Risk Factors in Indian Capital Market-Thimmarayappa-04117 (1)

Risk Factors In Indian Capital Markets

A RESEARCH REPORT

ON

“Risk factors in Indian capital market”

Submitted in partial fulfillment of the requirements of the M.B.A Degree Course of Bangalore University

Submitted By

THIMMARAYAPPA.S.M (REGD.NO:04XQCM 6111)

Under the Guidance and Supervision Of

PROF. B.V.RUDRA MURTHY

M.P.BIRLA INSTITUTE OF MANAGEMENT Associate Bharatiya Vidya Bhavan

# 43, Race Course Road, Bangalore-560001 2004-2006

1 M.P Birla Institute of Management


Declaration

I hereby declare that this report titled “Risk factors in Indian capital

market” is a record of independent work carried out by me, towards the partial

fulfillment of requirements for MBA course of Bangalore University at M.P.Birla

Institute of Management. This has not been submitted in part or full towards any

other degree.

PLACE: BANGALORE DATE: THIMMARAYAPPA.S.M



Principal’s Certificate This to certify that this report titled “Risk factors in Indian capital

market” have been prepared by THIMMARAYAPPA.S.M bearing the

registration no.04 XQCM 6111 under the guidance and supervision of PROF.

B.V.RUDRA MURTHY ,MPBIM, Bangalore.

Place: Bangalore Principal Date: (Dr.N.S.Malavalli)



GUIDE’S CERTIFICATE This is to certify that the Research Report entitled “Risk factors in Indian

capital market”, done by THIMMARAYAPPA.S.M bearing Registration

No.04 XQCM 6111 is a bonafide work done carried under my guidance during

the academic year 2005-06 in a partial fulfillment of the requirement for the

award of MBA degree by Bangalore University. To the best of my knowledge this

report has not formed the basis for the award of any other degree.

Place: Bangalore PROF.B.V.RUDRA MURTHY Date :



ACKNOWLEDGEMENT

I am thankful to Dr.N.S.Malavalli, Principal, M.P.Birla institute of

management, Bangalore, who has given his valuable support during my project.

I am extremely thankful to PROF.B.V.RUDRA MURTHY, M.P.Birla institute

of Management, Bangalore, who has guided me to do this project by giving

valuable suggestions and advice.

I equally thank Dr T.V.N Rao for his guidance and suggestion.

Finally, I express my sincere gratitude to all my friends and well wishers who

helped me to do this project.

THIMMARAYAPPA.S.M



TABLE OF CONTENTS

CHAPTER PARTICULARS ABSTRACT

1. INTRODUCTION CAPM (capital asset pricing model). CAPM in Indian context. CAPM and Indian stocks. Criticisms of CAPM Back ground of the study

2. REVIEW OF LITERATURE Risk factors in developing capital markets: Lakshman alles & Louis

Murray Structural change and asset pricing in emerging markets: Rene Garcia,

Eric Ghysels Distributional characteristics of emerging markets returns and asset

allocation: Geert Bekaert, Claude B. Erb, Campbell R, Harvey and Tadas E. Viskanta.

Skew ness preference and the valuation of the risk assets: Alan Kraus & Robert H Litzenberger

Equilibrium in an imperfect market: A constraint on the number of securities in the portfolio : Haim Levy

Common risk factors in the returns on stocks and bonds: Eugene F. Fama & Kenneth R .French

Tests of the Fama and French model in India: Gregory Connor and Sanjay Sehgal

Relationship between return and market value of common stocks: Rolf w Banz

3. METHODOLOGY Problem statement Objectives of the study

Scope of the study Limitations of the study Data Sources of data Period of study

Sample Sample size Statistical procedure Back ground of regression

Hypothesis Scatter diagrams

4 DATA ANALYSIS 5 CONCLUSION

GLOSSARY & BIBLIOGRAPHY



LIST OF TABLES

TABLE NO TABLE NAME 1

Showing return, beta, variance and skew ness for the year 2002.

2


3


4


5

Showing co efficient of beta

6

Showing co efficient of variance

7

Showing co efficient of skew ness

8

Showing co efficient of beta and variance.

9

Showing co efficient of beta and skew ness

10

Showing co efficient of beta, variance and skewness.



Abstract This project addresses the question as to whether the Capital Asset Pricing Model

(CAPM) offers an appropriate explanation of stock returns in the Indian capital markets.

The question is whether the CAPM is appropriate, given potential relevance of

unsystematic risk of market distortions, thin trading and its related effects on market

price. Arguments for considering additional factors like variance, skew ness in pricing

models to better deal with such situations are presented. Using BSE 100 stock returns

data for financial years 2002 to 2005, a series of empirical tests examine whether these

factors, in a cross sectional regression model, offer a statistically significant explanation

of company returns.



Introduction

Capital asset pricing model always referred to as CAPM, is one of the most

popular model used for in applications, such as estimating the cost of the capital for firms

and evaluating the performance of the managed portfolios. It is the center piece of MBA

investments courses. The attraction of the CAPM is that it offers predictions about how to

measure risk and the relation between expected return and risk.

The CAPM builds on the model of portfolio choice developed by Harry Markowitz

(1959). Sharpe (1964) and Lintner (1965) add two key assumptions to the Markowitz

model to identify a portfolio that must be mean-variance-efficient.

The first assumption is, given market clearing asset prices at t-1, investors agree

on the joint distribution of asset returns from t-1 to t. And this distribution is the true one,

that is, the distribution from which the returns we use to test the model are drawn.

The second assumption is that there is borrowing and lending at a risk free rate,

which is the same for all investors and does not depend on the amount borrowed or lent.

The set of assumptions employed in the development of the CAPM are follows:

1. Investors are risk-averse and they have a preference for expected return and a

dislike for risk.

2. Investors make investment decisions based on expected return and the

variances of security returns, i.e. two-parameter utility function.

3. Investors behave in a normative sense and desire to hold a portfolio that lies

along the efficient frontier.



4. There exists a risk less asset and investors can lend or invest at the risk less rate

and also borrow at this rate in any moment.

5. All investments are perfectly divisible. This means that every security and

portfolio is equivalent to a mutual fund and that fractional shares for any investment can

be purchased in any amount.

6. All investors have homogenous expectations with regard to investment

horizons or holding periods and to forecasted expected returns and risk levels on

securities. This means that investors form their investment portfolios and revise them at

the same interval of time. Furthermore, there is complete agreement among investors as

to the return distribution for each security or portfolio.

7. There are no imperfections or frictions in the market to impede investor buying

and selling. Specifically, there are no taxes or commissions involved with security

transactions. Thus there are no costs involved in diversification and there is no

differential tax treatment of capital gains and ordinary income.

8. There is no uncertainty about expected inflation; or, alternatively all security

prices fully reflect all changes in future inflation expectations.

9. Capital markets are in equilibrium. That is, all investment decisions have been

made and there is no further trading without new information.

According to CAPM

1. The risk of the project is measured by beta of the cash flow with respect to the

return on the market portfolio of all assets in the economy.

2. The relation between the required expected return and the beta are linear



According to CAPM equation,

E (Ri) = Rf + [E (RM)-Rf] β IM

Where, Rf is the risk free rate of return.

Rm is the market return.

E (Ri) expected rate of return.

β IM systematic risk of market.

E (Rm)-Rf is the risk premium.

Beta as a Measure of Systematic Risk

An asset exhibits both systematic and unsystematic risk. The portion of its

volatility which is considered systematic is measured by the degree to which its returns

vary relative to those of the overall market. To quantify this relative volatility, a

parameter called beta was conceived as a measure of the risk contribution of an

individual security to a well diversified portfolio:

βA= COV (RA, RM)/ σ2M

Where,

RA is the return of the asset.

Rm is the return of the market.

σ2M is the variance of the return of the market, and

Cov (RA, Rm) is covariance between the return of the market and the return of the asset.

In simple words beta is the ratio of the expected excess return of an asset relative

to the overall market’s excess return, where excess return is defined as the return on any

given asset less the return on a risk-free asset.



In practice, beta is calculated using historical returns for both the asset and the

market, with the market portfolio being represented by a broad market index like nifty

index, bse index, nifty junior etc.

One of the important outcomes of the CAPM assumptions is that all investors

hold a portfolio which is a combination between risk less portfolio and market portfolio.

This is because all investors will have identical efficient frontiers due to the assumption

of homogeneous expectations. They can however have different utility functions, which

will decide what combination of risk less portfolio and market portfolio the investor will

choose. This implies that all investors hold the same combination of risky securities

namely, the market portfolio. This is also known as the separation theorem.

The market portfolio in CAPM is the unanimously desirable risky portfolio which

contains all risky assets. Thus return on market portfolio is weighted average of return of

all risky assets in the market and in theory it should contain, besides ordinary shares, all

assets, like art objects, commodities, real estates and so on.

The total risk of a portfolio can be measured by the variance of its return. In a

more general situation of a portfolio p consists of n shares and any individual share i has

a weightage of Xi in the portfolio, then the total risk can be expressed as follows:

σ2p = σ

2ep + βp

2 σ

2m

Total Risk = Unsystematic Risk + Systematic Risk

If CAPM holds, then investors should hold diversified portfolios and the

systematic risk or non-diversifiable risk will be the only risk which will be of importance

to the investors. The other part of the risk, known as the diversifiable risk or unsystematic

risk will be reduced to nil by holding a diversified portfolio. Thus beta, which is a

measure of the non-diversifiable risk in a portfolio, is most important for investors, from

the point of view CAPM theory.



In case the CAPM holds in the market, an investor will no longer require any

sophisticated portfolio selection technique to select his portfolio. He will choose a mix

between risk-free rate and the market portfolio based on his utility function.

In other words optimal investment decision will be simply to buy the market

portfolio. This investment decision is independent from the decision about how to finance

the investment i.e. whether to lend or borrow at the risk-free rate. Ideally, if CAPM holds,

there will not be any identifiable inefficiency in the market and all securities will lie on

the security market line.

The graphic relationship between expected return on asset i and beta is called the

security market line. If CAPM is valid, all securities will lie in a straight line called the

security market line in the E(R), βi frontier. The security market line implies that return is

a linearly increasing function of risk. Moreover, only the market risk affects the return

and the investor receive no extra return for bearing diversifiable (residual) risk.

Essentially, the CAPM states that an asset is expected to earn the risk-free rate

plus a reward forbearing risk as measured by that asset’s beta. The chart below

demonstrates this predicted relationship between beta and expected return – this line is

called the Security Market Line.



The security market line (SML) provides a bench mark for the evaluation of

investment performance. Given the risk of an investment, as measured by its beta, the

SML provides the required rate of return necessary to compensate investors for both risk

as well as the time value of money.

Suppose the SML relation is used as a bench mark to assess the fair expected

return on a risky asset. Then security analysis is performed to calculate the return actually

expected. If a stock is perceived to be under priced, it will provide an expected return in

excess of the fair return stipulated by the SML. Under priced stocks therefore plot above

security market line: given their betas, their expected returns are greater than dictated by

the CAPM. Over priced stocks plot below the security market line. The difference

between the fair and actually expected rates of return on a stock is called the stock’s

alpha, which is denoted by α.

Some of the other uses of the CAPM are it helps in the capital budgeting

decisions. For a firm considering a new project, the CAPM can provide the required rate

of return that the project needs to yield, based on its beta, to be acceptable to investors.

Managers can use the CAPM to obtain the cutoff internal rate of return (IRR) or the

hurdle rate for the project.

Extensions of CAPM

The assumptions that Sharpe is considered to be unrealistic, so many financial

economists have worked to extend the model to more realistic situations. The following is

the extended model THE CAPM WITH RESTRICTED BORROWING: THE ZERO

BETA MODEL and other models.



