risk factors in indian stock market wrt capm

8/7/2019 Risk Factors in Indian Stock Market Wrt CAPM

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Risk Factors In Indian Capital Markets

M.P Birla Institute of Management Page 1

A RESEARCH REPORT

ON

Risk factors in Indian capital market

Submitted in partial fulfillment of the requirements of

The MBA Degree Course of Bangalore University

Submitted By :

PAWAN KUMAR

(REGD.NO:06XQCM 6058)

Under the Guidance and Supervision

Of

PROF.S. SANTHANAM

M.P.BIRLA INSTITUTE OF MANAGEMENT

Associate Bharatiya Vidya Bhavan

# 43, Race Course Road, Bangalore-560001

2006-2008


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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 forMBA 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 (PAWANKUMAR)

DATE: (06XQCM 6058)


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Principals Certificate

This to certify that this report titled Risk factors in Indian capital

market have been prepared by Pawan kumar bearing the

registration No.06XQCM6058 under the guidance and supervision of

PROF.S.SANTHANAM ,Faculty MPBIM, Bangalore.

Place: Bangalore

(Dr.N.S.Malavalli)

Date Principal


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GUIDES CERTIFICATE

This is to certify that the Research Report entitled Risk factors in

Indian capital market, done by Pawan kumar bearing Registration

No.06 XQCM 6058 is a bonafide work done carried under my

guidance during the academic year 2007-08 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.S.SANTHANAM

Date: MPBIM


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ACKNOWLEDGEMENT

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

institute of management, Bangalore, who has given his valuable

support during my project.

I am extremely thankful to PROF.S.SANTHANAM,

M.P.Birla institute of Management, Bangalore, who has guided me to

do this project by giving valuable suggestions and advice.

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

wishers who helped me to do this project.

Date PAWAN KUMAR


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TABLE OF CONTENTS

CHAPTER PARTICULARS

EXECUTIVE SUMMARY

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.

Skewness 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


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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


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LIST OF TABLES

TABLE

NO

TABLE NAME

1 Showing return, beta, variance and skewness for the year 2004.




5 Showing co efficient of beta

6 Showing co efficient of variance

7 Showing co efficient of skewness

8 Showing co efficient of beta and variance.

9 Showing co efficient of beta and skewness

10 Showing co efficient of beta, variance and skewness.


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EXECUTIVE SUMMARY

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, skewness

in pricing models to better deal with such situations are presented.

Using bse 100 stock returns data for financial years 2004 to 2007, a

series of empirical tests examine whether these factors, in a cross

sectional regression model, offer a statistically significant explanation

of company returns.


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CHAPTER 1

INTRODUCTION


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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.


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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 diversificationand 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) = R

f+ [E (R

M)-R

f]

IM

Where,

Rf is the risk free rate of return.

Rm is the market return.

E (Ri) expected rate of return.

IM

systematic risk of market.

E (Rm)-Rf is the risk premium.


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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:

A= COV (R

A, R

M)/

2

M

Where,

RA

is the return of the asset.

Rm

is the return of the market.

2

M

is the variance of the return of the market, and

Cov (RA, R

m) 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 markets 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


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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:

2

p =

2

ep +

p

2

2

m

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.


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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), ifrontier. 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 assets 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


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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 stocks alpha, which is

denoted by .

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)


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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 thequality 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 andManish 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.


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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 cant 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 shownthat 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 skewness 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 skewness 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


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other measures of systematic risk also. Besides macroeconomic variables, some

successful proxies for systematic risk include a firms 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 companys 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 betashould 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.


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However, whatever 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 skewness (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 betas 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 CAPMs 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 Basus (1977) evidence that when common


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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 capitalmarkets.


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CHAPTER 2

LITERATURE

REVIEW


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Lakshman Alles & Louis Murray:Risk factors in developing capital

markets 2005, 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 effectson 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, skewness, co-skewness.

