta and size of the firm. Similar studies
had been carried out in developed markets that had a confirmed that a statistically significant
positive relationship exists between the debt-equity ratio and the expected common stock
returns. The dependent variable in the study was the expected common stock returns while the
independent variables were the firm size, beta the risk measure and the debt-equity ratio. The
main objective was to determine whether the debt-equity ratio was positive. Secondary data
comprising of stock prices, dividends, financial statements of the listed companies and the
Nairobi stock exchange monthly 20 share index was obtained from Nairobi Stock exchange
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and analyzed using linear multiple regression for a period of 10 years, 1998 to 2007. The
results were inconclusive therefore there was no relationship that was found to exist between
the expected common stock returns and the debt-equity ratio in the Kenyan market. In the
Kenyan capital market, the debt-equity ratio of a firm was probably not a major factor to
consider when making investment decisions on common stock securities.
Khan (2010) studied the effects of P/E ratio and M/B ratio on stock return of listed
firms with Karachi Stock Exchange in the Textile sector of Pakistan. A total of 30 major firms
out of 162 in the textile sector listed with the Karachi Stock Exchange for the period of 20012006 were selected on the basis of their size in terms of total assets. Firms which have larger
size in terms of total assets among 162 firms were selected in this paper. The study revealed
that the firms in an exclusive sector exhibit unique attributes that were sector specific and
cannot be applied to or judged by combined analysis of the industry. The result showed that
coefficients of independent variables are statistically insignificant. This means that stock
return was not depending on any of the two independent variables. Besides insignificant
coefficients, coefficients of determination were also very low in each case. This means that a
very low percentage of change in stock return was explained by these two variables. The data
was analyzed by running linear regression. Two independent variables i.e. P/E ratio and M/B
ratio were selected to see their effects on stock return. Multiple regression models along with
a measure of correlation were used to study the effect of the independent variables on the
dependent variable. The results for the study revealed that stock return is independent of the
two independent variables studied in this paper.
The purpose of this paper was to investigate whether the current period earning
divided by stock price at the beginning of the stock market period, current period dividend
divided by stock price at the beginning of the stock market period, prior dividend divided by
stock price at the beginning of the stock market period and the reverse of stock price at the
beginning of the stock market period were relevant to explain stock market returns in Iran.
Ebrahimi and Chadegani (2011) used cross-section, pooled data and panel data regression
models for testing the effects of the above variables on stock returns. The results showed that
in some years, shareholders paid special attention to dividends and also the variable prior
dividend divided by stock price at the beginning of the stock market period affected stock
return. Moreover, there was a significant relationship between current period earning divided
by stock price at the beginning of the stock market period and stock return. Thus, results
theoretically supported the existence of relationship between earning, dividend and stock
return.
Khrawish et al (2010) examined the effect of interest rates on the stock market
capitalization rate in Amman Stock Exchange (ASE) over the period 1999-2008. Based on the
multiple linear regression model and simple regression model, the time series analysis
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revealed that there was significant and positive relationship between government prevailing
interest rate (R) and stock market capitalization rate (S). The study showed that Government
development stock rate (D) exerts negative influence on stock market capitalization rate (S),
also it found a significant and negative relationship between government prevailing interest
rate (R) and Government development stock rate (D).
Alroaia et al (2012) focused on two factors of return on stock and price-earnings ratio
and investigated the relationship between these two variables. In this study, the price-earnings
ratio and stock return were analyzed by the data of this ratio and the latest daily trading price
of the companies that in the calculation of stock return was used in April of 2001 to March of
2008 for 46 companies the member of sample population. By econometric tests, the validity
conditions of satisfaction of regression equation in the mentioned companies were analyzed.
The results of the regression indicated a positive and significant relationship between stock
return and price-earnings ratio; it means that this ratio was a significant variable to explain the
stock return.
Chan et al (2012) related cross-sectional differences in returns on Japanese stocks to
the underlying behavior of four variables: earnings yield, size, book to market ratio, and cash
flow yield. Alternative statistical specifications and various estimation methods were applied
to a comprehensive, high-quality data set that extended from 1971 to 1988. The sample
included both manufacturing and nonmanufacturing firms, companies from both sections of
the Tokyo Stock Exchange, and also delisted securities. Their findings revealed a significant
relationship between these variables and expected returns in the Japanese market. Of the four
variables considered, the book to market ratio and cash flow yield have the most significant
positive impact on expected returns.
Dash (2012) evaluated the pricing implication of unconditional five factor model to
explain the cross sectional stock return behavior in the context of Indian stock market. His
analysis aimed to examine the pricing nature of aggregate market wide sentiment risk in the
presence of other risk factors. He employed Fama and French time series regression approach
to examine the impact of market risk premium, size, book-to-market equity, momentum and
liquidity as risk factors on stock return. With the presence of liquidity factor in the five factor
model specification, the results suggested that liquidity is priced and explained a cross
sectional variation in stock returns.
Elisa et al (2012) presented a method of stock selection and evaluation based on
discriminant analysis. For this purpose, they investigated the cross-sectional relation between
fundamental and financial variables, besides the CAPM beta coefficient and the average stock
returns. They examined stocks traded on Sao Paulo Stock Exchange during the period January
2006 to December 2010. The results were quite satisfactory, as the discriminatory predictive
14
capacity obtained a level of success. They also concluded that the beta coefficient had
discriminatory capabilities.
Lalithakumari and Venugopal (2012) examined a thorough analysis about the high