CAPM in Indian context

The recent study CAPM in Indian context is worth while to consider given that

the project is about testing CAPM in Indian capital markets. So we get the back ground

as to the applicability of the CAPM in the Indian context. One of the assumptions of

CAPM is that there are no imperfections in the market (or) in other words the market is

efficient, however the study has identified some the important factors which may cause

CAPM to be ineffective in the Indian context and has the potential to reduce the

efficiency level of the Indian Capital Market. (R Vaidyanathan)

The following are the factors identified:

1) Non-Diversified Portfolio Holding

Indian Share Owners -A Survey, L.C. Gupta, clearly indicates that the average

investor in India holds very few scrips in their portfolio. This goes directly against the

expectations of CAPM where the investors are expected to hold a combination of risk-

free asset (or zero beta assets) and market portfolio. The investors are not expected to

hold an undiversified portfolio as they are not rewarded for bearing unsystematic risk

according to CAPM. Hence, holding small number of securities or undiversified

portfolios can add to market inefficiency.

2. Liquidity

Liquidity is possibly the most serious problem faced by the Indian investors. A

consultative paper by SEBI indicated a poor liquidity situation at the stock exchanges in

India. Lack of liquidity can violate the assumptions of CAPM in two ways. Firstly it

results in a transaction cost for the investors. If the transaction cost is added to the CAPM

model, there will be a price band around the SML in which the scrips can lie. Within this

band, it will not be profitable for investors to buy or sell shares.



Secondly, CAPM assumes that all assets are infinitely divisible and readily

marketable. This assumption is also violated in India, due to the low liquidity observed in

majority of the shares, as discussed earlier. Low liquidity can also result in inefficient

pricing of scrips and price setting behavior by investors (non-price taker).

3. Insider Trading

Insider trading is believed to be rampant in the Indian market. The lack of

transparency in the trading system facilitates insider trading. Earlier there was virtually

no law against insider trading. After SEBI was formed, it has taken several steps to

protect the small investors and prevent insider trading. However, the task of detecting

insider trading is a difficult one.

4. Lack of Transparency

Indian stock markets suffer from lack of transparency between members and

constituents. Members perceive that the prices of transactions are not properly reflected

in their gains. All intra-day quotations are not readily available. Since exact time of the

transaction is not known, disputes persist. Also it is felt that some transactions are not

reported. In such a context any analysis has to consider the limitations of available price

series.

5. Inadequate Infrastructure

The infrastructure in the stock markets in India is woefully inadequate. The stock

exchanges are faced with inadequate office space, lack of computerization and

communication system, etc. These inadequacies in turn have affected the quality of the

investor service provided by the members of the exchanges. Though the number of

investors as well as the volume of transaction has gone up many folds in recent years, the

basic infrastructure and system has almost remained unchanged.

The lack of infrastructure adds to the transaction cost of the investors. Moreover

inadequate infrastructure and delays in settlement can slow down the absorption of price

sensitive information in the market, affecting its overall efficiency. Both increased

transaction cost and low operational efficiency violates the assumptions of CAPM



CAPM and Indian stocks

Since we are testing the CAPM in Indian capital markets, so as to determine

whether it offers a better explanation of company returns, let us have the back ground of

the study CAPM and Indian stocks (C u Rao, Golaka c nath and Manish Malhotra).

The study aimed at measuring returns and risks of the representative sample of

Indian stocks. The study also explored different issues regarding application of CAPM in

calculating stock market risk measure, beta.

It was found that the time internal choice did not have any significance impact on

calculated values of beta, but the choice of market proxy could significantly change the

values of beta .It was found that the betas bear linear relationship with mean quarterly

returns . The study suggests that this factor can’t be treated as proof of validity of CAPM.

The plotting of security market line revealed the majority of stocks under analysis are not

rewarded investors appropriately.

Criticisms of CAPM

The various assumptions of the CAPM model are considered to be unrealistic:

1. There is no transaction cost, but there is evidence that at least a minimum

transaction cost exists.

2. Investors have homogenous expectation but empirical evidence have

shown that the investors have different expectations, leading to different

capital lines and no general equilibrium pricing model. This is the major

empirical problem of the CAPM.

3. There are no imperfections in market, but the imperfections are exhibited

by the markets.



4. The investors hold all the assets included in the market port folio, the

various studies has shown that it is impossible to determine a market

portfolio or market proxy which contains all assets.

5. There are no taxes, but most studies have shown that tax effects via the

dividend yield are important in the pricing process. In particular, there is

a positive relationship between dividend yields and average returns.

6. Investors make investment decisions based on expected return and the

variances of security returns, but the evidence indicate skew ness is also

important in asset pricing. Whenever the market portfolio is positively

(negatively) skewed, investors are willing to accept a lower average return

in exchange for positive skew ness with the market portfolio.

Apart from assumptions, according to CAPM beta is the measure of systematic risk, but

beta may not be the correct measure of systematic risk.

There may be other measures of systematic risk also. Besides macroeconomic

variables, some successful proxies for systematic risk include a firm’s size (as measured

by, for example, its market capitalization), its price/earnings ratio, and its market/book

ratio. All these are all firm-specific variables, which is not what the CAPM would

predict. The consequence of not measuring systematic risk correctly we will not

accurately predict a company’s risk premium. Much empirical evidence in this regard is

found.

Estimated betas are considered to be unstable. Major changes in a company

affecting the character of the stock or some unforeseen event not reflected in past returns

may decisively affect the security's future returns.



Other criticisms of Beta are, it can be easily rolled over. Richard Roll has

demonstrated that by changing the market index against which betas are measured, one

can obtain quite different measures of the risk level of individual stocks and portfolios.

As a result, one would make different predictions about the expected returns, and by

changing indexes, one could change the risk-adjusted performance ranking of a manager.

This is in consistent with the results which were found in the study CAPM and Indian

stocks. There also the study suggested that with changing of the market proxy the value

of betas also significantly changed.

Beta is a short-term performer. Some short-term studies have shown risk and

return to be negatively related. For example, Black, Jensen and Scholes found that from

April 1957 through December 1965, securities with higher risk produced lower returns

than less risky securities

Theory does not measure up to practice. In theory, a security with a zero beta

should give a return exactly equal to the risk-free rate. But actual results do not come out

that way, implying that the market values something besides a beta measure of risk.

However, what ever the flaws one can find in the CAPM model, it is one of the

model which is still popularly used in the academics, as mentioned in the introduction,

that the CAPM model is the center piece of the MBA investment courses. It is considered

that unrealistic assumptions can be relaxed, leading to different versions of the CAPM.

1. Inclusion of skew ness (third moment) in the pricing model has led to the

three moment CAPM.

2. Different borrowing and lending rates lead to different CAPM lines and no

general equilibrium pricing model.



3. No risk less asset exists, leading to the zero beta CAPM, which provides

for a theoretical explanation of the basic CAPM empirical results.

4. Consideration of taxes leads to an alternative CAPM model that

incorporates the differential tax effects of dividends and capital gains.

5. There is risk less lending but no risk less borrowing, leading to the zero

betas CAPM.

The CAPM model does not consider the additional factors:

It is certain that there are a variety of risk factors facing companies today. Some

of these factors are market risk, bankruptcy risk, currency risk, supplier risk, etc, and it is

known that the CAPM uses a single factor to describe aggregate risk. Effectively,

additional factors allow more specific attribution of the risks to which a company is

exposed, but CAPM considers only one factor that is the beta.

The attraction of the CAPM is that it offers powerful and intuitively pleasing

predictions about how to measure risk and the relation between expected return and risk.

Unfortunately, the empirical record of the model is poor enough to invalidate the way it is

used in applications. The CAPM’s empirical problems may reflect theoretical failings,

the result of many simplifying assumptions.

Empirical evidence mounts that much of the variation in expected return is

unrelated to market beta. First is Basu’s (1977) evidence that when common stocks are

sorted on earnings-price ratios, future returns on high E/P stocks are higher than predicted

by the CAPM. Banz (1981) documents a size effect; when stocks are sorted on market

capitalization (price times shares outstanding), average returns on small stocks are higher

than predicted by the CAPM.



Bhandari (1988) finds that high debt-equity ratios (book value of debt over the

market value of equity, a measure of leverage) are associated with returns that are too

high relative to their market betas. Statman (1980) and Rosenberg, Reid, and Lanstein

(1985) document that stocks with high book-to-market equity ratios have high average

returns that are not captured by their betas.

Fama and French (1992) update and synthesize the evidence on the empirical

failures of the CAPM. Using the cross-section regression approach, they confirm that

size, earnings-price, debt-equity, and book-to-market ratios add to the explanation of

expected stock returns provided by market beta.

Chan, Hamao, and Lakonishok (1991) find a strong relation between book-to-

market equity (B/M) and average return for Japanese stocks. Capaul, Rowley, and Sharpe

(1993) observe a similar B/M effect in four European stock markets and in Japan. Fama

and French (1998) find that the price ratios that produce problems for the CAPM in U.S.

data show up in the same way in the stock returns of twelve non-U.S. major markets, and

they are present in emerging market returns. This evidence suggests that the

contradictions of the CAPM associated with price ratios are not sample specific.

In the light of above, in this project we are testing whether the CAPM offers a

better explanation of the company returns in Indian capital markets or can we find

evidence of the other factors giving better explanation of the company returns in Indian

capital markets.



Lakshman Alles & Louis Murray:”Risk factors in developing capital markets” 2003, Annual conference of global finance association.

The purpose of this project is to explore alternative explanations of the risk

/reward relationship, in the developing capital markets .It is likely that these markets will

be characterized by various inefficiencies, which will impact on the relationship that is

implied by the capital pricing asset model.

This paper address the question as to whether the CAPM offers an appropriate

explanation of the company returns in less developed capital markets .The question is

whether the CAPM is appropriate, given the potential relevance of unsystematic risk,

Market distortions and of thin trading and its related effects on the market price.

Arguments for considering additional factors in pricing models to better deal with such

situations are presented.

The Methodology used is:

1) Single factor regressions

Average annual daily returns for each company are regressed on the different

measures of risk that is the beta, variance, skew ness, co skew ness.

2) Multiple factor regressions

Three alternative formulations of these tests are

Model 1: [ ] [ ] iiii ebVariancebBetaR +++= 21α ,

Model 2: [ ] [ ] iiii ebSkewnessbBetaR +++= 31α

Model 3: [ ] [ ] [ ] iiiii ebSkewnessbVariancebBetaR ++++= 321α

Model 4: [ ] [ ] [ ] iiiii ebCoskewnessbVariancebBetaR ++++= 421α

The analysis of above regression tests are:

Single factor regressions results:

They confirm the importance of beta, as coefficients of beta are significant in

most cases. It is interesting to note that Sri Lanka, the smallest market, provides the only

exception. Beta values do not offer a significant explanation of average daily returns.

Multiple regressions results:



If Model 1 is considered, it is difficult to identify a dominant explanatory factor.

If Model 2 is considered there is significant relation between company’s return and skew

ness. In Model 3, for most markets, when used in combination with beta, and with each

other, both variance and skew ness remain significantly related to company returns.

In Model 4 the coefficient estimates of the co skew ness variable are significantly

different from zero in at least one of the sub-periods examined in each market.

To conclude, they provide some evidence that, apart from beta, other measure of risk may

also be important in the group of developing markets .variance, and to a lesser extent co

skew ness, offer a more significant explanation of returns in these markets.

Garciaa, Rene, Ghyselsb, U Eric (1998) “Structural Change and Asset Pricing in

Emerging Markets” Journal of International Money and Finance, Vol. 17, pp. 455-

473.

This paper documents the importance of testing for structural change in contexts

of emerging markets. Typically asset pricing factor models for emerging markets are

conditioned on world financial markets factors such as world equity excess rut urns, risk

and maturity spreads as well as other variable.

They show that more may country one cannot reject the model according to one

usual chi square test for over identifying restrictions but they reject it on the basis of

structural change tests, especially when international factors are considered. In this paper

much better support and greater stability are found. When a local CAPM is tested it sized

ranked portfolios. Also some evidence of small size effect persists for some countries.