2) Multiple factor regressions

Three alternative formulations of these tests are

Model 1: R= +Beta[b]+varience[b2]+ei ,

Model 2: Ri=+ Beta[b]+Skewness [b3]+e,

Model 3: Ri=+ Beta[b]+ varience[b2]+Skewnessi[b3]+e,

Model 4: Ri= + Beta[b]+ varience[b2] +Coskewnessi[b4]+e,


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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 companys return and skewness. In Model 3, for most markets,

when used in combination with beta, and with each other, both variance and

skewness remain significantly related to company returns.In Model 4 the coefficient estimates of the co skewness 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 skewness, offer a more significant explanation of returns in

these markets.

Garcia, 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.


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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.


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They argue that the standard mean variance analysis somewhat 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 skewness 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

skewness and kurtosis. They undertake to test whether the 1990s is different

from 1980s for that they have used chow test and found that there was a little

evidence that mean returns are significantly different, there is substantialevidence that volatility changed in 1990s, there is also evidence that the

skewness in returns changed in 1990s and kurtosis is similar to skewness.

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 skewness and kurtosis on asset

allocation. They have found that the emerging markets allocation increases as

the skewness 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 skewness 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

skewness and kurtosis in emerging market return and they obverse the

persistence of skewness 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 skewness will play an

important role in explaining the company returns.


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Kraus and Litzenberger (1976) Skewness 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

skewness 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) skewness.

This three moment CAPM model is presented as follows;

R=b0 + [b1] + [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 ,withresults 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


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

evidence that the results are consistent with Vasichek-black CAPM without 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 skewness .The present paper has shown that when

CAPM is extended to include systematic skewness, the prediction of a

significant price of systematic skewness is confirmed and the prediction of a

zero intercept for the security market line in excess return space is not rejected.

Levy, Him (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


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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.


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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 corporate, 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 marketequity 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 cant 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


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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,

Skewness, Excess kurtosis, Auto correlation (1, 2, 3)

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.


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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. Thispaper 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.


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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 todiscount 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.


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CHAPTER 3

RESEARCH

METHODOLOGY


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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 skewness, variance, co- skewness 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 skewness in

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

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 skewness 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 whichexplains 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 skewness which are not considered by the capital asset pricing


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model, that are found in the Indian capital markets and have considerable

influence on the stock returns.

After finding the evidence of the additional factors namely variance and

skewness 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 Indianinvestors 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-skewness, kurtosis which is not considered in

this study. This can be considered for further research.


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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 relyupon 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

outcome of the results and there by affecting our analysis to an larger extent.

Also at the end, our conclusions would not be accurate.


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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.


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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


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Statistical procedure.

To test whether measures of variance, skewness 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 2004, 2005,

2006, and 2007 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=+i (b1) +Variance (b2) +ei


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Model 2:


competition with skewness of returns:

Ri=+i (b1) +Skewness (b3) +ei

Model 3:


competition with both the variance of returns and the skewness of returns:

Ri=+i (b1) +Variance (b2) +Skewness (b3) +ei

Back ground of Regression.

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


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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 variableare 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, skewness 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


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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 thisrelationship.

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.


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The following relationships are possible in a scatter diagram

1. Direct linear relationships.

Here the value of Y increases as X increases.

Ex:


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2. Inverse linear relationships.

Here the value of Y decreases as X decreases.

Ex:


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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:


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4. Inverse curvilinear relationships.

Here the value of Y decreases as X decreases

Ex:

Based on the scatter diagrams interpretation we find the relationships

between the return and beta, return and variance, return and skewness

in the project and draw necessary conclusions.


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CHAPTER 4

DATA ANALYSIS


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Table 1 showing return, beta, variance and skewness for the year 2004.