degree of security for the principal amount, as well as the return, within an expected period of
time. The objectives of the study were to determine the risk return relationship of the portfolio
stocks, to analyze the performance of the portfolio based on the investment strategies and to
find out the relationship between the performance of the portfolio and the investment
strategies. The research is descriptive in nature. The sampling method used for the study was
stratified sampling. For selecting the sample, population was divided into various stratas
based on the market capitalization, earnings per share and price earnings ratio. The data taken
for the study was secondary and was collected from Bombay Stock Exchange website and
Kotak Securities database for a period of 6 years from 2005 to 2011. The tools used for
analysis were mean, standard deviation, covariance, Sharpe measure, Treynor measure and
Jensen measure. According to the market capitalization investment strategy, high market
capitalization portfolio were outperforming the low market capitalization portfolio. According
to the earnings per share investment strategy, high earnings per share portfolio was
outperforming the low earnings per share portfolio. According to the price earnings ratio
investment strategy, low price earnings ratio portfolio was outperforming the high price
earnings ratio portfolio.
Lioui and Maio (2012) derived a macroeconomic asset pricing model in which the
key factor was the opportunity cost of money. The results showed that the model explained
well the cross-section of stock returns in addition to the excess market return. The interest rate
factor was priced and seemed to drive most of the explanatory power of the model. In this
model, both value stocks and past long-term losers enjoyed higher average (excess) returns
because they had greater interest rate risk than growth/past winner stocks. The model
significantly outperformed the nested models (Consumption-CAPM and CAPM) and
compared favorably with alternative macroeconomic models.
15
Chapter III
RESEARCH METHODOLOGY
The present chapter describes the research methodology of the study. In order to
achieve the objectives of the study as given in chapter I, various tools were adopted. It
includes selection of sample, collection of data and choice of statistical tools. This chapter
explains in detail the research methodology in following sections:3.1 Research Framework
3.2 Population and sample
3.3 Variables used in the study
3.4 Collection of data
3.5 Analysis of data
3.6 Limitation of study
3.1 Research Framework
The main theme of this research had been conceptualized within a framework to
avoid a disorder or an ambiguity in the process of conducting the study. The research has
been done to study the relationship between stock return with fundamental and market
variables. For the purpose of completion of objectives, secondary information was selected.
3.2 Population and sample
The population for the research consisted of all the stocks listed on NSE and BSE.
The sample for the study was chosen from stocks from BSE Sensex. The index consist of 30
stocks. The list of listed stocks was obtained from Ludhiana Stock Exchange (LSE) and the
sample was selected from there.
3.3 Variables used in the study
The study was conducted using various variables as discussed below:3.3.1 Book to Market Value
Book to market ratio is a ratio used to find the value of a company by comparing the
book value of a firm to its market value. Book value is calculated by looking at the
firm's historical cost, or accounting value. Market value is determined in the stock
market through its market capitalization.
Book to market value =
Book value of firm
Market value per quarter
16
Where, Book value is taken per annum.
And, Market value is the closing price per quarter.
The book-to-market ratio attempts to identify undervalued or overvalued securities by
taking the book value and dividing it by market value. In basic terms, if the ratio is above 1
then the stock is undervalued and if it is less than 1, the stock is overvalued.
3.3.2 Debt to Equity Ratio
The debt-to-equity ratio is a measure of the relationship between the capital
contributed by creditors and the capital contributed by shareholders. It also shows the extent
to which shareholders' equity can fulfill a company's obligations to creditors in the event of a
liquidation.
Debt to equity ratio =
Total liabilitie s
Shareholde rs equity
Sometimes, only interest-bearing long-term debt is used instead of total liabilities in
the calculation. It is also known as the Personal Debt/Equity Ratio, this ratio can be applied to
personal financial statements as well as corporate ones. A high debt/equity ratio generally
means that a company has been aggressive in financing its growth with debt. Lenders and
investors usually prefer low debt-to-equity ratios because their interests are better protected in
the event of a business decline. Thus, firms with high debt-to-equity ratios may not be able to
attract additional capital.
3.3.3 Earnings to Price Ratio
Earnings to price ratio is a valuation ratio of a company's current share price
compared to its per-share earnings.
Earnings to price ratio =
Earnings per share
Stock price per quarter
Where, Earnings per share is EPS after extraordinary items per quarter.
And, Stock price is closing price per quarter.
The E/P looks at the relationship between the company’s earnings and the stock price.
EPS is usually from the last four quarters (trailing E/P), but sometimes it can be taken from
the estimates of earnings expected in the next four quarters (projected or forward E/P).
3.3.4 Sales to Price Ratio
Sales to price ratio is a ratio for valuing a stock in relation to its own past
performance, other companies or the market itself. Sales to price is calculated by dividing by
revenue per share by its stock's current price for the trailing 12 months.
17
Sales to price ratio =
Re venue per share per quarter
Share price per quarter
Where, Share price is the closing price per quarter.
The sales to price ratio can vary substantially across industries; therefore, it's useful
mainly when comparing similar companies. Because it doesn't take any expenses or debt into
account, the ratio is somewhat limited in the story it tells.
3.3.5 Market Capitalization
Market capitalization (market cap) is the total value of the shares of a company,
sector or market. Market capitalization or market Cap is calculated by multiplying the current
stock price by the number of outstanding shares. This number gives you the total value of the
company.
Market capitalization = No. of outstanding shares × stock price
Where, Outstanding shares are taken per quarter.
And, Stock price is closing price per quarter.
For Example: A stock trading at Rs 55 with 100,000 outstanding shares would have a
market cap of Rs 5.5 lakhs.
3.3.6 Beta
Beta measures a stock’s degree of systematic or market risk. It can also be thought of
as the stock’s contribution to the risk of a well-diversified portfolio. Firms that supply basic
consumer goods (Proctor & Gamble) and utilities (phone, cable, gas, or electric) tend to have
low Betas (lower than 1.0, often around 0.4 to 0.6). Firms that are in economically cyclical
industries would have higher Betas (greater then 1.0).