The methodology applied in this paper is as follows:

They have applied test for structural stability to two leading conditional factors

models: conditional CAPM, conditional factors models on a set of sized portfolio for

each country. These models have been estimated via the generalized method of moments.

They have estimated these models for the following set of markets:

Argentina, Brazil, Chile, Mexico, Korea, India, Thailand, Greece, Jordan and Zimbabwe.



To asses these models the following tests are used.

1) J-test

2) Supremum Lagrangian multiplier test

To conclude, for the conditional world CAPM and conditional local and US factor

model test for structural stability of the GMM parameter estimates show that for most

countries and portfolios according to the case, although we cannot reject the model on the

basis of the over identifying restrictions criterion, the rejection of the absence of

structural change is quite strong. This is quite reasonable if one considers both political

and economical factors that have disrupted these emerging markets in comparison with

world events. This rejection means that the model yields a systematic mispricing of risk

factors.

A much more stable relationship is found however in a simple local CAPM model

for size ranked portfolios, although the small size effect appears to be present in a number

of countries. They show the empirical evidence that the emerging stock markets is also

dependent on structural changes.

Bekaert, G, C Erb, C Harvey, and T Vishkanta (1998), “Distributional

characteristics of Emerging Market Returns and Asset Allocation” The Journal of

Portfolio Management, Vol. 24, pp. 102-116.

They argue that the standard mean variance analysis some what problematic and

with respect to emerging markets. They argue that in this analysis investor care about

expected returns variance and co variances but emerging market returns cannot be

completely characterized by these measures alone. They show that there is significant

skew ness and kurtosis in these returns.

They have tested for non normality of returns in emerging markets and they found

evidence in one of the emerging market (Argentina), that the returns are non normal.

They analyze time varying returns characteristics, which are the skew ness and kurtosis.



They undertake to test whether the 1990’s is different from 1980’s for that they

have used chow test and found that there was a little evidence that mean returns are

significantly different, there is substantial evidence that volatility changed in 1990’s,

there is also evidence that the skew ness in returns changed in 1990’s and kurtosis is

similar to skew ness.

They have explained the fundamental characteristics of emerging market returns.

Then they have mentioned about higher moments and asset allocation .Here they have

looked at the impact of skew ness and kurtosis on asset allocation. They have found that

the emerging markets allocation increases as the skew ness increases up to the level of

1.5.They see that as the level of kurtosis raises beyond 5 the portfolio weight for the

emerging markets increases .hence they conclude that skew ness and the kurtosis impact

the asset allocation.

To conclude, in their research they suggest that it could be a mistake to treat the

emerging markets on par with the developed markets. They report that emerging market

equity index return distributions are highly non normal, in comparison with the

developed market equity index return. They identify significant skew ness and kurtosis in

emerging market return and they obverse the persistence of skew ness over time. They

suggest that investors will have preference for positively skewed investments and they

wish to avoid the negatively skewed distributions .Here one can notice that skew ness

will play an important role in explaining the company returns.

Kraus and Litzenberger (1976) “Skew ness Preference and the Valuation of Risk

Assets” Journal of Finance, Vol. 31, pp. 1085-1099

This paper extends the capital asset pricing model to incorporate the effect of

skew ness on valuation .The empirical evidence presented is consistent with the

prediction of the three moment extension of the traditional CAPM that the intercept is

equal to the risk less rate of interest. The evidence suggest that prior empirical findings

that are interpreted as in consistent with the traditional theory can be attributed to the

misspecification of the CAPM by omission of systematic (non diversifiable) skew ness.



This three moment CAPM model is presented as follows;

R=b0 +β [b1] +γ [b2] +u.

The Methodology used in this paper is as follows:

Stocks were ranked into deciles on the basis of betas and gamma estimates .The

monthly portfolio deflated excess rates of return in each of the subsequent 12 months

(January 1936 through December 1937)were calculated for each of the beta & gamma

decile portfolios. This procedure was repeated for the 120 month periods beginning each

January with the final period being January 1960 through December 1969 .for the final

periods, monthly portfolio returns were available for the subsequent 6 months .in this

way 34.5 years of monthly deflated excess returns from January 1970 through June 1970

for each of 20 portfolios were obtained .

The cross sectional OLS regression is used to estimate the bo,b1,b2.Also cross

sectional simple regression s were run to compare results of fitting the traditional CAPM

or the Vasichek-black or Brennan modifications of it ,with results of fitting the three

moment CAPM.

The Findings of the paper can be summarized as follows:

The results of the cross sectional regressions suggest that the mean intercept is

significantly greater than zero and the mean slope is positive much smaller than the mean

deflated excess rate of return on the market index .There is allows evidence that the

results are consistent with Vasichek-black CAPM with out risk less borrowing. Also

there is evidence that the results are consistent with three moments CAPM.There is also

evidence that higher beta portfolios tend to have more than proportionately higher

gammas .This provides a rationale for the empirical finding that the slope of the capital

market line is lower than predicted by the traditional theory.



To Conclude, investors are found to have an risk aversion to variance and a

preference for positive skew ness .The present paper has shown that when CAPM is

extended to include systematic skew ness, the prediction of a significant price of

systematic skew ness is confirmed and the prediction of a zero intercept for the security

market line in excess return space is not rejected.

Levy, Haim (1978): “Equilibrium in an Imperfect Market: Constraint on the

Number of Securities in the Portfolio” American Economic Review, Vol. 68, pp. 643-

658.

In this paper Levy has tried to narrow the gap between the theoretical model and

the empirical findings by deriving a new version of the CAPM in which investors are

assumed to hold in their portfolios some given no; of securities. He as denoted the

modified model as general capital asset pricing model (GCAPM).

He has relaxed the assumption of a perfect market and hence the k th investors

holds stocks of n companies in his portfolio, where n can be very small i.e. 1, 2 etc.He

has first derived an equilibrium relationship between the return and risk of each security.

He has found that the well known systematic risk of the traditional CAPM beta has little

to do with equilibrium price determination .on the other hand beta * which is a weighted

average of the k th investor systematic risk beta, is the correct measure of the i th security

risk .since variance is a major component of beta, it plays an important role in the risk

measure of each stock, which is contrary to the equilibrium results of the CAPM.

The Methodology applied in this paper is as follows:

The monthly rates of return of a sample of 101stocks traded on the New York

stock exchange were calculated for the period 1948-68 that is for each security there are

240 observations. By using time horizon 2 months, the no: of observations was reduced

to 120. In this paper various linear regressions with monthly data, semi-annual data, and

annual data are examined.



The Findings of this paper is presented as follows:

The empirical findings support the theoretical results. The simple regression of

variance performs much better than the regression of beta. The most important result is of

the regression of the variance & beta, where it was found that the regression co efficient

of the variance was significant, where as the regression co efficient of the beta did not

differ significantly. This confirms that in an imperfect market beta plays no role or at

least a negligible role in price determination.

To Conclude, he has mentioned that the variance plays an important role in the

risk-return relationship, but suggests that it is not the only measure of the i th security

risk. The variance is the only one component in this risk. For securities which are widely

held, beta will provide a better explanation for price behavior, while for most securities,

which are not held by many investors then variance provides a better explanation of the

price behavior.

Fama, Eugene F and French, Kenneth R :( 1993) “Common Risk Factors in the

Returns on Stocks and Bonds” Journal of Financial Economics, Vol. 33, pp. 3-56.

This paper identifies five common factors in the returns on stocks and bonds.

There are three stocks –market factors: an overall market factor and factors related to

firm size and book to market equity.

There are two bond market factors, related to maturity and default risks. Stock

returns have shared variation due to the stock market factors, and they are linked to bond

returns through shared variation in the bond market factors .Except for low grade

corporates, the bond market factors capture the common variation in bond returns. Most

important, the five factors seem to explain average returns on stocks and bonds.



The Methodology used in this can be summarized as follows:

This paper uses the time series regression approach of black, Jensen and scholes

(1972). Monthly returns on the stocks and bonds are regressed on the returns to a market

portfolio of stocks and mimicking portfolios for size, book to market equity and term

structure risk factors in returns. The time series regression slopes are factor loadings that,

unlike size or book to market equity have a clear interpretation as risk factors,

sensitivities for bonds as well as for stocks.

The Findings of the paper were:

The time series regressions for stocks say that size and book to market factors can

explain the differences in average returns across stocks. But these factors alone can’t

explain the large difference between the average returns on stocks and one month bills.

The time series regression for bonds say that the term structure factors also explain the

average returns on bonds, but the average premiums for the term structure factors , like

average excess bond returns are close to zero. The common variation in stock returns is

largely captured by 3 stock portfolio returns and in bond return is largely explained by

two bond portfolio returns.

To conclude, in a nutshell, their results suggest that there are at least three stock

market factors and two term structure factors in returns. Stock returns have shared

variation due to the three stock market factors, and they are linked to bond returns

through shared variations in the two term structure factors. Except for low grade

corporate bonds only the two term structure factors seem to produce common variation in

the returns on government and corporate bonds. There argue that if other variables ,such

as book to market equity, market value, or price earning ratios are considered ,the beta

has no significant influence on the observed returns.



Gregory Connor and Sanjay Sehgal: Tests of the Fama and French model in India:

This paper empirically examines the Fama-French three- factor model for the

Indian stock market. Objectives of the paper are: To test the one- factor linear pricing

relationship implied by the CAPM and the three- factor linear pricing model of Fama and

French, To analyze whether the market, size and value factors are pervasive in the cross-

section of random stock returns, To investigate whether there are market, size and value

factors in corporate earnings similar to those in returns, and whether the common risk

factors in earnings translate into common risk factors in returns.

The Methodology used in this paper can be summarized as follows: 1) Summary statistics on the portfolio returns

Mean, Standard deviation, Skew ness, Excess kurtosis, Auto correlation (ρ1, ρ2 ,ρ3)

2) Correlations between the factor portfolios.

3) Monthly seasonal in portfolio returns.

Estimated differences in mean returns

t-statistics for differences in mean returns

4) Regressions of size and book-to-market sorted portfolio excess returns (Rt) on

combinations of the market (MKT), size (SMB) and value (HML) factor portfolios

5) Constrained estimation of the three-factor model with an excess zero-beta return

6) Growth in earnings for the six size and value sorted portfolios (GE) regressed on

Contemporaneous market (GEMKT), size (GESMB) and value factors (GEHML) in

the growth in earnings.

7) Annual portfolio excess returns (R) regressed on portfolio specific growth in earnings

(GE) one year ahead.

8) Annual portfolio excess returns (R) regressed on market (GEMKT), size (GESMB)

and value (GEHML) factors in the growth in earnings one year ahead.



The findings of this paper can be summarized as follows: Fama and French offer three central findings in support of their three- factor Asset-

pricing model that are pervasive market, size and value factors. This paper examines

these three central findings on the Indian equity market. They confirm the first two of

them, but cannot draw a reliable conclusion on the third. They view their findings as

generally supportive of the Fama-French model applied to Indian equities.

To conclude, the evidence for pervasive market, size, and book-to-market factors in

Indian stock returns is found. They find that cross-sectional mean returns are explained

by exposures to these three factors, and not by the market factor alone. They find mixed

evidence for parallel market, size and book-to- market factors in earnings they do not

find any reliable link between the common risk factors in earnings and those in stock

returns. The empirical results, as a whole, are reasonably consistent with the Fama-

French three- factor model.

Rolf w Banz:(1981)Relationship between return and market value of common stocks: This paper examines the empirical relationship between the return and the market value

of the NYSE common stocks .It is found that smaller firms have had higher risk adjusted

returns on average than large firms and evidence that CAPM is mis specified.

To summarize, Single period CAPM postulates a simple linear relationship between

expected return and the market risk of a security .But results are inconclusive. Evidence

suggests that additional factors are relevant for asset pricing, litzenberger & Ramaswamy

(1979), Basu (1977).results of the study are not based on a particular equilibrium model.

So it is not possible to determine whether market value matters or whatever it is only

proxy for unknown true additional factors correlated with market value.