2004 RETURN BETA VARIANCE SKEWNESS

A B Ltd. 0.19793 0.43320 0.11437 -0.00111

Aditya Birla Nuvo Ltd. 0.25817 0.53506 0.17121 0.00481

Andhra Bank 0.94309 1.04413 0.21841 0.00534Arvind Mills Ltd. 0.89154 1.53131 0.36482 0.02000

Ashok Leyland Ltd. 0.35294 0.85887 0.23161 0.00616

Asian Paints Ltd. 0.17877 0.27961 0.05568 0.00016

Associated Cement

Cos. Ltd.

0.08399 0.96599 0.09876 0.00078

Bajaj Auto Ltd. 0.28179 0.70551 0.10107 0.00081

Bank Of Baroda 0.61456 1.13519 0.15860 0.00185

Bank Of India 0.88499 1.08309 0.17022 0.00196Bharat Electronics Ltd. 0.74636 1.88460 0.40970 0.01293

Bharat Forge Ltd. 0.86925 1.25259 0.25737 0.00439

Bharat Heavy

Electricals Ltd.

0.20506 1.06709 0.13443 0.00023

Bharat Petroleum

Corpn. Ltd.

0.13700 1.39587 0.27918 -0.00815

Century Textiles &

Inds. Ltd.

0.27162 1.72721 0.31729 0.01557

Chennai Petroleum

Corpn. Ltd.

0.29135 1.14678 0.21647 0.01138

Cipla Ltd. -0.23555 0.20112 0.04610 -0.00081

Colgate-Palmolive

(India) Ltd.

-0.21263 0.19006 0.04506 0.00001

Cummins India Ltd. -0.08012 0.59633 0.11213 0.00084

Dr. Reddy'S

Laboratories Ltd.

-0.02778 0.77842 0.10145 -0.00313

G A I L (India) Ltd. 0.10821 0.76377 0.10059 0.00108Glaxosmithkline

Pharmaceuticals Ltd.

0.06140 0.35467 0.09234 0.00109

Glenmark


0.23332 0.47375 0.14525 0.00317

Grasim Industries Ltd. 0.13805 0.57957 0.05630 0.00028


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Great Eastern

Shipping Co. Ltd.

0.31616 0.78747 0.12282 -0.00067

Gujarat Ambuja

Cements Ltd.

-0.15100 0.80540 0.08225 0.00115

H C L TechnologiesLtd.

-0.38526 1.75626 0.30928 -0.00791

H D F C Bank Ltd. -0.02569 0.31753 0.05811 0.00047

Hero Honda Motors

Ltd.

0.07934 1.10184 0.17703 0.00088

Hindalco Industries

Ltd.

-0.08710 0.39205 0.06030 -0.00039

Hindustan Lever Ltd. -0.20745 0.83878 0.07182 0.00014

Hindustan Petroleum

Corpn. Ltd.

0.72401 1.52649 0.34599 -0.01636

Housing Development

Finance Corpn. Ltd.

0.07740 0.15433 0.05999 0.00000

I C I C I Bank Ltd. 0.46823 0.78730 0.18350 0.00480

I T C Ltd. -0.02445 0.54589 0.07264 -0.00001

I-Flex Solutions Ltd. 0.56336 0.42512 0.06592 0.00021

Indian Hotels Co. Ltd. 0.19886 0.59984 0.09058 0.00018

Indian Oil Corpn. Ltd. 0.60333 1.06888 0.19798 0.01167

Indian Overseas Bank 0.72361 0.72286 0.15382 -0.00088Indian Petrochemicals

Corpn. Ltd.

0.40705 0.85083 0.31532 -0.05355

IndustrialDevelop.Ban

k Of India Ltd.

0.31491 0.99961 0.24684 0.00724

Infosys Technologies

Ltd.

0.15806 1.44348 0.15403 -0.00106

J S W Steel Ltd. 0.93031 1.69710 0.54058 0.01444

Jindal Steel & Power

Ltd.

0.80466 1.29590 0.22191 0.00617


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Satyam Computer

Services Ltd.

