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Validity of Capital Asset Pricing Model & Stability of

Systematic Risk (Beta): An Empirical Study on Indian Stock

Market

ABSTRACT:

The capital asset pricing model (CAPM) is the standard risk-return model used by most

academicians and practitioners. The underlying concept of CAPM is that investors are rewarded

for only that portion of risk which is not diversifiable. This non-diversifiable risk is termed as

beta, to which expected returns are linked. The objective of the study is to test the validity of this

theory in Indian capital market & the stability of this non diversifiable risk (i.e. systematic risk or

beta). The study has used the data of 10 stocks & 10 sectoral indices listed on the BSE, for a

period of 4 years (January 2005 to December 2008) for the analysis. The studies provide

evidence against the CAPM hypothesis. And finally, the studies also provide the evidence

against the stability of systematic risk.

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1. INTRODUCTION:

CAPITAL ASSET PRICING MODEL is a model that starts with a specification of investors‘

choice. From the investors‘ point of view, investors like overall portfolio reward (expected

return) and dislike overall portfolio risk (variance or standard deviation of return). So as a result

investors immediately will grab those projects—that have low risk and high expected rate of

return. In fact, those projects with lower risk will ask for a higher price, which in turn

immediately drives down the expected rate of return. Consequently, what is available for

purchase in the real world must be subject to some trade-off: Projects that have more market-risk

must offer a higher expected rate of return if they want to be purchased by investors. But what

exactly does this relation look like? It is actually the domain of the capital asset pricing model.

Capital Asset Pricing Model (CAPM) is based on two parameter portfolio analysis developed by

Markowitz (1952). It is the standard risk return model used by most academicians &

practitioners. The underlying concept of CAPM is that, investors are rewarded for only that

portion of risk which is not diversifiable. This non-diversifiable variance is termed as beta, to

which expected returns are linked.

This model was simultaneously & independently developed by John Linter (1965), Jan Mossin

(1966) & William Sharpe (1964).

In the equation form model can be expressed as follows:

E (R i) =R f βi [E (R M) R f]……………………………………………... (1)

Where, E (R i) = expected rate of return on ith asset

R f = risk free rate of return

E (R M) = expected rate of return on market portfolio

β i = estimate of beta for the ith stock, i.e. the non diversifiable risk for ith asset.

This relation between expected rate of return on market portfolio & expected rate of return on

asset i, as described by equation (1) also known as Security Market Line (SML). If CAPM is

valid, all security will lie in a straight line in the E (R i), β i space, called SML. The SML

implies that, return is a linearly increasing function of risk. Moreover, only the market risk

affects the return. The non diversifiable risk is also known as the market risk, which is also

referred as "systematic risk". The beta of a stock is a measure of how much market risk faced by

a particular stock, i.e. the sensitivity of an asset with respect to market portfolio. Stability of β is

very important, since for almost all investment decisions βs are play a significant role in risk

measurement & risk management. Now if βs are not stable over time then it loses its importance.

The set of assumptions employed to develop CAPM can be summarized as follows:

(a) Investors are risk averse & they have a preference for expected return & dislike of risk.

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(b) Investors make investment decision based on expected rate of return & the variance of

the underlying asset return. i.e. assumptions of two-parameter utility function.

(c) Investors desire to hold a portfolio that lies along the efficient frontier. (The efficient

frontier is also known as diversification frontier)

These 3 assumptions were made in the development of the Markowitz & Sharpe single index

portfolio analysis model. In addition to these three assumptions, CAPM also made the following

assumptions:

(d) There is a risk less asset & investors can lend or borrow at that risk free rate.

(e) All the investments are perfectly divisible. That is, the fractional shares for any

investment can be purchased in any moment.

(f) All the investors have the homogeneous expectations regarding investment horizon or

holding period and to forecasted expected return & level of risk on securities. At the same

time, there is a complete agreement among investors as to the return distribution for each

security & portfolio.

(g) There are no imperfections in the market that prevent the investors to buying or selling

the assets. More importantly, there are no commissions or taxes involved with the

security transaction. That means, there are no costs involved in diversification & there is

no differential tax treatment of capital gain & ordinary income.

(h) There is no uncertainty about expected inflation, or alternatively, all security prices are

fully reflect all changes in future inflation expectations.

(i) Capital market is in equilibrium. That is all the investment decisions have been made &

there is no further trading without new information.