The data used in this paper, Sample includes all common stocks quoted on the NYSE

between 1926 and 1975, monthly price and return data & no of shares outstanding at the

end of each month. Three different market indices are used CRSP-equally and value

weighted indices, combination of value weighted index & return data on corporate &

government bonds.

The Methodology used is, they have selected 25 portfolios first one to five on the basis of

market value. Then securities in each of those five are in assigned to one of five

portfolios on the basis of their beta. Next five years data are used for the re estimation of

the security beta .stock prices and number of shares outstanding at the end of five year

periods is used for the calculation of the market proportion. The cross-sectional

regression is performed in each month.

To conclude, evidence presented in this paper suggests that the CAPM is mis specified

.Small NYSE firms have had significantly larger risk adjusted returns than large NYSE

firms over a forty year period. The size effect exists but it is not at all clear why it exists

.so it should be interpreted with caution. it might be tempting to use the size effect e g: as

the basis for the theory of mergers larger firms are able to pay a premium for the smaller

stocks since they will be able to discount the same cash flows at a smaller discount rate

.Naturally, this might turn out to be complete nonsense if size were to be shown to be just

a proxy.



Problem statement

CAPM one of the most popular methods used for estimating the required returns,

which states that only beta, the systematic risk has the power to explain the returns. But

recent empirical studies have suggested apart from beta others factors like skew ness,

variance, co skew ness etc also have a significant power to explain the returns and not

alone the beta as suggested by traditional CAPM. In light of this, here in this project we

address the question whether the CAPM offers a better explanation of stock returns in the

Indian capital markets, or can we find the existence of any other factors apart from

systematic risk which offers better explanation of the stock returns in Indian stock

market.

Objectives

1. To test whether the CAPM is appropriate in Indian capital markets

conditions.

2. To find the evidence of other risk factors namely variance and skew ness

in addition to beta (systematic risk) that is present in the Indian capital

markets.

3. To find whether the additional risk factors namely variance and skew ness

present in Indian capital market, offer a better explanation of the stock

returns when compared to beta.

A brief explanation of the above objectives: 1) To test whether the CAPM is appropriate in Indian capital markets conditions

The question is whether the CAPM is appropriate given the potential relevance of

unsystematic risk of the market distortions, thin trading and its related effects on the

market prices. Also to find out whether the CAPM offers a better explanation of stock

returns in the Indian capital market.

2) To find the evidence of other risk factors namely variance and skew ness in addition to

beta (systematic risk) those are present in the Indian capital markets.



Since several researchers have found that the beta is not only the factor which

explains the company returns, but there are also other factors to be considered, so in this

project there is an attempt to find out the additional factors namely variance and skew

ness which are not considered by the capital asset pricing model, that are found in the

Indian capital markets and have considerable influence on the stock returns.

3) To find whether the additional risk factors namely variance and skew ness present in

Indian capital market, offer a better explanation of the stock returns when compared to

beta.

After finding the evidence of the additional factors namely variance and skew

ness that are present in the Indian capital markets, the next objective would be to identify

whether these factors explains the stock returns better than the beta as predicted by the

capital asset pricing model. So that the importance of considering the additional factors is

highlighted.

Scope of the study.

Since many empirical studies have shown that there are also other factors which

explain the company returns, apart from beta, which according to CAPM is the only

factor which explains the company returns ,the study will help the Indian investors to

consider other factors while determining the returns of the company and arrive at proper

decisions.

Limitations of the study 1) The study is restricted to BSE 100 companies.

The sample companies consisted of the stocks in the BSE100 index, out of which,

only 87 companies are considered for the research

2) The research is not done by taking into consideration a bigger index.

The research should have been done taking into consideration a much bigger

index, so that the company sample would be more and the conclusions would have been

more accurate. But it is limited to BSE 100



3) Only 4years data have been taken for the purpose of the study.

Only 4 years data is considered for the purpose of the analysis. However since the

daily data is considered the 4 years data is considered to be relevant and the conclusions

arrived at are accurate.

4) Consideration of limited additional factors.

Only measures like variance, skewness is considered, apart from beta. However

there also other measures like co-skew ness, kurtosis which are not considered in this

study. This can be considered for further research.

Data

Secondary data

Daily adjusted closing price, of the companies included in the BSE 100 and also

for the BSE 100 index is collected for 4 years, which is essential for the purpose of

calculation and analysis.

Sources of Data.

The required data was taken from the prowess 2.5 database and capital line plus

,center for monitoring Indian economy private limited (CMIE).

Period of the study

The study is conducted for a period of 4 years starting from 2002 to 2005.

Four years is taken, so that the results presented are more accurate, and we can rely

upon the results that are calculated for the purpose of analysis.

Sample

The sample consists of companies included in the BSE 100. The sampling

technique used here is convenience sampling, which is by selecting the companies in

the BSE 100.



Sample size

The size of the sample is 87 companies, included in the BSE 100. The

other thirteen companies is not included in the study, because in early years of the

study they were not listed in the BSE 100 and hence the data for the company in that

years as a listed company in the BSE 100 is not available, if these companies are

selected there would be lot of deviations, which would affect the out come of the

results and there by affecting our analysis to an larger extent. Also at the end, our

conclusions would not be accurate.

The companies included in the sample are as follows:

A B B Ltd. G A I L (India) Ltd.

Aditya Birla Nuvo Ltd. Glaxosmithkline Pharmaceuticals Ltd.

Andhra Bank Glenmark Pharmaceuticals Ltd.

Arvind Mills Ltd. Grasim Industries Ltd.

Ashok Leyland Ltd. Great Eastern Shipping Co. Ltd.

Asian Paints Ltd. Gujarat Ambuja Cements Ltd.

Associated Cement Cos. Ltd. H C L Technologies Ltd.

Bajaj Auto Ltd. H D F C Bank Ltd.

Bank Of Baroda Hero Honda Motors Ltd.

Bank Of India Hindalco Industries Ltd.

Bharat Electronics Ltd. Hindustan Lever Ltd.

Bharat Forge Ltd. Hindustan Petroleum Corpn. Ltd.

Bharat Heavy Electricals Ltd. Housing Development Finance Corpn. Ltd.

Bharat Petroleum Corpn. Ltd. I C I C I Bank Ltd.

Century Textiles & Inds. Ltd. I T C Ltd.



Chennai Petroleum Corpn. Ltd. I-Flex Solutions Ltd.

Cipla Ltd. Indian Hotels Co. Ltd.

Colgate-Palmolive (India) Ltd. Indian Oil Corpn. Ltd.

Cummins India Ltd. Indian Overseas Bank

Dr. Reddy'S Laboratories Ltd. Indian Petrochemicals Corpn. Ltd.

Industrial Development Bank Of India Ltd. Pfizer Ltd.

Infosys Technologies Ltd. Ranbaxy Laboratories Ltd.

J S W Steel Ltd. Raymond Ltd.

Jindal Steel & Power Ltd. Reliance Capital Ltd.

Kochi Refineries Ltd. Reliance Energy Ltd.

Kotak Mahindra Bank Ltd. Reliance Industries Ltd.

Larsen & Toubro Ltd. Satyam Computer Services Ltd.

Lupin Ltd. Sesa Goa Ltd.

Mahanagar Telephone Nigam Ltd. Shipping Corpn. Of India Ltd.

Mahindra & Mahindra Ltd. Siemens Ltd.

Mangalore Refinery & Petrochemicals Ltd. State Bank Of India

Matrix Laboratories Ltd. Steel Authority Of India Ltd.

Moser Baer India Ltd. Sterlite Industries (India) Ltd.

Motor Industries Co. Ltd. Sun Pharmaceutical Inds. Ltd.

National Aluminium Co. Ltd. Tata Chemicals Ltd.

Nestle India Ltd. Tata Motors Ltd.

Neyveli Lignite Corpn. Ltd. Tata Power Co. Ltd.

Nicholas Piramal India Ltd. Tata Steel Ltd.

Oil & Natural Gas Corpn. Ltd. Tata Tea Ltd.

Oriental Bank Of Commerce Tata Teleservices (Maharashtra) Ltd.

U T I Bank Ltd. Wipro Ltd.

United Phosphorus Ltd. Wockhardt Ltd.

Videsh Sanchar Nigam Ltd. Zee Telefilms Ltd.

Vijaya Bank



Companies not included in the sample size:

Allahabad Bank

Bharti Airtel Ltd.

Biocon Ltd.

Canara Bank

Jaiprakash Associates Ltd.

Maruti Udyog Ltd.

N T P C Ltd.

Patni Computer Systems Ltd.

Petronet L N G Ltd.

Punjab National Bank

Tata Consultancy Services Ltd.

Ultratech Cement Ltd.

Union Bank Of India



Statistical procedure.

To test whether measures of variance, skew ness might offer an improved

explanation of company returns, individual estimates were prepared for the BSE 100

companies.

Estimates were prepared on an annual basis, for financial years 2002, 2003, 2004,

and 2005 using individual daily market returns for each company.

For each of the sample companies, annual estimates of beta, variance and skewness are

initially estimated. Second pass regressions then offer an indication of whether any of

these estimates offer a significant explanation of company returns. To do this, measures

of average annual daily returns for each company are regressed on the different measures

of risk.

The following two regressions are run;

1. Simple single factor regression tests. It offers an indication of whether individual measures are significant in explaining

the company returns. Here the average annual returns are considered as dependent

variable and the beta, variance and skewness individually as independent variable and

regression is run.

2. Multiple regression tests.

It offers an indication of whether a combination of measures will provide a fuller

explanation of the company returns. Here two independent variables are considered like

beta and variance, beta and skewness and so on.

Three alternative formulations of multiple regression tests are:

Model 1:

A test of the cross sectional explanatory power of market model betas in

competition with the variance of returns:

Ri=α+βi (b1) +Variance (b2) +ei



Model 2:


competition with skew ness of returns:

Ri=α+βi (b1) +Skew ness (b3) +ei

Model 3:


competition with both the variance of returns and the skew ness of returns:

Ri=α+βi (b1) +Variance (b2) +Skew ness (b3) +ei

Back ground of Regression.

Regression shows us how to determine both the nature and the strength of a

relationship between two variables. We will learn to predict, with some accuracy, the

value of an unknown variable based on past variable based on past observations of that

variable and others.

Origin of terms regression and multiple regression.

The term regression was first used as a statistical concept in 1877 by Francis

Galton. Galton made a study that showed that the height of children born to tall parents

tends to move back or regress towards the mean height of the population. He designated

the word regression as the name of the general process of predicting one variable from

another. Later, statisticians coined the term multiple regression to describe the process by

which several variables are used to predict another.

In regression analysis, we develop an estimating equation that is the mathematical

formula that relates the known variables to the unknown variables; here we learn the

pattern of relationship between variables. Regression analysis is based on the relationship

or association between two or more variables. The known variables are called the

independent variables. The variables we are trying to predict are called dependent

variables.



In regression, we can have only one dependent variable in our estimating

equation. However we can use more than one independent variable. Often when we add

independent variables, we can improve the accuracy of our prediction. We can find two

relationships between the variables that is direct relationship, as the independent variable

increases, the dependent variable also increases. The slope of such line is called the

positive slope and inverse relationship, as the independent variable decreases dependent

variable also decreases. The slope of such line is called the negative slope.

Here in regression we have to consider the relationships found by regression to be

relationships of associations but not necessarily of cause and effect. Unless we have

specific reasons for believing that the values of the dependent variable are caused by the

values of the independent variables, we should not infer causality from the relationships

we find by regression.

Multiple regressions

When we use more than one independent variable to estimate the dependent

variable, it is called as multiple regressions. Here we can increase the accuracy of the

estimate.

The principal advantage of multiple regressions is that it allows us to use more of

the information available to us to estimate the dependent variable. In addition, in multiple

regressions, we can look at each individual independent variable and test whether it

contributes significantly to the way the regression describes the data. In this project this is

What we are going do using regression that is testing whether the independent variables

like beta, variance, skew ness individually contribute significantly to the returns and also

in combination whether these independent variables contribute significantly to the

returns.