0.16216 2.12208 0.24852 0.00219

Sesa Goa Ltd. 0.31493 0.97901 0.30088 0.01183

Shipping Corpn. Of

India Ltd.

0.80760 1.75218 0.38044 0.00560

Siemens Ltd. 0.50190 0.88537 0.14063 0.00076

State Bank Of India 0.43719 0.87216 0.09544 0.00107

Steel Authority Of

India Ltd.

0.74830 1.66982 0.36365 0.02150

Sterlite Industries

(India) Ltd.

0.01889 0.04288 0.02683 0.00012

Sun Pharmaceutical

Inds. Ltd.

0.04850 0.20038 0.05197 -0.00004

Tata Chemicals Ltd. 0.38420 0.97490 0.15869 0.00323

Tata Motors Ltd. 0.48041 1.20408 0.17384 0.00168

Tata Power Co. Ltd. -0.06792 1.08603 0.08377 -0.00056

Tata Steel Ltd. 0.55244 1.13058 0.12657 0.00068

Tata Tea Ltd. 0.03004 0.85333 0.09405 0.00213

Tata Teleservices

(Maharashtra) Ltd.

-0.23428 0.40687 0.15680 0.01041

U T I Bank Ltd. 0.52884 1.04190 0.17668 0.00224

United PhosphorusLtd.

1.23431 1.33303 0.68649 0.02597

Videsh Sanchar

Nigam Ltd.

-0.73903 0.59410 0.32061 -0.08455

Vijaya Bank 0.68962 0.72884 0.19705 0.01053

Wipro Ltd. 0.01744 1.55578 0.21510 0.00224

Wockhardt Ltd. -0.08095 0.24939 0.04228 0.00031

Zee Telefilms Ltd. -0.13552 1.77132 0.28333 0.00383

showing return, beta, variance and skew ness for the year 2005.


ABB Ltd. 0.99681 0.42642 0.12532 0.00208

Aditya Birla Nuvo Ltd. 1.05460 0.79380 0.18934 0.00785

Andhra Bank 0.95032 1.08433 0.28733 0.00358

Arvind Mills Ltd. 1.10089 1.13725 0.25367 0.00728

Ashok Leyland Ltd. 1.08542 0.92432 0.18363 0.00097


54/87



Asian Paints Ltd. 0.44029 0.25811 0.05688 0.00107

Associated Cement

Cos. Ltd.

0.39695 1.14099 0.13456 0.00062

Bajaj Auto Ltd. 0.81726 0.41746 0.07961 0.00072

Bank Of Baroda 1.11826 1.21131 0.35114 0.00410Bank Of India 0.58160 1.17937 0.21465 0.00041

Bharat Electronics Ltd. 1.24895 1.02922 0.16351 0.00342

Bharat Forge Ltd. 1.35325 0.69741 0.14927 0.00216

Bharat Heavy

Electricals Ltd.

1.07941 0.83865 0.11584 0.00143

Bharat Petroleum

Corpn. Ltd.

0.73106 0.90037 0.13325 0.00083

Century Textiles &

Inds. Ltd.

1.04348 1.43463 0.30431 0.00798

Chennai Petroleum

Corpn. Ltd.

1.20012 0.71294 0.22379 0.01211

Cipla Ltd. 0.38160 0.47566 0.10556 0.00027

Colgate-Palmolive

(India) Ltd.

0.16882 0.27244 0.05315 0.00128

Cummins India Ltd. 0.96944 0.60378 0.15668 0.00293

Dr. Reddy'S

Laboratories Ltd.

0.46373 0.50132 0.12377 0.00131

G A I L (India) Ltd. 1.31068 1.15422 0.14796 0.00216

Glaxosmithkline


0.63218 0.27608 0.07611 0.00142

Glenmark


1.07258 0.82689 0.23513 0.00899

Grasim Industries Ltd. 1.15833 0.89613 0.11528 0.00248

Great Eastern

Shipping Co. Ltd.