Even though, some of the assumptions are clearly unrealistic, since its introduction in early

1960s, CAPM has been one of the most challenging topics in financial economics.

2. LIMITATIONS OF THE CAPM:

The CAPM allows focus on the risk that is important in asset pricing—market risk. However,

there are some drawbacks to applying the CAPM.

(a) A beta is an estimate of systematic risk. For stocks, the beta is typically estimated using

historical returns. But the estimate for beta depends on the method and period in which is

it is measured. For assets other than stocks, beta estimation is more difficult.

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(b) The CAPM includes some unrealistic assumptions. Like, it assumes that all investors can

borrow and lend at the same rate or all the investors have the homogeneous expectations.

But this assumption of homogeneous expectation is unrealistic even if all the investors

are equally & fully informed.

(c) In studies of the CAPM applied to common stocks, the CAPM does not explain the

differences in returns for securities that differ over time, differ on the basis of dividend

yield, and differ on the basis of the market value of equity (the so called ―size effect‖).

Though it lacks reality and is difficult to apply, the CAPM makes some sense regarding the role

of diversification and the type of risk that should be considered in investment decisions making.

Nowadays almost every investor who wants to undertake a project used to justify his decision

partly based on CAPM. The reason is that the model provides the means of calculating the return

for a particular asset. This model was the first successful attempt to show how to assess the risk

of the cash flows of a potential investment project. The CAPM can estimate the project‘s cost of

capital and the expected rate of return that investors will demand if they are to invest in the

project.

The model was developed to explain the differences in the risk premium across assets.

According to the theory these differences are due to differences in the riskiness of the returns on

the assets. The model states that the correct measure of the riskiness of an asset is its beta and the

risk premium per unit of riskiness is the same across all assets. Given the risk free rate and the

beta of an asset, the CAPM can predict the expected risk premium for an asset.

The theory itself has created an academic debate about its usefulness and validity. In general, the

empirical testing of CAPM has two broad purposes:

1. Test whether or not the theories should be rejected

2. Provide information that can aid financial decisions.

To execute (1) tests are conducted which could potentially at least reject the model. The model

passes the test if it is not possible to reject the hypothesis that it is true. Methods of statistical

analysis could be applied in order to draw reliable conclusions on whether the model is

supported by the data or not.

To execute (2) the empirical work uses the theory as a vehicle for organizing and interpreting the

data without seeking ways of rejecting the theory. This kind of approach is found in the area of

portfolio decision-making, in particular with regards to the selection of assets to the bought or

sold. For example, investors are advised to buy or sell assets that according to CAPM are

underpriced or overpriced respectively. In this case empirical analysis evaluates the assets, assess

their riskiness, analyze them, and place them into their respective categories is very important. A

second illustration of the latter methodology appears in corporate finance where the estimated

beta coefficients are used in assessing the riskiness of different investment projects.

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3. THE CLASSIC SUPPORT OF THE THEORY:

The model was developed in the early 1960‘s by Sharpe [1964], Lintner [1965] and Mossin

[1966]. In its simple form, the CAPM predicts that the expected return on an asset above the

risk-free rate is proportionately related to the non-diversifiable risk, which is measured by the

asset‘s beta. One of the earliest empirical studies that found supportive evidence for CAPM is

that of Black, Jensen and Scholes [1972]. Using monthly return data and portfolios rather than

individual stocks, Black et al tested whether the cross-section of expected returns is linear in

beta. The authors found that the data are consistent with the predictions of the CAPM i.e. the

relation between the average return and beta is very close to linear and that portfolios with high

(low) betas have high (low) average returns.

Another classic empirical study that supports the theory is that of Fama and McBeth [1973]; they

examined whether there is a positive linear relation between average returns and beta. Moreover,

the authors investigated whether the squared value of beta and the volatility of asset returns can

explain the residual variation in average returns across assets that are not explained by beta

alone.

4. CHALLENGES TO THE VALIDITY OF THE THEORY:

In the early 1980s several studies suggested that there were deviations from the linear CAPM

risk return trade-off due to other variables that affect this tradeoff. The purpose of the above

studies was to find the components that CAPM was missing in explaining the risk-return trade-

off and to identify the variables that created those deviations.

Banz [1981] tested the CAPM by checking whether the size of firms can explain the residual

variation in average returns across assets that remain unexplained by the CAPM‘s beta. The

author concluded that the average returns on stocks of small firms (those with low market values

of equity) were higher than the average returns on stocks of large firms (those with high market

values of equity). This finding has become known as the size effect.