β = 1: The stock has average market risk. The stock generally tends to go up
(down) by the same percentage amount as the market.

β = 1.5: The stock generally tends to go up (down) by 50% (1.5x) more than the
market.

β = 0.5: The stock generally tends to go up (down) by half as much as the market.

β = 0: The stock has no correlation with movements in the overall stock market.
All of this firm’s risk would actually be firm-specific risk.

β < 0: The stock generally tends move in a direction opposite that of the market
(very rare).
3.3.7 Return
Return is the gain or loss of a security in a particular period. The return consists of the
income and the capital gains relative on an investment. It is usually quoted as a percentage.
18
The general rule is that the more risk you take, the greater the potential for higher return - and
loss.
Return on a stock is:-
=
Where,
= return on stock,
NAV = net asset value of stock,
t = the time period.
Quarterly returns of stocks for the period were taken and simple averages of such
returns were calculated.
3.3.8 Risk-free Return
A risk-free return is the return, which investor can get without assuming any risk. The
risk-free rate represents the interest on an investor’s money that he or she would expect from
an absolutely risk-free investment over a specified period of time. The return is guaranteed on
the purchase of such an asset. In this study, 3-month MIBOR rates were used as a proxy for
risk free rates for the period.
3.4 Collection of data
To meet the objective of the study, secondary source of information were utilized for
the collection of required data. Quarterly closing prices were collected from Ace Equity
Software provided by LSE. The data was collected for the period of 5 years from 1st April,
2007 to 31st March, 2012.
3.5 Analysis of data
The analysis form a crucial part of research. After collection of data, tables were
constructed and analysis of data was done using suitable statistical tools and techniques.
Secondary data was analyzed using the following statistical tools:
Mean

Standard Deviation

Minimum Value

Maximum Value

Range

Standard Error of Mean
19

Skewness

Kurtosis

Coefficient of Variation (CV)