1.54851 1.01456 0.22610 0.00527

Gujarat Ambuja

Cements Ltd.

0.62056 0.78847 0.09536 -0.00007

HCL Technologies Ltd. 0.49592 1.51513 0.30789 -0.01214

HDFC Bank Ltd. 0.51534 0.49287 0.08520 0.00088

Hero Honda Motors

Ltd.

0.50310 0.77570 0.16390 0.00089


55/87



Hindalco Industries

Ltd.

0.87612 0.59818 0.08230 0.00025

Hindustan Lever Ltd. 0.11891 0.79144 0.08388 0.00011

Hindustan Petroleum

Corpn. Ltd.

0.41829 0.82779 0.13918 -0.00161

Housing Development

Finance Corpn. Ltd.

0.58715 0.39320 0.12248 0.00145

ICICI Bank Ltd. 0.74378 0.73126 0.13501 0.00258

ITC Ltd. 0.39931 0.56187 0.05805 0.00011

I-Flex Solutions Ltd. 0.65593 0.88708 0.22068 0.00572

Indian Hotels Co. Ltd. 0.86017 0.61145 0.12932 0.00194

Indian Oil Corpn. Ltd. 1.05649 0.92479 0.13861 0.00159

Indian Overseas Bank 0.81130 0.69412 0.18947 0.00085

Indian Petrochemicals

Corpn. Ltd.

1.05106 1.14184 0.16084 0.00150

IDBI Ltd. 1.07947 0.95685 0.37104 0.01618


Ltd.

0.15368 1.34154 0.28466 -0.03083

JSW Steel Ltd. 0.88000 1.45122 0.51416 0.01194


Ltd.

1.26716 1.38539 0.25876 0.00518


Kochi Refineries Ltd. 1.34532 0.89423 0.31670 0.01226

Kotak Mahindra Bank

Ltd.

0.80171 0.92485 0.26903 0.00685

Larsen & Toubro Ltd. 0.90399 0.84825 0.09988 0.00082

Lupin Ltd. 1.56980 1.22823 0.33680 0.00350

Mahanagar

Telephone NigamLtd.

0.37278 0.67570 0.18111 0.00425

M & M Ltd. 1.23900 1.18076 0.14772 0.00097

Mangalore Refinery &

Petrochemicals Ltd.

1.97978 1.21008 0.42117 0.02673

Matrix Laboratories 2.09761 0.72072 0.17159 -0.00090


56/87



Ltd.

Moser Baer India Ltd. 1.49219 0.61016 0.29511 -0.00638

Motor Industries Co.

Ltd.

1.54259 0.47964 0.09888 0.00084

National AluminiumCo. Ltd.

0.74829 1.14966 0.18047 0.00112

Nestle India Ltd. 0.27591 0.04129 0.04100 0.00035

Neyveli Lignite Corpn.

Ltd.

1.03115 1.09994 0.25110 0.00407

Nicholas Piramal

India Ltd.

1.20538 0.74458 0.17358 0.00486

Oil & Natural Gas

Corpn. Ltd.

0.82662 1.17326 0.12185 -0.00008

Oriental Bank Of

Commerce

1.64073 1.29374 0.35378 0.00334

Pfizer Ltd. 0.34077 0.35523 0.12131 0.00296

Ranbaxy Laboratories

Ltd.

0.61580 0.59209 0.06826 -0.00003

Raymond Ltd. 0.81376 0.64331 0.15519 0.00354

Reliance Capital Ltd. 0.81732 1.11401 0.17044 0.00253

Reliance Energy Ltd. 0.83237 1.05436 0.13293 0.00270

Reliance IndustriesLtd.

0.65480 1.02005 0.08415 -0.00003

Satyam Computer

Services Ltd.

0.27905 1.76588 0.28573 -0.00242

Sesa Goa Ltd. 2.15369 1.21987 0.42205 0.01180

Shipping Corpn. Of

India Ltd.