Multiple regressions will also enable us to fit curves as well as lines. Using the

technique of dummy variables, we can even include qualitative factors such as gender in

our multiple regressions. This technique will enable us to analyze the discrimination

problem.



Dummy variables and fitting curves are only two of the many modeling technique

that can be used in the multiple regression to increase the accuracy of our estimating

equations.

Hypothesis testing Null hypothesis (H0): There is no significant relationship between the risk factors

namely beta, variance, skewness and returns.

Alternative hypothesis (H1): There is significant relationship between the risk factors

namely beta, variance, skewness and returns.

T test is used to test the hypothesis.

For the purpose of running the single factor and multiple regressions and also for testing

hypothesis the SPSS (statistical package for social science) software is used.

We use scatter diagram to find the relationship between return and beta, return and

skewness, return and variance .a brief background of scatter diagram is given below.



SCATTER DIAGRAMS

The first step in determining whether there is relationship between two variables is to examine the graph of the observed (known) data. This graph or chart is known as scatter diagram.

A scatter diagram can give us two types of information. Visually, we can look for patterns that indicate that the variables are related. Then if variables are related we can see what kind of line, or estimation equation, describes this relationship.

In scatter diagrams the pattern of points results because each pair of data will be recorded as a single point. When all these points are visualized together, we can visualize the relationship that exists between the two variables. The following relationships are possible in a scatter diagram 1. Direct linear relationships.

Here the value of Y increases as X increases. Ex:

0

10

20

30

40

50

60

70

80

0 20 40 60 80

2. Inverse linear relationships. Here the value of Y decreases as X decreases. Ex:

0

10

20

30

40

50

60

70

0 20 40 60 80



The relationship between two variables can take the form of a curve. 3. Direct curvilinear relationships.

Here the value of Y increases as X increases Ex:

0

50

100

150

200

250

0 20 40 60 80 100

4. Inverse curvilinear relationships. Here the value of Y decreases as X decreases Ex:

0

50

100

150

200

250

0 20 40 60 80



5. Inverse linear relationship with a widely scattered pattern of points. The wider scattering indicates that there is a lower degree of association between the independent and dependent variables.

Ex:

0102030405060708090

100

0 5 10 15 20 25 30

6. No linear relationship between two variables. Ex:

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40

Based on the scatter diagrams interpretation we find the relationships between the

return and beta, return and variance, return and skew ness in the project and draw

necessary conclusions.



Table 1 showing return, beta, variance and skew ness for the year 2002.

2002 RETURN BETA VARIANCE SKEWNESS A B B Ltd. 0.19793 0.43320 0.11437 -0.00111Aditya Birla Nuvo Ltd. 0.25817 0.53506 0.17121 0.00481Andhra Bank 0.94309 1.04413 0.21841 0.00534Arvind Mills Ltd. 0.89154 1.53131 0.36482 0.02000Ashok Leyland Ltd. 0.35294 0.85887 0.23161 0.00616Asian Paints Ltd. 0.17877 0.27961 0.05568 0.00016Associated Cement Cos. Ltd. 0.08399 0.96599 0.09876 0.00078Bajaj Auto Ltd. 0.28179 0.70551 0.10107 0.00081Bank Of Baroda 0.61456 1.13519 0.15860 0.00185Bank Of India 0.88499 1.08309 0.17022 0.00196Bharat Electronics Ltd. 0.74636 1.88460 0.40970 0.01293Bharat Forge Ltd. 0.86925 1.25259 0.25737 0.00439Bharat Heavy Electricals Ltd. 0.20506 1.06709 0.13443 0.00023Bharat Petroleum Corpn. Ltd. 0.13700 1.39587 0.27918 -0.00815Century Textiles & Inds. Ltd. 0.27162 1.72721 0.31729 0.01557Chennai Petroleum Corpn. Ltd. 0.29135 1.14678 0.21647 0.01138Cipla Ltd. -0.23555 0.20112 0.04610 -0.00081Colgate-Palmolive (India) Ltd. -0.21263 0.19006 0.04506 0.00001Cummins India Ltd. -0.08012 0.59633 0.11213 0.00084Dr. Reddy'S Laboratories Ltd. -0.02778 0.77842 0.10145 -0.00313G A I L (India) Ltd. 0.10821 0.76377 0.10059 0.00108Glaxosmithkline Pharmaceuticals Ltd. 0.06140 0.35467 0.09234 0.00109Glenmark Pharmaceuticals Ltd. 0.23332 0.47375 0.14525 0.00317Grasim Industries Ltd. 0.13805 0.57957 0.05630 0.00028Great Eastern Shipping Co. Ltd. 0.31616 0.78747 0.12282 -0.00067Gujarat Ambuja Cements Ltd. -0.15100 0.80540 0.08225 0.00115H C L Technologies Ltd. -0.38526 1.75626 0.30928 -0.00791H D F C Bank Ltd. -0.02569 0.31753 0.05811 0.00047Hero Honda Motors Ltd. 0.07934 1.10184 0.17703 0.00088Hindalco Industries Ltd. -0.08710 0.39205 0.06030 -0.00039Hindustan Lever Ltd. -0.20745 0.83878 0.07182 0.00014Hindustan Petroleum Corpn. Ltd. 0.72401 1.52649 0.34599 -0.01636Housing Development Finance Corpn. Ltd. 0.07740 0.15433 0.05999 0.00000I C I C I Bank Ltd. 0.46823 0.78730 0.18350 0.00480I T C Ltd. -0.02445 0.54589 0.07264 -0.00001I-Flex Solutions Ltd. 0.56336 0.42512 0.06592 0.00021Indian Hotels Co. Ltd. 0.19886 0.59984 0.09058 0.00018Indian Oil Corpn. Ltd. 0.60333 1.06888 0.19798 0.01167Indian Overseas Bank 0.72361 0.72286 0.15382 -0.00088Indian Petrochemicals Corpn. Ltd. 0.40705 0.85083 0.31532 -0.05355Industrial Development Bank Of India Ltd. 0.31491 0.99961 0.24684 0.00724Infosys Technologies Ltd. 0.15806 1.44348 0.15403 -0.00106J S W Steel Ltd. 0.93031 1.69710 0.54058 0.01444Jindal Steel & Power Ltd. 0.80466 1.29590 0.22191 0.00617



2002 RETURN BETA VARIANCE SKEWNESS Kochi Refineries Ltd. 0.51154 1.27096 0.30601 0.01909Kotak Mahindra Bank Ltd. 1.22813 1.40661 0.49172 0.03073Larsen & Toubro Ltd. 0.10951 0.76142 0.06075 -0.00010Lupin Ltd. 0.42996 1.23017 0.23784 0.00787Mahanagar Telephone Nigam Ltd. -0.28913 1.16727 0.19518 0.00153Mahindra & Mahindra Ltd. 0.23318 1.31713 0.16839 0.00072Mangalore Refinery & Petrochemicals Ltd. 0.03611 1.22052 0.48264 0.02313Matrix Laboratories Ltd. 1.68520 0.07639 0.47048 0.01051Moser Baer India Ltd. -0.58266 0.87107 0.21425 -0.00897Motor Industries Co. Ltd. 0.56347 0.25264 0.07876 0.00060National Aluminium Co. Ltd. 0.62632 1.74012 0.41006 0.01521Nestle India Ltd. 0.01395 0.23889 0.03786 0.00030Neyveli Lignite Corpn. Ltd. 0.81903 2.40589 0.60749 0.02370Nicholas Piramal India Ltd. 0.08416 0.68088 0.08027 -0.00019Oil & Natural Gas Corpn. Ltd. 0.95654 0.92798 0.24390 0.01293Oriental Bank Of Commerce 0.40346 0.66824 0.07685 -0.00057Pfizer Ltd. -0.15453 0.44627 0.04968 0.00142Ranbaxy Laboratories Ltd. 0.31846 0.62777 0.08845 0.00145Raymond Ltd. 0.06428 0.43010 0.08036 0.00044Reliance Capital Ltd. 0.07976 1.29885 0.14228 0.00284Reliance Energy Ltd. 0.11377 0.41141 0.07340 0.00051Reliance Industries Ltd. -0.02472 1.00028 0.09799 0.00252Satyam Computer Services Ltd. 0.16216 2.12208 0.24852 0.00219Sesa Goa Ltd. 0.31493 0.97901 0.30088 0.01183Shipping Corpn. Of India Ltd. 0.80760 1.75218 0.38044 0.00560Siemens Ltd. 0.50190 0.88537 0.14063 0.00076State Bank Of India 0.43719 0.87216 0.09544 0.00107Steel Authority Of India Ltd. 0.74830 1.66982 0.36365 0.02150Sterlite Industries (India) Ltd. 0.01889 0.04288 0.02683 0.00012Sun Pharmaceutical Inds. Ltd. 0.04850 0.20038 0.05197 -0.00004Tata Chemicals Ltd. 0.38420 0.97490 0.15869 0.00323Tata Motors Ltd. 0.48041 1.20408 0.17384 0.00168Tata Power Co. Ltd. -0.06792 1.08603 0.08377 -0.00056Tata Steel Ltd. 0.55244 1.13058 0.12657 0.00068Tata Tea Ltd. 0.03004 0.85333 0.09405 0.00213Tata Teleservices (Maharashtra) Ltd. -0.23428 0.40687 0.15680 0.01041U T I Bank Ltd. 0.52884 1.04190 0.17668 0.00224United Phosphorus Ltd. 1.23431 1.33303 0.68649 0.02597Videsh Sanchar Nigam Ltd. -0.73903 0.59410 0.32061 -0.08455Vijaya Bank 0.68962 0.72884 0.19705 0.01053Wipro Ltd. 0.01744 1.55578 0.21510 0.00224Wockhardt Ltd. -0.08095 0.24939 0.04228 0.00031Zee Telefilms Ltd. -0.13552 1.77132 0.28333 0.00383




2003 RETURN BETA VARIANCE SKEWNESS A B B Ltd. 0.99681 0.42642 0.12532 0.00208Aditya Birla Nuvo Ltd. 1.05460 0.79380 0.18934 0.00785Andhra Bank 0.95032 1.08433 0.28733 0.00358Arvind Mills Ltd. 1.10089 1.13725 0.25367 0.00728Ashok Leyland Ltd. 1.08542 0.92432 0.18363 0.00097Asian Paints Ltd. 0.44029 0.25811 0.05688 0.00107Associated Cement Cos. Ltd. 0.39695 1.14099 0.13456 0.00062Bajaj Auto Ltd. 0.81726 0.41746 0.07961 0.00072Bank Of Baroda 1.11826 1.21131 0.35114 0.00410Bank Of India 0.58160 1.17937 0.21465 0.00041Bharat Electronics Ltd. 1.24895 1.02922 0.16351 0.00342Bharat Forge Ltd. 1.35325 0.69741 0.14927 0.00216Bharat Heavy Electricals Ltd. 1.07941 0.83865 0.11584 0.00143Bharat Petroleum Corpn. Ltd. 0.73106 0.90037 0.13325 0.00083Century Textiles & Inds. Ltd. 1.04348 1.43463 0.30431 0.00798Chennai Petroleum Corpn. Ltd. 1.20012 0.71294 0.22379 0.01211Cipla Ltd. 0.38160 0.47566 0.10556 0.00027Colgate-Palmolive (India) Ltd. 0.16882 0.27244 0.05315 0.00128Cummins India Ltd. 0.96944 0.60378 0.15668 0.00293Dr. Reddy'S Laboratories Ltd. 0.46373 0.50132 0.12377 0.00131G A I L (India) Ltd. 1.31068 1.15422 0.14796 0.00216Glaxosmithkline Pharmaceuticals Ltd. 0.63218 0.27608 0.07611 0.00142Glenmark Pharmaceuticals Ltd. 1.07258 0.82689 0.23513 0.00899Grasim Industries Ltd. 1.15833 0.89613 0.11528 0.00248Great Eastern Shipping Co. Ltd. 1.54851 1.01456 0.22610 0.00527Gujarat Ambuja Cements Ltd. 0.62056 0.78847 0.09536 -0.00007H C L Technologies Ltd. 0.49592 1.51513 0.30789 -0.01214H D F C Bank Ltd. 0.51534 0.49287 0.08520 0.00088Hero Honda Motors Ltd. 0.50310 0.77570 0.16390 0.00089Hindalco Industries Ltd. 0.87612 0.59818 0.08230 0.00025Hindustan Lever Ltd. 0.11891 0.79144 0.08388 0.00011Hindustan Petroleum Corpn. Ltd. 0.41829 0.82779 0.13918 -0.00161Housing Development Finance Corpn. Ltd. 0.58715 0.39320 0.12248 0.00145I C I C I Bank Ltd. 0.74378 0.73126 0.13501 0.00258I T C Ltd. 0.39931 0.56187 0.05805 0.00011I-Flex Solutions Ltd. 0.65593 0.88708 0.22068 0.00572Indian Hotels Co. Ltd. 0.86017 0.61145 0.12932 0.00194Indian Oil Corpn. Ltd. 1.05649 0.92479 0.13861 0.00159Indian Overseas Bank 0.81130 0.69412 0.18947 0.00085Indian Petrochemicals Corpn. Ltd. 1.05106 1.14184 0.16084 0.00150Industrial Development Bank Of India Ltd. 1.07947 0.95685 0.37104 0.01618Infosys Technologies Ltd. 0.15368 1.34154 0.28466 -0.03083J S W Steel Ltd. 0.88000 1.45122 0.51416 0.01194Jindal Steel & Power Ltd. 1.26716 1.38539 0.25876 0.00518