Quartile

Regression Analysis

t-test

Analysis of Variance (ANOVA)
3.5.1 Mean
The arithmetic mean or simply the mean of a list of numbers is the sum of the entire
list divided by the number of items in the list. The mean is the most commonly used type of
average and is often referred to simply as the average. Mean values were calculated for both
the dependent and independent variables. Its formula is:-
=
Where,
=
= mean,
= number of observations,
= a set of data.
3.5.2 Standard Deviation
In probability theory and statistics, standard deviation is a measure of the variability
or dispersion of a population, a data set, or a probability distribution. A low standard
deviation indicates that the data points tend to be very close to the same value (the mean),
while high standard deviation indicates that the data are spread out over a large range of
values. Its formula is:-
S=
Where, S = standard deviation,
= number of observations,
= a particular observation,
= mean of sample.
3.5.3 Minimum Value
It tells us the minimum value in the series.
20
3.5.4 Maximum Value
It tells us the maximum value in the series.
3.5.5 Range
In descriptive statistics, this concept of range has a more complex meaning. The
range is the size of the smallest interval which contains all the data and provides an indication
of statistical dispersion. It is measured in the same units as the data. Since it only depends on
two of the observations, it is most useful in representing the dispersion of small data sets. It
is defined as the difference between the maximum and the minimum value in the series.
3.5.6 Standard Error of Mean
The standard error of the mean tells us how the mean varies with different
experiments measuring the same quantity. Thus, if the effect of random changes are
significant, then the standard error of the mean will be higher. If there is no change in the data
points as experiments are repeated, then the standard error of mean is zero. Mathematically,
the standard error of the mean formula is given by:
=
Where,
= standard error of the mean,
= the standard deviation of the original distribution,
N = the sample size,
= root of the sample size.
It can be seen from the formula that the standard error of the mean decreases as N
increases. This is expected because if the mean at each step is calculated using a lot of data
points, then a small deviation in one value will cause less effect on the final mean.
3.5.7 Skewness
Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A
distribution, or data set, is symmetric if it looks the same to the left and right of the center
point.
S=
Where,
=
=
= third central moment,
21
= sample mean,
= a particular observation,
= second central moment i.e. the variance.
3.5.8 Kurtosis
Kurtosis is a measure of whether the data are peaked or flat relative to a normal
distribution. That is, data sets with high kurtosis tend to have a distinct peak near the mean,
decline rather rapidly, and have heavy tails. Data sets with low kurtosis tend to have a flat top
near the mean rather than a sharp peak. A uniform distribution would be the extreme case.
K=
Where,
=
=
= fourth central moments,
= sample mean,
= a particular observation,
= second central moment i.e. the variance.
3.5.9 Coefficient of Variation (CV)
The coefficient of variation allows you to determine how much volatility (risk) you
are assuming in comparison to the amount of return you can expect from your investment. In
simple language, the lower the ratio of standard deviation to mean return, the better your riskreturn tradeoff.
It is a normalized measure of dispersion of a probability distribution.
CV =
Where,
= standard deviation,
= mean.
The coefficient of variation represents the ratio of the standard deviation to the mean,
and it is a useful statistic for comparing the degree of variation from one data series to
another, even if the means are drastically different from each other.
3.5.10 Quartile
Quartile is a useful concept in statistics and is conceptually similar to the median. The
first quartile is the data point at the 25th percentile, and the third quartile is the data point at
the 75th percentile. The 50th percentile is the median.
22
The first quartile is at the 25th percentile. This means that 25% of the data is smaller
than the first quartile and 75% of the data is larger than this. Similarly, in case of the third
quartile, 25% of the data is larger than it while 75% of it is smaller. For the second quartile,
which is nothing but the median, 50% or half of the data is smaller while half of the data is
larger than this value.
3.5.11 Regression Analysis
In statistics, regression analysis is a statistical technique for estimating the
relationships among variables. It includes many techniques for modeling and analyzing
several variables, when the focus is on the relationship between a dependent variable and one
or more independent variables. More specifically, regression analysis helps one understand
how the typical value of the dependent variable changes when any one of the independent
variables is varied, while the other independent variables are held fixed.
We applied ordinary least squares regression technique to carry out the analysis using
following equations for the CAPM:-
=
Where,
= average return from the stocks for ith quarter,
= returns earned in excess of those predicted by the model,
= measure of exposure to market,
= return from the market portfolio during ith quarter,
= risk free return during ith quarter,
= random error term.
To conduct the study, three regression analysis were carried out:1. Regression analysis between stock return and all variables.
2. Regression analysis between stock return and fundamental variables.
3. Regression analysis between stock return and market variables.
To carry out the above analysis, Enter Method was used. It failed to give the
appropriate results, so another method, named, Stepwise Method was adopted.
3.5.12 T-test
T-test is used to determine whether there is a significant linear relationship between
an independent variable X and a dependent variable Y. The test focuses on the slope of the
regression line.
=
23
Where,
= the value of dependent variable,
= an intercept,
= the slope (also called regression coefficient),
= the value of independent variable.
If there is a significant linear relationship between the independent variable X and the
dependent variable Y, the slope will not be equal to zero.
3.5.13 Analysis of Variance (ANOVA)
Analysis of variance (ANOVA) is a collection of statistical models used to analyze
the differences between group means and their associated procedures, in which the observed
variance in a particular variable is partitioned into components attributable to different
sources of variation. In its simplest form, ANOVA provides a statistical test of whether or not
the means of several groups are all equal, and therefore generalizes t-test to more than two
groups.
Analysis of variance (ANOVA) consists of calculations that provide information
about levels of variability within a regression model and form a basis for tests of significance.
The basic regression line concept:Data = fit + residual
This equation may also be written as:SST = SSR + SSE
Source of
variation
S.S. (Sum of squares)
v (Degrees
of freedom)
Regression
(model)
v1 = 2-1 =1
MSR =
SSR =
v2 = n – 2
Error
MSE =
SSE =
Total
M.S.S
(Mean sum
of squares)
SST
n-1
Where, n = total number of observations,
SST = total sum of squares of variations,
SSR = regression sum of squares,
SSE = error sum of squares.
For the purpose of analysis, Excel, Megastat add-ins have been used.
24
Variance
ratio of F
3.6 Limitation of study
The study has been undertaken objectively and every effort has been made to make
the study effective, strong and up to the mark. However, study suffered from certain
constraints and limitations. These are listed below so that findings of the study could be
understood in their perspective:1. Since secondary data was used for the purpose of research, the weakness inherent in
the secondary data could not be avoided.
2. Only selected market and accounting based fundamental variables were being used,