The research has been expanded by examining different sets of variables that might affect the

risk return tradeoff. In particular, the earnings yield (Basu [1977]), leverage, and the ratio of a

firm‘s book value of equity to its market value (e.g. Statman [1980], Rosenberg, Reid and

Lanstein [1983] and Chan, Hamao, Lakonishok [1991]) have all been utilized in testing the

validity of CAPM.

The general reaction to Banz‘s [1981] findings, that CAPM may be missing some aspects of

reality, was to support the view that although the data may suggest deviations from CAPM, these

deviations are not so important as to reject the theory.

However, this idea has been challenged by Fama and French [1992]. They showed that Banz‘s

findings might be economically so important that it raises serious questions against the validity

of the CAPM. Fama and French [1992] used the same procedure as Fama and McBeth [1973]

but arrived at very different conclusions. Fama and McBeth find a positive relation between

return and risk while Fama and French find no relation at all.

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The Fama and French [1992] study has itself been criticized. Kothari, Shaken and Sloan [1995]

argue that Fama and French‘s [1992] findings depend essentially on how the statistical findings

are interpreted.

Amihudm, Christensen and Mendelson [1992] and Black [1993] support the view that the data

are too noisy to invalidate the CAPM. In fact, they show that when a more efficient statistical

method is used, the estimated relation between average return and beta is positive and

significant. Black [1993] suggests that the size effect noted by Banz [1981] could simply be a

sample period effect i.e. the size effect is observed in some periods and not in others.

Jagannathan and Wang [1993] argue that the lack of empirical support for the CAPM may be due

to the inappropriateness of basic assumptions made to facilitate the empirical analysis. For

example, most empirical tests of the CAPM assume that the return on broad stock market indices

is a good proxy for the return on the market portfolio of all assets in the economy. However,

these types of market indexes do not capture all assets in the economy such as human capital.

Other empirical evidence on stock returns is based on the argument that the volatility of stock

returns is constantly changing. When one considers a time-varying return distribution, one must

refer to the conditional mean, variance, and covariance that change depending on currently

available information.

All the studies above aim to improve the empirical testing of CAPM. There have also been

numerous modifications to the models and whether the earliest or the subsequent alternative

models validate or not the CAPM is yet to be determined.

5. LITERATURE REVIEW:

Grigoris Michailidis, Stavros Tsopoglou, Demetrios Papanastasiou (2006) examines the Capital

Asset Pricing Model (CAPM) for the Greek stock market. The findings of this article were not

supportive of the theory‘s basic statement that higher risk (beta) is associated with higher levels

of return. The tests were conducted to examine the nonlinearity of the relationship between

return and betas support the hypothesis that the expected return-beta relationship is not non-

linear. Additionally, this paper investigates whether the CAPM adequately captures all-important

determinants of returns or not. For that reason the study includes the residual variance of stocks

as an explanatory variable. The results demonstrate that residual risk has no effect on the

expected returns of portfolios.

Attiya Y. Javid & Eatzaz Ahmad (2008) attempt to empirically investigate the risk and return

relationship of individual stocks traded at Karachi Stock Exchange (KSE), the main equity

market in Pakistan. The empirical findings do not support the standard CAPM model as a model

to explain assets pricing in Pakistani equity market. The critical condition of CAPM, i.e. there is

a positive trade-off between risk and return—is rejected and residual risk plays some role in

pricing risky assets.

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Jonali Sarma & Pranita Sarmah (September 2008) empirically study the stability of stock βs

using chow test on Bombay stock exchange and the result shows that betas are unstable over

time.

Sromon Das (2007) test the stability of betas of individual stocks over a period of time using two

econometric tests on NSE Nifty (February 1999 to September 2007), and sub-divided the sample

period into 3 sub-periods, two bullish and one bearish. The author found that under one method

(regression using time as a variable) 85% of the stocks had a stable beta, while using the second

method (regression using dummy variables) 65% of the stocks had stable betas.

This study will try to address two of the most important questions regarding CAPM.

(a) The study will examine whether of the relationship between asset return & corresponding

β value as posed by CAPM is valid in Indian context or not. For that reason study will

examine the validity of CAPM for 10 stocks listed at BSE, and after that it will examine

the validity of CAPM for 10 different industries to get a broader idea.