2003 RETURN BETA VARIANCE SKEWNESS Kochi Refineries Ltd. 1.34532 0.89423 0.31670 0.01226Kotak Mahindra Bank Ltd. 0.80171 0.92485 0.26903 0.00685Larsen & Toubro Ltd. 0.90399 0.84825 0.09988 0.00082Lupin Ltd. 1.56980 1.22823 0.33680 0.00350Mahanagar Telephone Nigam Ltd. 0.37278 0.67570 0.18111 0.00425Mahindra & Mahindra Ltd. 1.23900 1.18076 0.14772 0.00097Mangalore Refinery & Petrochemicals Ltd. 1.97978 1.21008 0.42117 0.02673Matrix Laboratories Ltd. 2.09761 0.72072 0.17159 -0.00090Moser Baer India Ltd. 1.49219 0.61016 0.29511 -0.00638Motor Industries Co. Ltd. 1.54259 0.47964 0.09888 0.00084National Aluminium Co. Ltd. 0.74829 1.14966 0.18047 0.00112Nestle India Ltd. 0.27591 0.04129 0.04100 0.00035Neyveli Lignite Corpn. Ltd. 1.03115 1.09994 0.25110 0.00407Nicholas Piramal India Ltd. 1.20538 0.74458 0.17358 0.00486Oil & Natural Gas Corpn. Ltd. 0.82662 1.17326 0.12185 -0.00008Oriental Bank Of Commerce 1.64073 1.29374 0.35378 0.00334Pfizer Ltd. 0.34077 0.35523 0.12131 0.00296Ranbaxy Laboratories Ltd. 0.61580 0.59209 0.06826 -0.00003Raymond Ltd. 0.81376 0.64331 0.15519 0.00354Reliance Capital Ltd. 0.81732 1.11401 0.17044 0.00253Reliance Energy Ltd. 0.83237 1.05436 0.13293 0.00270Reliance Industries Ltd. 0.65480 1.02005 0.08415 -0.00003Satyam Computer Services Ltd. 0.27905 1.76588 0.28573 -0.00242Sesa Goa Ltd. 2.15369 1.21987 0.42205 0.01180Shipping Corpn. Of India Ltd. 0.98443 1.39992 0.35671 0.00784Siemens Ltd. 1.24047 0.56709 0.11731 0.00202State Bank Of India 0.64458 0.95004 0.08732 -0.00017Steel Authority Of India Ltd. 1.60651 1.77821 0.48743 0.02191Sterlite Industries (India) Ltd. 2.24900 0.81212 0.34436 0.02082Sun Pharmaceutical Inds. Ltd. 0.68272 0.63405 0.14261 0.00055Tata Chemicals Ltd. 0.96807 0.90181 0.15071 0.00175Tata Motors Ltd. 1.03077 1.13564 0.11387 0.00038Tata Power Co. Ltd. 1.03326 1.10910 0.11061 -0.00007Tata Steel Ltd. 1.07534 1.23763 0.12775 0.00034Tata Tea Ltd. 0.67853 0.78654 0.10453 -0.00028Tata Teleservices (Maharashtra) Ltd. 1.29418 1.08729 0.37820 0.01730U T I Bank Ltd. 1.10418 0.80987 0.30032 0.02102United Phosphorus Ltd. 1.09948 0.83535 0.37902 0.00613Videsh Sanchar Nigam Ltd. 0.40377 0.65194 0.16287 0.00262Vijaya Bank 1.08676 0.88655 0.29907 0.00551Wipro Ltd. 0.06351 1.64074 0.23497 -0.00707Wockhardt Ltd. 0.47824 0.48647 0.13579 -0.00103Zee Telefilms Ltd. 0.43112 1.01861 0.24644 0.00255




2004 RETURNS BETA VARIANCE SKEWNESS A B B Ltd. 0.36454 0.54424 0.09708 -0.00240Aditya Birla Nuvo Ltd. 0.36323 0.94027 0.19619 -0.00337Andhra Bank 0.50729 1.58318 0.33849 -0.00962Arvind Mills Ltd. 0.69542 1.30318 0.30072 -0.00493Ashok Leyland Ltd. -0.18539 0.92429 0.19723 -0.00310Asian Paints Ltd. -0.04877 0.42765 0.05171 0.00035Associated Cement Cos. Ltd. 0.32161 0.96706 0.12107 -0.00090Bajaj Auto Ltd. -0.00520 0.60641 0.09011 -0.00142Bank Of Baroda 0.02679 1.81104 0.40715 -0.01257Bank Of India 0.35213 1.63588 0.36360 -0.00518Bharat Electronics Ltd. 0.07663 0.82577 0.14924 -0.00060Bharat Forge Ltd. 0.30987 0.67883 0.11605 -0.00065Bharat Heavy Electricals Ltd. 0.41588 1.31412 0.23905 -0.01061Bharat Petroleum Corpn. Ltd. 0.01892 0.98547 0.21463 -0.00227Century Textiles & Inds. Ltd. 0.22706 1.20627 0.27361 -0.00275Chennai Petroleum Corpn. Ltd. 0.92955 1.53102 0.48744 -0.00799Cipla Ltd. 0.18583 0.72287 0.11702 -0.00186Colgate-Palmolive (India) Ltd. 0.11636 0.39375 0.07187 0.00100Cummins India Ltd. -0.04474 0.56142 0.13919 0.00057Dr. Reddy'S Laboratories Ltd. -0.50099 0.47389 0.14089 -0.00799G A I L (India) Ltd. -0.12091 1.81447 0.36452 -0.00115Glaxosmithkline Pharmaceuticals Ltd. 0.29109 0.47140 0.08108 -0.00130Glenmark Pharmaceuticals Ltd. 1.22049 1.00370 0.30255 0.00492Grasim Industries Ltd. 0.27547 0.85670 0.13619 -0.00080Great Eastern Shipping Co. Ltd. 0.08334 1.17205 0.24862 0.00043Gujarat Ambuja Cements Ltd. 0.27888 0.99121 0.13325 -0.00249H C L Technologies Ltd. 0.11357 0.77797 0.16307 0.00111H D F C Bank Ltd. 0.34721 0.88817 0.16164 -0.00236Hero Honda Motors Ltd. 0.24088 0.90643 0.15497 -0.00036Hindalco Industries Ltd. 0.01305 0.71315 0.13267 -0.00045Hindustan Lever Ltd. -0.35521 0.64500 0.10685 -0.00397Hindustan Petroleum Corpn. Ltd. -0.08836 0.96807 0.17425 -0.00362Housing Development Finance Corpn. Ltd. 0.17307 0.62504 0.13646 0.00295I C I C I Bank Ltd. 0.22618 0.85708 0.15667 -0.00064I T C Ltd. 0.28539 0.68335 0.09801 0.00064I-Flex Solutions Ltd. -0.28357 1.06118 0.18538 -0.00020Indian Hotels Co. Ltd. 0.18511 0.63240 0.09142 -0.00093Indian Oil Corpn. Ltd. 0.11599 1.36981 0.24139 -0.00551Indian Overseas Bank 0.82613 1.58263 0.44407 -0.01105Indian Petrochemicals Corpn. Ltd. -0.21422 1.74912 0.33762 -0.00765Industrial Development Bank Of India Ltd. 0.56991 1.64443 0.55262 -0.00287Infosys Technologies Ltd. 0.40671 0.80470 0.11239 -0.00023J S W Steel Ltd. 0.25344 1.17618 0.30537 0.00558Jindal Steel & Power Ltd. 0.37109 1.07791 0.22494 -0.00081



2004 RETURNS BETA VARIANCE SKEWNESSKochi Refineries Ltd. 0.23523 1.09420 0.24291 -0.00511Kotak Mahindra Bank Ltd. 0.39136 0.70127 0.14532 -0.00364Larsen & Toubro Ltd. 0.26461 0.73571 0.14560 -0.00075Lupin Ltd. -0.02093 0.79748 0.16610 -0.00018Mahanagar Telephone Nigam Ltd. 0.11770 1.02643 0.20550 -0.00206Mahindra & Mahindra Ltd. 0.33613 0.99881 0.15545 -0.00039Mangalore Refinery & Petrochemicals Ltd. 0.06172 1.65620 0.35269 -0.00431Matrix Laboratories Ltd. 0.44669 0.35186 0.10451 0.00196Moser Baer India Ltd. -0.39228 0.90833 0.23089 -0.00202Motor Industries Co. Ltd. 0.16719 0.69577 0.12163 -0.00069National Aluminium Co. Ltd. 0.02647 1.28363 0.22957 -0.00609Nestle India Ltd. -0.16487 0.22172 0.04987 -0.00013Neyveli Lignite Corpn. Ltd. 0.11163 1.66963 0.36859 -0.01823Nicholas Piramal India Ltd. 0.67325 0.60957 0.12658 -0.00106Oil & Natural Gas Corpn. Ltd. 0.02477 1.21350 0.19310 -0.00332Oriental Bank Of Commerce 0.26829 1.72223 0.36390 -0.01852Pfizer Ltd. 0.25167 0.69080 0.11901 -0.00132Ranbaxy Laboratories Ltd. 0.13059 0.46697 0.06528 -0.00035Raymond Ltd. 0.32017 0.88980 0.15886 0.00038Reliance Capital Ltd. 0.00228 1.46647 0.25461 -0.00892Reliance Energy Ltd. 0.02608 1.38482 0.27383 -0.01827Reliance Industries Ltd. -0.07086 1.11896 0.12972 -0.00483Satyam Computer Services Ltd. 0.10960 0.93562 0.15582 0.00026Sesa Goa Ltd. 0.55403 1.04848 0.37692 0.00042Shipping Corpn. Of India Ltd. -0.04965 1.57102 0.33996 -0.01597Siemens Ltd. 0.20816 0.65362 0.11059 -0.00516State Bank Of India 0.19195 1.37198 0.20009 -0.00635Steel Authority Of India Ltd. 0.20298 1.73992 0.37098 -0.01006Sterlite Industries (India) Ltd. -0.18585 0.84841 0.18881 -0.00036Sun Pharmaceutical Inds. Ltd. 0.62196 0.51600 0.15634 -0.00035Tata Chemicals Ltd. 0.07637 1.16474 0.21690 -0.00399Tata Motors Ltd. 0.11051 1.27835 0.19118 -0.00040Tata Power Co. Ltd. 0.21848 1.48270 0.25828 -0.01116Tata Steel Ltd. 0.26395 1.34781 0.20594 -0.00189Tata Tea Ltd. 0.32204 1.00435 0.16020 -0.00139Tata Teleservices (Maharashtra) Ltd. 0.36367 1.13212 0.29744 0.00667U T I Bank Ltd. 0.31505 1.05188 0.32542 -0.00172United Phosphorus Ltd. 0.33204 0.64445 0.14370 -0.00007Videsh Sanchar Nigam Ltd. 0.44967 0.95607 0.24440 0.00046Vijaya Bank 0.55192 1.41138 0.35045 -0.01342Wipro Ltd. 0.25576 1.17886 0.19296 0.00056Wockhardt Ltd. 0.38727 0.53259 0.16386 0.00357Zee Telefilms Ltd. 0.13128 0.73739 0.26005 0.00221