this limits the scope of study.
3. The accuracy of the result was also limited by data analysis and the knowledge of the
researcher.
4. The data was collected only of 5 years which limits the time period.
5. The time period was further reduced to quarterly basis which added another limitation
to the research.
6. As the study was to be completed in a short time, the time factor acted as a
considerable limit on the scope and the extensiveness of the study.
25
Chapter IV
RESULTS AND DISCUSSION
This chapter contains results and discussions of the empirical study conducted on the
basis of methodology described earlier in Chapter III. The analysis of secondary data
collected was done to study relationship of stock return with market and fundamental
variables. As the study is divided into 2 portions, therefore, this chapter is divided into 2
parts, namely:4.1 Descriptive Statistics.
4.2 Application of Multi-factor Model.
4.3 Discussion
4.1 Descriptive Statistics
Descriptive statistics are procedures used to summarize, organize, and make sense of
a set of scores or observations. Descriptive statistics are typically presented graphically, in
tabular form (in tables), or as summary statistics (single values). It is measured in 2 ways, viz.
numeric data and non-mean based. Numeric data was calculated using mean, variance
(standard deviation), skewness and kurtosis. Non-mean based measure was calculated through
mode, median, range and inter-quartile range.
Table 1 showed that mean was more than in case of market capitalization i.e.
635.4685 as compared to all other variables namely stock beta with 0.9190, debt to equity
with 0.6280, book to market value with 0.6740, earnings to price with 0.0250, sales to price
with 203.4435, interest rate with 8.3720 and stock return with 5.7320.
Table 1: Descriptive Statistics for quarterly returns, market variables and fundamental
variables.
Stock
beta
Count
20
Mean
0.9190
Sample
0.0516
standard
deviation
Minimum
0.82
Maximum
1.02
Range
0.2
Standard error 0.0115
of the mean
Skewness
-0.0844
Kurtosis
-0.1668
Coefficient of 5.61%
variation (CV)
1st quartile
0.8900
3rd quartile
0.9475
Debt to
equity
20
0.6280
0.0352
Book to
market
value
20
0.6740
0.2850
0.58
0.68
0.1
0.0079
Market
Earnings to Sales to Interest
capitalization
price
price
rate
Stock
return
20
635.4685
251.3830
20
0.0250
0.0095
20
20
203.4435 8.3720
47.4876 2.1436
20
5.7320
17.9686
0.32
1.38
1.06
0.0637
302.37
980.7
678.33
56.2109
0.01
0.04
0.03
0.0021
132.7
293.94
161.24
10.6186
4.6
11.86
7.26
0.4793
-24.72
54.17
78.89
4.0179
0.1843
-1.0947
5.60%
1.1394
1.0017
42.28%
0.1184
-1.6598
39.56%
-0.0000
-0.7193
37.84%
0.6921
-0.6207
23.34%
-0.5758 0.7873
-0.5763 1.5635
25.60% 313.48%
0.6100
0.6500
0.4650
0.8625
407.8150
881.1550
0.0200
0.0300
26
168.9925 7.2425
234.8625 9.8250
-5.0800
13.9450
Table 1 shows that minimum value in case of stock beta was 0.82, in case of debt to
equity 0.58, in case of book to market value 0.32, in case of market capitalization 302.37, in
case of earnings to price 0.01, in case of sales to price 132.7, in case of interest rate 4.6 and 24.72 in case of stock return. The maximum value in case of stock beta was 1.02, debt to
equity was 0.68, book to market value 1.38, market capitalization 980.7, earnings to price
0.04, sales to price 293.94, interest rate 11.86 and that of stock return was 54.17. Range which
was based on lowest and highest value in the series was 0.2 in case of stock beta, 0.1 in case
of debt to equity, 1.06 in case of book to market value, 678.33 in case of market
capitalization, 0.03 in case of earnings to price, 161.24 in case of sales to price, 7.26 in case of
interest rate and in case of stock return was 78.89. Standard deviation was higher in case of
market capitalization with 251.3830, sales to price with 47.4876 and stock return with
17.9686 denoting that the data were spread out on a large range of value and it was lower in
case of interest rate with 2.1436, book to market value with 0.2850, stock beta with 0.0516
and debt to equity with 0.0352 & lowest in case of earnings to price with 0.0095 denoting that
the data points tend to be very close to same value. Coefficient of variation which measures
risk per unit of return was low in case of debt to equity with 5.60% and stock beta with 5.61%
& it was high in case of stock return with 313.48% in comparison to book to market value
with 42.28%, market capitalization with 39.56%, earnings to price 37.84%, sales to price
23.34% and interest rate with 25.60%. Standard error of mean in case of stock beta was
0.0115, in case of debt to equity 0.0079, in case of book to market value 0.0637, in case of
market capitalization 56.2109, in case of earnings to price 0.0021, in case of sales to rice
10.6186, in case of interest rate 0.4793 and 4.0179 in case of stock return. Skewness
quantifies how symmetrical the distribution is; where positive skewness means the right tail is
heavier than the left tail and negative skewness means that the left tail of the distribution is
dominant. It was -0.0844 in stock beta, 0.1843 in debt to equity, 1.1394 in book to market
value, 0.1184 in market capitalization, -0.0000 in earnings to price, 0.6921 in sales to price, 0.5758 in interest rate and 0.7873 in stock return. Kurtosis measures the degree of
peakedness. It was -0.1668, -1.0947, -1.5698, -0.7193, -0.6207 and -0.5763 in case of stock
beta, debt to equity, market capitalization, earnings to price, sales to price & interest rate
respectively, indicating longer left tail and it was 1.0017 & 1.5635 in case of book to market
value and stock return respectively, indicating longer right tail. 1st quartile in case of stock
beta was 0.8900, in case of debt to equity 0.6100, in case of book to market value 0.4650, in
case of market capitalization 407.8150, in case of earnings to price 0.0200, in case of sales to
price 168.9925, in case of interest rate 7.2425 and -5.0800 in case of stock return. The 3rd
quartile in case of stock beta was 0.9475, debt to equity was 0.6500, book to market value
0.8625, market capitalization 881.1550, earnings to price 0.0300, sales to price 234.8625,
interest rate 9.8250 and that of stock return was 13.9450.
27
4.2 Application of Multi-factor Model
Regression is a means of predicting a dependent variable based on an independent
variables. Regression is also convenient for studying two important asset pricing issues. If
assets are priced rationally, variables that are related to average returns, such as size and book
to market ratio, must proxy for sensitivity to common risk factors in returns. The regressions
give direct evidence on this issue. In particular, the slopes and R2 values show whether
mimicking portfolios for risk factors related to size and BV/MV capture shared variation in
stock return not explained by other factors. The regression analysis use stock returns as
dependent variables and size, book to market, earnings to price, sales to price, and beta as
independent variables. The estimated intercepts provide a simple return metric and a formal
test of how well different combinations of the common factors capture the cross-section of
average returns.
To conduct the study, three regression analysis were carried out:1. Regression analysis between stock return and all variables.
2. Regression analysis between stock return and fundamental variables.
3. Regression analysis between stock return and market variables.
To carry out the above analysis, two methods of regression analysis were adopted,
namely:
Enter Method.
Enter method is a procedure for variable selection in which all variables in a block are
entered in a single step. This is an appropriate analysis when dealing with a small set of
predictors. Each predictor is assessed as though it were entered after all the other independent
variables were entered, and assessed by what it offers to the prediction of the dependent
variable that is different from the predictions offered by the other variables entered into the
model. The results obtained depend upon variables entered in the model. It is important,
therefore, to have good theoretical reasons for including a particular variable.