0.98443 1.39992 0.35671 0.00784

Siemens Ltd. 1.24047 0.56709 0.11731 0.00202

State Bank Of India 0.64458 0.95004 0.08732 -0.00017

Steel Authority Of

India Ltd.

1.60651 1.77821 0.48743 0.02191

Sterlite Industries

(India) Ltd.

2.24900 0.81212 0.34436 0.02082

Sun Pharm.Inds. Ltd. 0.68272 0.63405 0.14261 0.00055

Tata Chemicals Ltd. 0.96807 0.90181 0.15071 0.00175


57/87



Tata Motors Ltd. 1.03077 1.13564 0.11387 0.00038

Tata Power Co. Ltd. 1.03326 1.10910 0.11061 -0.00007

Tata Steel Ltd. 1.07534 1.23763 0.12775 0.00034

Tata Tea Ltd. 0.67853 0.78654 0.10453 -0.00028

Tata Teleservices(Maharashtra) Ltd.

1.29418 1.08729 0.37820 0.01730

U T I Bank Ltd. 1.10418 0.80987 0.30032 0.02102

United Phosphorus

Ltd.

1.09948 0.83535 0.37902 0.00613

Videsh Sanchar

Nigam Ltd.

0.40377 0.65194 0.16287 0.00262

Vijaya Bank 1.08676 0.88655 0.29907 0.00551

Wipro Ltd. 0.06351 1.64074 0.23497 -0.00707

Wockhardt Ltd. 0.47824 0.48647 0.13579 -0.00103

Zee Telefilms Ltd. 0.43112 1.01861 0.24644 0.00255

Table 3 showing return, beta, variance and skew ness for the year 2006.

2006 RETURNS BETA VARIANCE SKEWNESS

ABB Ltd. 0.36454 0.54424 0.09708 -0.00240

Aditya Birla Nuvo

Ltd.

0.36323 0.94027 0.19619 -0.00337

Andhra Bank 0.50729 1.58318 0.33849 -0.00962

Arvind Mills Ltd. 0.69542 1.30318 0.30072 -0.00493

Ashok Leyland Ltd. -0.18539 0.92429 0.19723 -0.00310

Asian Paints Ltd. -0.04877 0.42765 0.05171 0.00035

Associated Cement

Cos. Ltd.

0.32161 0.96706 0.12107 -0.00090

Bajaj Auto Ltd. -0.00520 0.60641 0.09011 -0.00142

Bank Of Baroda 0.02679 1.81104 0.40715 -0.01257

Bank Of India 0.35213 1.63588 0.36360 -0.00518

Bharat Elect.Ltd. 0.07663 0.82577 0.14924 -0.00060

Bharat Forge Ltd. 0.30987 0.67883 0.11605 -0.00065

BHEL 0.41588 1.31412 0.23905 -0.01061

Bharat Petroleum

Corpn. Ltd.

0.01892 0.98547 0.21463 -0.00227


58/87



Century Textiles &

Inds. Ltd.

0.22706 1.20627 0.27361 -0.00275

Chennai Petroleum

Corpn. Ltd.

0.92955 1.53102 0.48744 -0.00799

Cipla Ltd. 0.18583 0.72287 0.11702 -0.00186Colgate-Palmolive

(India) Ltd.

0.11636 0.39375 0.07187 0.00100

Cummins India Ltd. -0.04474 0.56142 0.13919 0.00057

Dr. Reddy'S

Laboratories Ltd.

-0.50099 0.47389 0.14089 -0.00799

G A I L (India) Ltd. -0.12091 1.81447 0.36452 -0.00115

Glaxosmithkline


0.29109 0.47140 0.08108 -0.00130

Glenmark


1.22049 1.00370 0.30255 0.00492

Grasim Industries

Ltd.

0.27547 0.85670 0.13619 -0.00080

Great Eastern

Shipping Co. Ltd.