2005 RETURN BETA VARIANCE SKEWNESSA B B Ltd. 0.68733 0.56230 0.07949 0.00113Aditya Birla Nuvo Ltd. 0.54144 0.63611 0.09735 0.00030Andhra Bank 0.03248 1.41889 0.15994 0.00133Arvind Mills Ltd. -0.32490 1.42359 0.14341 0.00035Ashok Leyland Ltd. 0.26645 1.18014 0.12413 0.00150Asian Paints Ltd. 0.58975 0.38312 0.04597 0.00006Associated Cement Cos. Ltd. 0.45566 0.78671 0.06151 -0.00005Bajaj Auto Ltd. 0.57005 0.83693 0.07988 0.00008Bank Of Baroda 0.00249 1.67011 0.16343 -0.00039Bank Of India 0.30521 1.92050 0.24596 0.00226Bharat Electronics Ltd. 0.41352 0.99744 0.08103 0.00059Bharat Forge Ltd. 0.60433 1.04559 0.10995 0.00107Bharat Heavy Electricals Ltd. 0.58810 1.01439 0.08969 0.00087Bharat Petroleum Corpn. Ltd. -0.05522 0.78746 0.08925 0.00072Century Textiles & Inds. Ltd. 0.53213 1.47440 0.17210 0.00194Chennai Petroleum Corpn. Ltd. 0.00391 0.94124 0.12865 0.00173Cipla Ltd. 0.33478 0.92365 0.09178 0.00029Colgate-Palmolive (India) Ltd. 0.40667 0.69686 0.07029 0.00017Cummins India Ltd. 0.25909 0.72127 0.10582 0.00038Dr. Reddy'S Laboratories Ltd. 0.12294 0.80844 0.07950 -0.00008G A I L (India) Ltd. 0.14163 1.17547 0.09399 0.00063Glaxosmithkline Pharmaceuticals Ltd. 0.37576 0.65054 0.06706 0.00031Glenmark Pharmaceuticals Ltd. 0.26058 0.94289 0.18307 0.00351Grasim Industries Ltd. 0.05079 0.82979 0.05680 0.00021Great Eastern Shipping Co. Ltd. 0.32386 0.75147 0.11656 0.00114Gujarat Ambuja Cements Ltd. 0.39659 0.97810 0.08971 0.00025H C L Technologies Ltd. 0.45135 1.06485 0.11000 0.00037H D F C Bank Ltd. 0.31005 0.89002 0.08415 0.00073Hero Honda Motors Ltd. 0.40902 0.87481 0.10820 0.00012Hindalco Industries Ltd. 0.06623 1.06545 0.08119 -0.00046Hindustan Lever Ltd. 0.31814 0.86538 0.08610 0.00050Hindustan Petroleum Corpn. Ltd. -0.19742 0.81942 0.07023 0.00051Housing Development Finance Corpn. Ltd. 0.45321 0.73121 0.08658 0.00029I C I C I Bank Ltd. 0.45557 1.13989 0.10018 0.00004I T C Ltd. 0.48625 0.76281 0.07928 0.00169I-Flex Solutions Ltd. 0.52373 0.84289 0.10467 0.00099Indian Hotels Co. Ltd. 0.60528 0.76267 0.06919 0.00026Indian Oil Corpn. Ltd. 0.08173 0.61423 0.06057 0.00033Indian Overseas Bank 0.17448 1.18389 0.16346 0.00146Indian Petrochemicals Corpn. Ltd. 0.25606 1.16404 0.08939 0.00050Industrial Development Bank Of India Ltd. -0.12240 1.39002 0.19486 0.00126Infosys Technologies Ltd. 0.36084 1.08935 0.06813 -0.00016J S W Steel Ltd. -0.47233 1.19740 0.17477 0.00034Jindal Steel & Power Ltd. 0.56515 1.13367 0.11705 0.00139



2005 RETURN BETA VARIANCE SKEWNESSKochi Refineries Ltd. -0.21071 0.63388 0.09583 -0.00399Kotak Mahindra Bank Ltd. 0.67701 0.92825 0.17829 0.00358Larsen & Toubro Ltd. 0.63021 0.90305 0.08950 0.00082Lupin Ltd. 0.11222 0.66753 0.11536 0.00205Mahanagar Telephone Nigam Ltd. -0.07158 1.04561 0.11109 0.00019Mahindra & Mahindra Ltd. 0.63170 1.03528 0.07757 0.00019Mangalore Refinery & Petrochemicals Ltd. -0.14438 1.11142 0.10965 0.00165Matrix Laboratories Ltd. -0.00627 1.15814 0.22333 -0.00013Moser Baer India Ltd. -0.16894 0.87158 0.14446 0.00282Motor Industries Co. Ltd. 0.40437 0.34630 0.06555 0.00185National Aluminium Co. Ltd. 0.08966 1.20197 0.10180 -0.00105Nestle India Ltd. 0.47073 0.20209 0.06152 0.00052Neyveli Lignite Corpn. Ltd. 0.08352 0.95099 0.10252 -0.00023Nicholas Piramal India Ltd. -0.12518 0.94544 0.14832 0.00044Oil & Natural Gas Corpn. Ltd. 0.36023 0.91666 0.06075 -0.00033Oriental Bank Of Commerce -0.21254 1.04959 0.10720 0.00101Pfizer Ltd. 0.38319 0.32336 0.06844 0.00036Ranbaxy Laboratories Ltd. -0.54626 0.83206 0.11334 -0.00055Raymond Ltd. 0.24239 0.68849 0.10548 0.00082Reliance Capital Ltd. 1.20268 1.61032 0.29718 0.00993Reliance Energy Ltd. 0.14215 1.12895 0.09640 0.00168Reliance Industries Ltd. 0.51081 1.04758 0.05993 0.00009Satyam Computer Services Ltd. 0.58776 1.33560 0.10608 -0.00017Sesa Goa Ltd. 0.67566 1.26157 0.26786 0.01017Shipping Corpn. Of India Ltd. -0.05408 0.93192 0.08275 0.00036Siemens Ltd. 1.00475 0.67999 0.09780 0.00224State Bank Of India 0.32990 1.28917 0.08244 -0.00025Steel Authority Of India Ltd. -0.14778 1.35039 0.14779 -0.00030Sterlite Industries (India) Ltd. 0.52117 1.33778 0.14437 -0.00002Sun Pharmaceutical Inds. Ltd. 0.20727 0.54665 0.07213 -0.00034Tata Chemicals Ltd. 0.35064 0.75069 0.08674 0.00119Tata Motors Ltd. 0.25672 1.21681 0.09928 0.00017Tata Power Co. Ltd. 0.10951 1.30215 0.11091 0.00068Tata Steel Ltd. -0.01345 1.17558 0.08243 -0.00051Tata Tea Ltd. 0.69510 0.80180 0.06041 0.00043Tata Teleservices (Maharashtra) Ltd. -0.16719 1.24510 0.17521 0.00554U T I Bank Ltd. 0.43578 0.78224 0.14316 0.00126United Phosphorus Ltd. 0.43478 0.56786 0.12070 0.00364Videsh Sanchar Nigam Ltd. 0.50349 1.59614 0.22694 0.00306Vijaya Bank -0.17999 1.30804 0.15583 0.00205Wipro Ltd. 0.21444 1.30068 0.09141 0.00007Wockhardt Ltd. 0.22963 0.72962 0.10680 0.00039Zee Telefilms Ltd. -0.08664 0.99997 0.16794 0.00016



SCATTER DIAGRAMS X axis= Return Y axis=Beta Return v/s Beta: 2002

2002

-1.0000

-0.5000

0.0000

0.5000

1.0000

1.5000

2.0000

0.0000 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000

Beta

Ret

urn

Return v/s Beta: 2003

2003

0.0000

0.5000

1.0000

1.5000

2.0000

2.5000

0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000

Beta

Ret

urns



Return v/s Beta: 2004 2004

-0.6000

-0.4000

-0.2000

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

1.4000

0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000

Beta

Ret

urn

Return v/s Beta: 2005

2005

-0.80000

-0.60000

-0.40000

-0.20000

0.00000

0.20000

0.40000

0.60000

0.80000

1.00000

1.20000

1.40000

0.00000 0.50000 1.00000 1.50000 2.00000 2.50000

Beta

Ret

urns



Interpretation:

Excepting in the years 2002 and 2003, where we can find a direct linear

relationship with wide scattering, in other two years there is no evidence of linear

relationship between beta and return as propounded by the CAPM model. However one

cannot rule out the CAPM completely in the Indian context, because there is evidence of

beta being the significant explanatory variable.

RETURN V/S VARIANCE X axis: Return Y axis: Variance Return v/s Variance 2002

2002

-1.0000

-0.5000

0.0000

0.5000

1.0000

1.5000

2.0000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000

Variance

Ret

urn



Return v/s Variance 2003

2003

0.0000

0.5000

1.0000

1.5000

2.0000

2.5000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000

Variance

Ret

urns


2004

-0.6000

-0.4000

-0.2000

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

1.4000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000

Variance

Ret

urns




2005

-0.80000

-0.60000

-0.40000

-0.20000

0.00000

0.20000

0.40000

0.60000

0.80000

1.00000

1.20000

1.40000

0.00000 0.05000 0.10000 0.15000 0.20000 0.25000 0.30000 0.35000

Variance

Ret

urns

Interpretation:

In the above scatter diagrams we can find that, the variance and the return as a

direct linear relationship with wide scattering in three years that is 2002, 2003 & 2004

indicating that the variance is better proxy than the beta. The variance can be considered

as a better explanatory variable of the returns than the beta when both are considered

individually. However the variance and the return relationship in the year 2005 cannot be

found as indicated by the scatter diagram, where we can find that the points are widely

scattered indicating no relationship what so ever between return and variance in the year

2005. It can also be noted that the variance is considered to be the alternative proxy,

which came to be true in this analysis.



Return v/s skew ness X axis: Return Y axis: skewness Return v/s skew ness 2002

2002

-1.0000

-0.5000

0.0000

0.5000

1.0000

1.5000

2.0000

-0.1000 -0.0800 -0.0600 -0.0400 -0.0200 0.0000 0.0200 0.0400

Skewness

Ret

urns

Return v/s skew ness 2003

2003

0.0000

0.5000

1.0000

1.5000

2.0000

2.5000

-0.0400 -0.0300 -0.0200 -0.0100 0.0000 0.0100 0.0200 0.0300

Skewness

Ret

urns



Return v/s skew ness 2004 2004

-0.6000

-0.4000

-0.2000

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

1.4000

-0.0200 -0.0150 -0.0100 -0.0050 0.0000 0.0050 0.0100

Skewness

Ret

urns

Return v/s skew ness 2005

2005

-0.80000

-0.60000

-0.40000

-0.20000

0.00000

0.20000

0.40000

0.60000

0.80000

1.00000

1.20000

1.40000

-0.00002000 -0.00001000 0.00000000 0.00001000 0.00002000 0.00003000 0.00004000 0.00005000

Skewness

Ret

urns



Interpretation:

In the above scatter diagrams we can find that, the skew ness and the return has a

direct linear relationship with scattering in three years that is 2002, 2003 & 2005

indicating that the skew ness is better proxy than the beta. The skew ness can be

considered as a better explanatory variable of the returns than the beta when both are

considered individually. However the skew ness and the return relationship in the year

2004 cannot be found as indicated by the scatter diagram, where we can find that the

points are widely scattered indicating no relationship what so ever between return and

skew ness in the year 2004.