Stepwise Method.
In statistics, stepwise regression includes regression models in which the choice of
predictive variables is carried out by an automatic procedure. Stepwise is the most
sophisticated method. Each variable is entered in sequence and its value assessed. If adding
the variable contributes to the model then it is retained, but all other variables in the model are
then re-tested to see if they are still contributing to the success of the model. If they no longer
contribute significantly they are removed. Thus, this method ensures that one ends up with the
smallest possible set of predictor variables included in the model. The main approaches are
forward selection and backward elimination. Forward selection starts with the independent
28
variable that is the best predictor of the dependent variable and checks that the coefficient is
significantly different from zero, at the 5% level. Backward elimination starts with all
independent variables in the regression, then removes the one with the smallest t-statistic,
provided that its p value is at least 0.10.

ENTER METHOD
Table 2: Regression results of relationship between stock return and all variables.
Regression output
Variables
Coefficients Standard Error
Intercept
53.4223
173.311
Stock beta
29.156
88.991
Debt to equity
-189.4068
217.9356
Book to market value
14.0181
41.5662
Market capitalization
0.06
0.0571
Earnings to price
1,530.23
863.267
Sales to price
0.0273
0.1599
Interest rate
-5.6054
2.2238
* n = 20; k = 7; Dependent variable = stock return.
t-statistics (df=12)
0.308
0.328
-0.869
0.337
1.051
1.773
0.171
-2.521
p-value
0.7632
0.7488
0.4018
0.7418
0.3138
0.1017
0.8671
0.0269
** df = degrees of freedom; n = number of observations; k = number of independent
variables.
Model
1
Model Summary
R
R²
Adjusted R²
0.71 0.503
0.214
Source
Sum of
Squares
Regression
3,088.21
Residual
3,046.33
Total
6,134.54
The regression equation is:-
Standard Error
15.933
ANOVA Table
Degrees of
Mean Sum of
Freedom
Squares
7
441.1734
12
253.8605
19
Variance
Ratio of F
1.74
p-value
0.191
Stock return = 53.4223 + 29.1560 stock beta – 189.4068 debt to equity + 14.0181 book to
market value + 0.0600 market capitalization + 1530.2313 earnings to price + 0.0273 sales
to price – 5.6054 interest rate.
Table 2 shows regression results of dependent variable, viz. stock return and
independent variable, viz. beta, debt to equity, book to market value, market capitalization,
earnings to price, sales to price and interest rate. The t-test statistics is each coefficient
divided by its standard error. The standard error is the average amount each data point differs
from the predicted data point. The p-value of various variables as calculated was beta 0.7488,
debt to equity 0.4018, book to market value 0.7418, market capitalization 0.3138, earnings to
price 0.1017 and sales to price 0.8671. All the variables were more than 0.05. So, these
29
coefficients were insignificant. But the only variable whose value was below significant level
i.e. 0.05, was interest rate with p-value 0.0269.
Under model summary table were listed the independent and dependent variables. In
the table, the value of R2 tells which was 0.503 or 50% of the variance of stock return was
explained by the regression on fundamental and market variables. R2 always increases with
inclusion of additional independent variable. Adjusted R2 which was also given, takes account
of number of independent variables and also number of cases.
The F ratio in the ANOVA table tests whether the overall regression model is a good
fit for data. The table shows that the independent variables statistically significantly predict
the dependent variable. The variance ratio of F was 1.74 with 7 and 12 degrees of freedom
with the probability above 0.05. So, the regression is non-significant.
Table 3:
Regression results of relationship between stock return and fundamental
variables.
Regression output
Variables
Coefficient
Standard error
t-statistics
p-value
(df=14)
Intercept
127.6395
88.6291
1.44
0.1718
Debt to equity
-155.022
173.743
-0.892
0.3873
Book to market
-23.9713
20.6568
-1.16
0.2653
value
Earnings to price
844.7023
558.2762
1.513
0.1525
Sales to price
0.0734
0.1424
0.516
0.6141
Interest rate
-5.3101
2.1221
-2.502
0.0254
* n = 20; k = 5; Dependent variable = stock return.
Model
1
R
0.675
Model Summary
R²
Adjusted R²
0.456
0.262
Standard Error
15.441
ANOVA Table
Source
Sum of
Degrees of
Mean Sum
Squares
Freedom
of Squares
Regression
2,796.57
5
559.3131
Residual
3,337.97
14
238.4267
Total
6,134.54
19
The regression equation is:-
Variance
Ratio of F
2.35
p-value
0.0958
Stock return = 127.6395 – 155.0218 debt to equity – 23.9713 book to market value +
844.7023 earnings to price + 0.0734 sales to price – 5.3101 interest rate.
Table 3 shows regression analysis of dependent variable, viz. stock return and
independent variable, viz. debt to equity, book to market value, earnings to price, sales to
price and interest rate. The t-test statistics is each coefficient divided by its standard error. The
standard error is the average amount each data point differs from the predicted data point. The
30
p-value of various variables as calculated was debt to equity 0.3873, book to market value
0.2653, earnings to price 0.1525 and sales to price 0.6141. All the variables were more than
0.05. So, these coefficients were insignificant. But the only variable whose value was below
significant level i.e. 0.05, was interest rate with p-value 0.0254.
Under model summary table were listed the independent and dependent variables. In
the table, the value of R2 tells which was 0.456 or 45% of the variance of stock return was
explained by the regression on fundamental variables. R2 always increases with inclusion of
additional independent variable. In this table, R2 decreases as compared to table 2 because of
decrease in independent variables. Adjusted R2 which was also given, takes account of
number of independent variables and also number of cases.
The F ratio in the ANOVA table tests whether the overall regression model is a good
fit for data. The table shows that the independent variables statistically significantly predict
the dependent variable. The variance ratio of F was 2.35 with 5 and 14 degrees of freedom
with the probability above 0.05. So, the regression is non-significant.
Table 4: Regression results of relationship between stock return and market variables.
Regression output
Variables
Coefficients Standard Error
Intercept
-63.5801
108.1132
Stock beta
66.1196
77.4305
Book to market value
7.5306
40.5038
Market capitalization
0.0476
0.0547
Earnings to price
1,408.59
843.7913
Sales to price
-0.0637
0.1196
Interest rate
-5.8533
2.1845
* n = 20; k = 6; Dependent variable = stock return.
Model
1
Model Summary
R
R²
Adjusted R²
0.687 0.472
0.229
Source
Regression
Residual
Total
Sum of
Squares
2,896.47
3,238.07
6,134.54
t-statistics (df=12)
-0.588
0.854
0.186
0.869
1.669
-0.532
-2.679
p-value
0.5665
0.4086
0.8554
0.4005
0.1189
0.6035
0.0189
Standard Error
15.782
ANOVA Table
Degrees of
Mean Sum of
Freedom
Squares
6
482.7444
13
249.0825
19
Variance
Ratio of F
1.94
p-value
0.1493
The regression equation is:Stock return = – 63.5801 + 66.1196 stock beta + 7.5306 book to market value + 0.0476
market capitalization + 1408.5923 earnings to price – 0.0637 sales to price – 5.8533
interest rate.
31
Table 4 shows regression analysis of dependent variable, viz. stock return and
independent variable, viz. beta, book to market value, market capitalization, earnings to price,
sales to price and interest rate. The t-test statistics is each coefficient divided by its standard
error. The standard error is the average amount each data point differs from the predicted data
point. The p-value of various variables as calculated was beta 0.4086, book to market value
0.8554, market capitalization 0.4005, earnings to price 0.1189 and sales to price 0.6035. All
the variables were more than 0.05. So, these coefficients were insignificant. But the only
variable whose value was below significant level i.e. 0.05, was interest rate with p-value
0.0189.
Under model summary table were listed the independent and dependent variables. In
the table, the value of R2 tells which was 0.472 or 47% of the variance of stock return was
explained by the regression on market variables. R2 always increases with inclusion of
additional independent variable. In this table, the value of R2 decreased as compared to table 2
because of decrease in independent variables. But the value of R2 increased in comparison
with the value in table 3 because the number of independent variables were less in table 3
than in table 4. Adjusted R2 which was also given, takes account of number of independent
variables and also number of cases.
The F ratio in the ANOVA table tests whether the overall regression model is a good
fit for data. The table shows that the independent variables statistically significantly predict
the dependent variable. The variance ratio of F was 1.94 with 6 and 13 degrees of freedom
with the probability above 0.05. So, the regression is non-significant.
The method used in above three analysis did not give the appropriate. So, to achieve
the objective of studying the relationship between stock return with market and fundamental
variables, another method i.e. stepwise selection had been implemented.