0.08334 1.17205 0.24862 0.00043

Gujarat Ambuja

Cements Ltd.

0.27888 0.99121 0.13325 -0.00249

HCL TechnologiesLtd.

0.11357 0.77797 0.16307 0.00111

HDFC Bank Ltd. 0.34721 0.88817 0.16164 -0.00236

Hero Honda Motors

Ltd.

0.24088 0.90643 0.15497 -0.00036

Hindalco Industries

Ltd.

0.01305 0.71315 0.13267 -0.00045

Hindustan Lever Ltd. -0.35521 0.64500 0.10685 -0.00397

Hindustan Petroleum

Corpn. Ltd.

-0.08836 0.96807 0.17425 -0.00362

Housing

Development

Finance Corpn. Ltd.

0.17307 0.62504 0.13646 0.00295

ICICI Bank Ltd. 0.22618 0.85708 0.15667 -0.00064

ITC Ltd. 0.28539 0.68335 0.09801 0.00064


59/87



I-Flex Solutions Ltd. -0.28357 1.06118 0.18538 -0.00020

Indian Hotels Co.

Ltd.

0.18511 0.63240 0.09142 -0.00093

Indian Oil Corpn. Ltd. 0.11599 1.36981 0.24139 -0.00551

Indian OverseasBank

0.82613 1.58263 0.44407 -0.01105

Indian

Petrochemicals

Corpn. Ltd.

-0.21422 1.74912 0.33762 -0.00765

IDBI Ltd. 0.56991 1.64443 0.55262 -0.00287


Ltd.

0.40671 0.80470 0.11239 -0.00023

J S W Steel Ltd. 0.25344 1.17618 0.30537 0.00558


Ltd.

0.37109 1.07791 0.22494 -0.00081

Kochi Refineries Ltd. 0.23523 1.09420 0.24291 -0.00511

Kotak Mahindra Bank

Ltd.

0.39136 0.70127 0.14532 -0.00364

Larsen & Toubro Ltd. 0.26461 0.73571 0.14560 -0.00075

Lupin Ltd. -0.02093 0.79748 0.16610 -0.00018Mahanagar

Telephone Nigam

Ltd.

0.11770 1.02643 0.20550 -0.00206

M & M Ltd. 0.33613 0.99881 0.15545 -0.00039

Mangalore Refinery

& Petrochemicals

Ltd.

0.06172 1.65620 0.35269 -0.00431

Matrix Laboratories

Ltd.

0.44669 0.35186 0.10451 0.00196

Moser Baer India Ltd. -0.39228 0.90833 0.23089 -0.00202

Motor Industries Co.

Ltd.

0.16719 0.69577 0.12163 -0.00069

National Aluminium

Co. Ltd.

0.02647 1.28363 0.22957 -0.00609


60/87



Nestle India Ltd. -0.16487 0.22172 0.04987 -0.00013

Neyveli Lignite

Corpn. Ltd.

0.11163 1.66963 0.36859 -0.01823

Nicholas Piramal

India Ltd.

0.67325 0.60957 0.12658 -0.00106

Oil & Natural Gas

Corpn. Ltd.

0.02477 1.21350 0.19310 -0.00332

Oriental Bank Of

Commerce

0.26829 1.72223 0.36390 -0.01852

Pfizer Ltd. 0.25167 0.69080 0.11901 -0.00132

Ranbaxy

Laboratories Ltd.

0.13059 0.46697 0.06528 -0.00035

Raymond Ltd. 0.32017 0.88980 0.15886 0.00038

Reliance Capital Ltd. 0.00228 1.46647 0.25461 -0.00892

Reliance Energy Ltd. 0.02608 1.38482 0.27383 -0.01827

Reliance Industries

Ltd.

-0.07086 1.11896 0.12972 -0.00483

Satyam Computer

Services Ltd.

0.10960 0.93562 0.15582 0.00026

risk factors in indian stock market wrt capm

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