Conclusion:

When the scatter diagram is used to find the linear relationship between the beta

and return as indicated by the CAPM model, we can conclude that the beta cannot be

completely ruled out, since it is being an significant explanatory variable in as many as

two years i.e. 2002 and 2003. But we can also find the evidence of other risk factor’s

presence in the Indian capital markets that is the variance and skew ness. However we

cannot find complete linear relationship between the beta and the return as indicated by

the traditional CAPM model. Also the beta in combination with other risk factors is a

better explanatory variable of the returns, giving an indication of not rejecting the CAPM

model completely.



Single factor regression results: Dependent variable: Return Independent variable: Beta Table 5 showing co efficient of beta Year Constant T value Beta

coefficient T value

2002 0.053121 0.592316 0.259056 3.053341*2003 0.648909 4.873816 * 0.299030 2.152819*2004 0.135658 1.636895 ** 0.070013 0.9173552005 0.406188 3.641318 * -0.145037 -1.336002

* and ** statistically significant coefficients, at the 5% and 10% respectively.

When beta is considered, it can be seen that it offers a significant explanation of

the company returns in the years 2002 & 2003 at 5%level of significance, there by

rejecting the null hypothesis and accepting the alternative hypothesis. But in the years

2004 & 2005 it does not explain the returns significantly either at 5% or 10% level of

significance, where the null hypothesis is accepted. However the constant explains the

returns significantly in the years 2003 & 2005 at 5% level of significance and in the year

2004 at 10%level of significance, if beta is assumed to be zero.

When variance is considered as second independent variable, Dependent variable: Return Independent variable: Variance Table 6 showing co efficient of variance Year Constant T value Variance

coefficient T value

2002 -0.023788 -0.376796 1.672537 6.224444*2003 0.514651 5.719405* 2.065359 5.081366*2004 0.043934 0.682388 0.774762 2.818348*2005 0.300456 3.507213* -0.321938 -0.462548

*& ** statistically significant coefficients, at the 5% and 10% respectively.



When variance is considered it offers a significant explanation of the returns in

the years 2002, 2003 & 2004 at 5% level of significance, there by rejecting the null

hypothesis and accepting the alternative hypothesis. The only exception is in the year

2005 where it does not explain the return significantly either at 5% or 10% levels where

the null hypothesis is accepted. However the constant explains the returns significantly in

the years 2003 & 2005 at 5% level of significance when variance is assumed to be zero.

However in the years 2002 and 2004 it does not offer a significant explanation of the

returns.

Dependent variable: Return Independent variable: Skew ness Table 7 showing co efficient of skew ness Year Constant T value Skew ness

coefficient T value

2002 0.259265 6.473280* 14.320617 4.940990*

2003 0.805578 17.889902* 35.087666 6.008564*

2004 0.220013 6.340402* 4.419038 0.7442542005 0.210835 5.862882* 56.450537 3.236677*

* & ** statistically significant coefficients, at the 5% and 10% respectively.

When skew ness is considered it offers a significant explanation of the returns in

the years 2002, 2003 and 2005 at 5% level of significance there by rejecting the null

hypothesis and accepting the alternative hypothesis. The only exception is in the year

2004 where it does not offer significant explanation of returns either at 5% or 10% where

the null hypothesis is accepted and alternative hypothesis is rejected. However the

constant explains the returns significantly in all the four years at 5% level of significance,

when the skew ness is assumed to be zero.



Multiple regression results Model 1:

Dependent variable: Return

Independent variables: Beta, Variance

Table 8 showing co efficient of beta and variance.

Beta Variance Year Constant T value co efficient

T value coefficient

T value

2002 0.025550 0.325816 -0.107718 -1.059313 1.940456 5.260523*

2003 0.598629 4.981936* -0.169693 -1.053701 2.414156 4.607231*

2004 0.178635 2.317112* -0.394317 -2.915611* 2.037230 4.019109*

2005 0.399778 3.545930* -0.191651 -1.346446 0.460701 0.509472 * & ** statistically significant coefficients, at the 5% and 10% respectively.

In combination the variance explains the returns significantly better than beta in

the years 2002 and 2003 at 5% level of significance. However in the year 2004 both beta

and variance offer a significant explanation of the returns at 5% level of significance .in

the year 2005 none of the measures explain the returns significantly either at 5% or 10%

level of significance .The constant explains the returns significantly in the years 2003,

2004 and 2005 at 5% level of significance when the beta and variance is assumed zero.

Only exception is in the year 2002, it either offers significant explanation of returns at 5%

or10% level significance.



Model 2:

Dependent variable: Return

Independent variable: Beta, skew ness

Table 9 showing co efficient of beta and skew ness

Beta Skew ness Year Constant T value co efficient

T value coefficient

T value

2002 0.111587 1.345463 0.163014 2.022704* 12.644533 4.264370*

2003 0.591528 5.242652* 0.242601 2.061831* 34.129826 5.935795*

2004 0.070142 0.774876 0.172755 1.788721** 12.790120 1.705094**

2005 0.434837 4.177870* -0.237706 -2.286103* 65.936665 3.763235*


When beta and skew ness is considered both in combination explain the return

significantly in the years 2002, 2003, and 2005 at 5 % level of significance in the year

2004 both in combination explain the return significantly at 10% level of significance.

The constant explains the returns significantly in the years 2003 and 2005 at 5% level of

significance. The exception being in the years 2002 and 2004 where it does not explain

the returns either at 5% and 10% level of significance, when beta and skew ness is

assumed to be zero.

Model 3: Dependent variable: Return Independent variable: Beta, Variance, Skew ness Table 10 showing co efficient of beta, variance and skew ness

Beta co- Variance Skew nessYear Constant T value efficient

T value Co efficient

T value coefficient

T value

2002 0.0786 1.0795 -0.1565 -1.6698** 1.7596 5.1738* 10.9219 4.1764*

2003 0.5806 5.2195* 0.0369 0.2335 1.1224 1.9116** 26.7290 3.8973*

2004 0.1279 1.5004 -0.2985 -1.9678* 1.9543 1.3669 9.5706 3.8475*

2005 0.4946 4.8228* 0.0060 0.0445 -2.9895 -2.7527* 107.7892 4.7457*




When all the measures are considered, it remains inconclusive whether all the

measures explain the returns , in combination at a particular level of significance however

in the year 2002 and 2005 the variance and skew ness offer an significant explanation of

the returns at 5% level of significance , in the year 2004 the skew ness and beta offer

explanation to returns at 5% level of significance .considering individual measures the

skew ness offers an better explanation of returns in the year 2004 at 5% level of

significance ,the variance explains the returns in the year 2003 at 10% level of

significance ,the beta explains returns in the year 2004 and 2002 at 5% and 10% level of

significance respectively.

The constant explains the returns significantly in the years 2002 and 2005 at 5%

level of significance , the years 2002 and 2004 both being an exception either at 5% and

10% level of significance when all the measures are assumed to be zero.



Conclusion: BETA

Year T tabulated T calculated Null Hypothesis Alternative Hypothesis Since 2002 1.96 3.053341* Rejected Accepted T CAL > T TAB 2003 1.96 2.152819* Rejected Accepted T CAL > T TAB 2004 1.96 0.917355 Accepted Rejected T CAL < T TAB 2005 1.96 -1.336002 Accepted Rejected T CAL < T TAB

VARIANCE

Year T tabulated T calculated Null Hypothesis Alternative Hypothesis since 2002 1.96 6.224444* Rejected Accepted T CAL > T TAB 2003 1.96 5.081366* Rejected Accepted T CAL > T TAB 2004 1.96 2.818348* Rejected Accepted T CAL > T TAB 2005 1.96 -0.462548 Accepted Rejected T CAL < T TAB

SKEWNESS

Year T tabulated T calculated Null Hypothesis Alternative Hypothesis Since 2002 1.96 4.940990*

Rejected Accepted T CAL > T TAB 2003 1.96 6.008564*

Rejected Accepted T CAL > T TAB 2004 1.96 0.744254 Accepted Rejected T CAL < T TAB 2005 1.96 3.236677*

Rejected Accepted T CAL > T TAB The T tabulated is taken at 5% or 10% (two tail test). This study provides some evidence that apart from beta, other measures of risk

may also be important in estimating company returns or cost of equity. Variance and

skew ness offer a more significant explanation of returns in the Indian capital markets.



There is evidence to show in the project that beta is not only the risk factor which

explains the company returns, there are evidence of other risk factors such as variance

and skew ness significantly explaining the company returns. It can also be seen that the

variance and skew ness is significantly explaining the returns in most of the years either

in either at 5% or 10% level of significance, when compared to the beta.

In combination it seems that the variance is a better proxy than the beta when

model 1 is considered signifying that the variance is better proxy than the beta. Even

skew ness is considered to be a significant explanatory variable of the returns. In multiple

regression results we can see that the skew ness dominating the other risk factors that is

the beta and variance in all most all the years.

However we cannot completely rule out the CAPM in the Indian context, because

in the results it can also be seen that the beta can also be a significant explanatory

variable of the returns in the years 2002 & 2004. Also in combination it seems that beta is

the dominating variable in model 2, in all the years. There fore we cannot completely rule

out the CAPM model.

It can be concluded that beta is not only the factor which explains the returns

significantly as predicted by the CAPM, but also other risk factors are present in Indian

capital markets which explains the return significantly, indicating consideration of the

other factors.

When we consider scatter diagram we can see that the beta has direct linear

relationship with wide scattering with returns in two years that is 2002 &2003 as

predicted by the CAPM. However there is strong evidence that variance and the skewness

are present in the Indian capital markets. In most of the years the skewness and the

variance have direct linear relationship with returns with wide scattering.



The scatter diagram is giving the indication of CAPM being appropriate in the

Indian capital market in the years 2002 and 2003, indicating that the model cannot be

completely ruled out. Even the regression results are indicating that beta is a significant

explanatory variable of the return either individually or in combination. However the

other risk factors namely the variance and skewness are found to be present in Indian

capital markets. These factors also significantly explain the returns in the Indian capital

markets. Both variance and skewness explain return better than beta in most of the years.

As an extension of the study, sample size may be expanded and co-skewness

may be included as another measure of risk. Industry-wise time-series/cross-sectional

analysis also can be done to identify industry-wise risk factors.



GLOSSARY: Beta: Is the measure of systematic risk (non diversifiable risk).

Return: Return is a financial term that refers to the benefit derived from an investment.

Risk: Risk is the potential impact (positive or negative) to an asset or some characteristic

of value that may arise from some present process or from some future event

Skew ness: skewness is a measure of the asymmetry of the probability distribution of a

real-valued random variable.

Scatter diagram: The graphical relationship between two variables is called scatter

diagram.

Security market line: The graphic relationship between expected return on asset i and

beta is called the security market line.

Variance: The variance of a random variable is a measure of its statistical dispersion,

indicating how far from the expected value its values typically are. The variance of a real-

valued random variable is its second central moment, and it also happens to be its second

cumulant. The variance of a random variable is the square of its standard deviation.



Bibliography: Websites: 1. www.bse.com

2. www.google.com

Books and Journals

1. Statistical methods- Levin and Lubin.

2. Investments-Marcus and Boodie.

3. Journal of finance.

4. Journal of portfolio management.

5. Journal of International Money and Finance.

6. Review of Economics and Statistics.

References

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