STEPWISE METHOD
Stepwise regression combines forward selection and backward elimination. At each
step, the best remaining variable was added, provided it passes the significant at 5% criterion,
then all variables currently in the regression were checked to see if any can be removed, using
the greater than 10% significance criterion. The process continued until no more variables
were added or removed.
32
Table 5: Regression results of relationship between stock return and all variables.
Nvar
Stock
beta
1
2
3
4
5
6
7
Debt
to
equity
.1772
.6726
.7488
.1797
.2445
.3165
.4018
p-values for the coefficients
Book to
Market
Earnings Sales to Interest Adjusted p-value
market capitalization to price
price
rate
R²
value
.0138
.253
.0138
.0480
.292
.0206
.1186
.0907
.0041
.316
.0283
.1383
.0800
.0125
.351
.0310
.1323
.0796
.6390
.0142
.315
.0620
.6521
.2687
.0887
.0202
.272
.1118
.7418
.3138
.1017
.8671
.0269
.214
.1910
Table 5 shows regression analysis of dependent variable, viz. stock return and
independent variable, viz. beta, debt to equity, book to market value, market capitalization,
earnings to price, sales to price and interest rate. It shows that interest rate was the best
predictor of stock return and was entered first which gave p-value 0.0138. In second, with
debt to equity and interest rate, the p-value was 0.0206. In third, book to market, earnings to
price and interest rate gave p-value 0.0283. In forth, debt to equity, market capitalization,
earnings to price and interest rate gave p-value 0.0310. In fifth, debt to equity, market
capitalization, earnings to price, sales to price and interest rate were taken which gave p-value
0.0620. In sixth, stock beta, debt to equity, book to market value, market capitalization,
earnings to price and interest rate were taken which gave p-value 0.1118. In seventh, all the
variables were taken which gave p-value 0.1910. The p-value in first 4 steps was less than
0.05 and last 3 was more than significant level. So out of the first 4 steps, where the p-value
was less than 0.05, maximum value of adjusted R2 had been considered. After considering the
value of adjusted R2 in the first 4 steps, the maximum value was at step 4 i.e. 0.351. So the
objective is fulfilled at step 4 where p-value was 0.0310.
Table 6:
Nvar
1
2
3
4
5
Regression results of relationship between stock return and fundamental
variables.
p-values for the coefficients
Debt to Book to Earnings Sales Interest
Adjusted
p-value
equity market to price
to
rate
R²
value
price
.0138
.253
.0138
.1772
.0480
.292
.0206
.1186
.0907
.0041
.316
.0283
.4556
.3032
.1651
.0232
.298
.0521
.3873
.2653
.1525
.6141
.0254
.262
.0958
33
Table 6 shows regression analysis of dependent variable, viz. stock return and
independent variable, viz. debt to equity, book to market value, earnings to price, sales to
price and interest rate. It shows that interest rate was the best predictor of stock return and was
entered first which gave p-value 0.0138. In second, with debt to equity and interest rate, the pvalue was 0.0206. In third, book to market, earnings to price and interest rate gave p-value
0.0283. In forth, debt to equity, book to market value, earnings to price and interest rate gave
p-value 0.0521. In fifth, all the variables were taken which gave p-value 0.0958. The p-value
in first 3 steps was less than 0.05 and last 2 was more than significant level. So out of the first
3 steps, where the p-value was less than 0.05, maximum value of adjusted R2 had been
considered. After considering the value of adjusted R2 in the first 3 steps, the maximum value
was at step 3 i.e. 0.316. So the objective is fulfilled at step 3 where p-value was 0.0283.
Table 7: Regression results of relationship between stock return and market variables.
Nvar
1
2
3
4
5
6
Stock
beta
p-values for the coefficients
Book to
Market
Earnings Sales
market capitalization to price
to
value
price
.2982
.1186
.3197
.4009
.4086
.8554
.0907
.0639
.0956
.1189
.1260
.1819
.4005
.5685
.6035
Interest Adjusted
rate
R²
.0138
.0424
.0041
.0034
.0132
.0189
.253
.260
.316
.313
.282
.229
pvalue
.0138
.0302
.0283
.0449
.0818
.1493
Table 7 shows regression analysis of dependent variable, viz. stock return and
independent variable, viz. beta, book to market value, market capitalization, earnings to price,
sales to price and interest rate. It shows that interest rate was the best predictor of stock return
and was entered first which gave p-value 0.0138. In second, with sales to price and interest
rate, the p-value was 0.0302. In third, book to market, earnings to price and interest rate gave
p-value 0.0283. In forth, stock beta, market capitalization, earnings to price and interest rate
gave p-value 0.0449. In fifth, stock beta, market capitalization, earnings to price, sales to price
and interest rate were taken which gave p-value 0.0818. In sixth, all the variables were taken
which gave p-value 0.1493. The p-value in first 4 steps was less than 0.05 and last 2 was more
than significant level. So out of the first 4 steps, where the p-value was less than 0.05,
maximum value of adjusted R2 had been considered. After considering the value of adjusted
R2 in the first 4 steps, the maximum value was at step 3 i.e. 0.316. So the objective is fulfilled
at step 3 where p-value was 0.0283.
34
4.3 Discussion
In this section, overall discussion is done about the results. The mean value was more
in case of market capitalization as compared to all other variables. Standard deviation was
high in case of market capitalization, sales to price, and stock return. Standard deviation was
lowest in case of earnings to price. Coefficient of variation was high in case of stock return
and low in case of debt to equity and stock beta.
The regression analysis was performed with stock return as a dependent variable, and
market and fundamental variables as the independent variables. All the variables except
interest rate were observed to be insignificant from the three analysis that were carried out. To
solve the purpose of the study another method was adopted. It was found that among all the
variables, debt to equity, book to market value, market capitalization, earnings to price and
interest rate proved to be significant. The best relationship was between stock return with
earnings to price and interest rate.
35
Chapter V
SUMMARY
In this chapter, a brief summary of the study have been presented, so as to understand
the implications of the findings.
5.1 Summary
The research aimed at studying the relationship between stock return with
fundamental variables and market variables on the basis of pooled cross-sectional data of a
five year period ranging from 1 April 2007 – 31 March 2012 by applying two statistical tools,
viz. regression analysis and descriptive statistics. Following were the objectives of the study:1. To study the relationship between stock returns and selected accounting based
fundamental variables.
2. To study the relationship between stock returns and selected market variables.
Regression analysis was carried out to meet the above objective. Enter method was
adopted to fulfill both the objectives. The method used did not give the appropriate results, so
another method i.e. stepwise method was adopted. The method proved statistically significant
with respect to book to market value, earnings to price, interest rate, debt to equity and market
capitalization.
The relationship between book to market value, earnings to price, interest rate and
stock return proved more stable as compared to other variables and the stock return. Three
different regression analysis were made which gave three different results. In first, debt to
equity, market capitalization, earnings to price and interest rates proved significant with stock
return. The relationship between book to market value, earnings to price and interest rate
proved significant in the second and third analysis.
In no year was there a significant relationship between stock beta, sales to price ratio
and stock return. Due to instability in the relationship between these two variables and stock
return, one should not place great emphasis on them.
Another statistical tool used was descriptive statistics under which mean, standard
deviation, minimum, maximum, range, standard error of mean, skewness, kurtosis, coefficient
of variation, 1st quartile and 3rd quartile were calculated for dependent and independent
variables. The mean value proved to be more in case of market capitalization. Standard
deviation was high in case of market capitalization, sales to price, and stock return and lowest
in case of earnings to price. Coefficient of variation was high in case of stock return and low
in case of debt to equity and stock beta.
36
1.2 Conclusion

In kurtosis, stock beta, debt to equity, market capitalization, earnings to price, sales to
price and interest rate being negative indicated longer left tail. Book to market value
and stock return being positive indicated longer right tail.

Positive skewness in debt to equity, book to market value, market capitalization,
sales to price and stock return indicated heavier right tail. Negative skewness in stock
beta, earnings to price and interest rate showed dominance of left tail.

Coefficient of variation which measures risk per unit of return was low in case of debt
to equity and stock beta with 5.60% and 5.61%. It was high in case of stock return
with 313.48%.

Standard deviation was higher in case of market capitalization, sales to price and
stock return. It was lowest in case of earnings to price with 0.0095.

The mean value was highest in case of market capitalization i.e. 635.46885.

Enter method was used for regression analysis which did not provide appropriate
results. p-value of all the variables came out to be more than significant level i.e.
0.05.

Stepwise method proved to be more significant:
3 cases were taken into account and significant level was judged at a point where
adjusted R2 was maximum and p-value was less than 0.05.

In first case, 7 steps were calculated where significant level was at step 4 with
adjusted R2 0.351 and p-value 0.0310.

In second case, 5 steps were calculated where significant level was at step 3 with
adjusted R2 0.316 and p-value 0.0283.

In third case, 6 steps were calculated where significant level was at step 3 with
adjusted R2 0.316 and p-value 0.0283.

The method proved statistically significant with respect to book to market value,
earnings to price, interest rate, debt to equity and market capitalization.

No relationship was found between beta and sales to price with stock return.
37
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40
VITA
Name of the student
Father’s name
Mother’s name
Nationality
Date of birth
Permanent home address
:
:
:
:
:
:
Pavneet Khara
Parminder Singh
Sukhminder Kaur
Indian
9 May, 1990
99 – K,
Sarabha Nagar,
Ludhiana - 141001
Bachelor degree
University and year of award
OGPA/OCPA/% marks
Master’s degree
OCPA
:
:
:
:
:
B.COM
Punjab University, 2011
66%
MBA
6.64
Title of Master’s Thesis
:
Returns from stock investment :
An application of multifactor
model
EDUCATIONAL QUALIFICATION
41
RETURNS FROM STOCK INVESTMENT : AN
APPLICATION OF MULTI-FACTOR
MODELS
Research Project Report
Submitted to the Punjab Agricultural University
in partial fulfillment of the requirements
for the degree of
MASTER OF BUSINESS ADMINISTRATION
in
FINANCIAL MANAGEMENT
(Minor subject: Economics)
By
Pavneet Khara
(L-2011-BS-17-MBA)
School of Business Studies
College of Basic Sciences and Humanities
© PUNJAB AGRICULTURAL UNIVERSITY
LUDHIANA-141004
2013
42
CERTIFICATE I
This is to certify that the project report entitled, “Returns from stock
investment : An application of multi factor model” submitted for the degree of
Master of the Business Administration, in the subject of Financial Management
(Minor subject: Economics) of Punjab Agricultural University, Ludhiana, is a
bonafide research work carried out by Pavneet Khara (L-2011-BS-17-MBA) under
my supervision and that no part of this thesis has been submitted for any other degree.
The assistance and help received during the course of investigation have been
fully acknowledged.
_____________________________
(Dr. Navdeep Aggarwal)
Major Advisor
Assistant Professor,
School of Business Studies,
College of Basic Sciences & Humanities,
Punjab Agricultural University,
Ludhiana – 141004
43
CERTIFICATE II
This is to certify that the project report entitled, “Returns from stock
investment : An application of multi factor model” submitted by Pavneet Khara
(L-2011-BS-17-MBA) to the Punjab Agricultural University, Ludhiana, in partial
fulfillment of the requirements for the degree of Master of the Business
Administration, in the subject of Financial Management (Minor subject:
Economics) has been approved by external examiner along with the internal examiner
after an oral examination on the same.
___________________
___________________
Internal Examiner
External Examiner
(Dr. Sandeep Kapur)
Head of the Department
44
ACKNOWLEDGEMENT
I would like to express my indebtedness to my Major Advisor, Dr. Navdeep
Aggarwal, Assistant Professor, School of Business Studies, for his dexterous
guidance, inspiration, sustained encouragement, keen interest and precious time
given to me during the course of research project and in successful completion of the
manuscript. I consider myself extremely fortunate to have an opportunity to work with
him.
I express my deep appreciation to Dr. Lalit Mohan Kathuria, Associate
Professor, School of Business Studies for his expert guidance. I owe my thanks to Dr.
Jagroop Singh Sidhu, Professor of Economics, Department of Economics and
Sociology, for his valuable guidance throughout my research work. I would also like
to thank Dr. Pratibha Goyal, Associate Professor, School of Business Studies for her
valuable suggestions during the preparation of this manuscript. I express my sincere
thanks to all other faculty members of Department of Business Management for
providing necessary facilities during the tenure of my studies.
A special thanks to my fiancé Vikram Toor for his help and support without
which I would not have been able to prepare my thesis. Finally, I would like to thank,
God, my family members and friends, for being there on my side, and within me
always.
Dated:
Place: Ludhiana
_________________
(Pavneet Khara)
45
Title of the Project Report
:
Returns from stock investment: An
application of multi-factor model.
Name of the Student
and Admission No.
:
Pavneet Khara
L-2011-BS-17-MBA
Major Subject
:
Financial Management
Minor Subject
:
Economics
Name and Designation
of Major Advisor
:
Dr. Navdeep Aggarwal
Assistant Professor
School of Business Studies
Degree to be Awarded
:
MBA
Year of award of Degree
:
2013
Total pages in Project Report
:
40 + VITA
Name of University
:
Punjab Agricultural University,
Ludhiana- 141004, Punjab, India
ABSTRACT
The research project “Returns from stock investment : An application of
multi-factor model” was undertaken with the objectives to study the relationship
between stock returns and selected accounting based fundamental variables and to
study the relationship between stock returns and selected market variables. For the
purpose of achieving the objectives, the following factors were used in explanation of
returns from stock investment, via stock beta, debt to equity ratio, book to market
value ratio, size of company measured in terms of market capitalization, earnings to
price ratio and sales to price ratio. The study was conducted for the period of 5 years
ranging from April 2007 to March 2012. Data on the selected explanatory factors
were used for all the stocks constituting the popular BSE Sensex index. Regression
analysis and descriptive statistics were used to study the relationship between the
stock returns and the identified explanatory variables. Regression results from enter
method proved insignificant while that from stepwise method proved statistically
significant. The best relationship was found between stock return with earnings to
price and interest rate.
Key Words: Stock return, beta, book to market, market capitalization, investment,
multi-factor model.
_______________________
Signature of Major Advisor
______________________
Signature of the student
46
CONTENTS
_____________________________________________________________________
Chapter
Topic
Page
_____________________________________________________________________
II.
INTRODUCTION
1–7
III.
REVIEW OF LITERATURE
8 – 15
IV.
RESEARCH METHODOLOGY
16 – 25
V.
RESULTS AND DISCUSSION
26 - 35
VI.
SUMMARY
36 - 37
REFERENCES
38 - 40
VITA
_____________________________________________________________________
47