(b) The study will also examine whether stock βs are stable over time or not, & if not what

are the reasons behind its movement over time. While addressing the question the study

will try to examine what are the effects of stock market crash (January 2008) on

individual stock βs. i.e. what are the effects of stock market crash on individual stock‘s

systematic risk.

The study is arranged as follows:

The initial part of the study contains the description of the selected data & the selection criteria.

Then it empirically tests the validity of CAPM. Under this part of the study, there are 4

subsections; first two of them contain the estimation methodology & hypotheses testing. And

next two of them contain the empirical finding, interpretation of results & interpretation of

results. In the empirical testing part the study first test the validity of CAPM on selected stocks

using SENSEX, and then BSE 100, BSE 200 & BSE 500 as the proxy of market index. Then the

study empirically tests the validity of CAPM on different industry indices using SENSEX as the

proxy market portfolio.

And the final part of the study contains the test for stability of systematic risk. This section is

also sub-divided into four sub-sections. First two of them contain the estimation methodology &

hypotheses testing. And next two of them contain the result & interpretation of results.

And finally the conclusion of whole study contains in the final conclusion part.

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6. SAMPLE SELECTION AND DATA SELECTION:

The econometric analysis to be performed in the study is based on the data of 10 selected firms

listed on the Bombay stock exchange, one of the important stock exchanges of India & 10

important industry indices published by BSE for the period from January 2005 to December

2008. This particular time period has chosen because it is characterized by historically high &

low values of the weighted proxy market indices. These 10 companies are selected out of 30

companies represented in the SENSEX according to the BSE listing at April 10, 2000. In

selecting the firms two criteria were used:

Companies had represented in SENSEX at the day April 10, 2000.

Almost all the important sectors are covered in data, namely information technology,

FMCG, oil & gas, finance & Healthcare.

The selected companies, their respective sectors, along with their market capitalization (Rs.Cr.)

given in the following table (As at April 10, 2000, pre-open):

TABLE-1:

DESCRIPTIONS OF SELECTED COMPANIES:

As at April 10, 2000, pre-open

All selected securities are traded on the BSE (Bombay Stock Exchange) on a continuous basis.

Next as far as industry indices are concern, the study selected almost all available BSE industry

indices except a few to get a broader idea regarding the market. The selected industries & their

descriptions are given in the following table (table 2):

Company Name Sector

Market

Capitalization.(Rs.Cr.)

Infosys Tech. Information Tech 60321.07

ITC FMCG 17915.29

State Bank Of India Finance 11380.82

ICICI Finance 10782.33

Ranbaxy Healthcare 7971.61

NIIT Information Tech 6155.74

HPCL Oil & Gas 4608.1

Castrol India Oil & Gas 3889.22

Nestle FMCG 3587.15

Novartis Healthcare 2969.5

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TABLE-2:

DESCRIPTIONS OF SELECTED INDUSTRY INDICES:

NAME OF

THE

INDEX DESCRIPTION

BSE AUTO BSE Auto Index comprises all the major auto stocks in the BSE 500 Index.

BSE

POWER

BSE POWER is an index to track the performance of companies in the power

and energy sector. BSE Power index comprises companies that are into the

business of generation, transmission and distribution of electricity.

BSE

BANKEX

Bankex was launched by BSE to track the performance of the leading banking

sectors as bank stocks are emerging as a major segment of the stock market.

Bankex Index includes 12 selected major stocks which represent total 90%

market capitalization of all the banking sector stocks listed on the BSE.

BSE FMCG

Products that show a sudden shelf turnover, at comparatively low cost are

classified as Fast Moving Consumer Goods. Eatables, soft drinks, and cleaning

materials fall in FMCG category. FMCG Index monitors the performance of the

major brands in the FMCG category.

BSE HC

Health Care and Pharmacy sector are emerging as strong effectors on the

economy of India. BSE Health Care Index monitoring the health care sector

performance individually.

BSE IT

Keeping track of the changing trends in Indian Economy, BSE launched new

sectoral index named IT Index. Stocks capturing 90% market capitalization

from the IT sector are listed on the IT Index.

BSE OIL &

GAS

Oil and Gas sector is gaining its own weight age in the economy. The stocks

from oil and gas sectors have lot of effect on the stock market movement. The

index covers 90% of the sectoral market capitalization and is based on the Free-

Float methodology.

BSE CD

Products whose life expectancy is at least three years are known as consumer

durable. BSE classified the 90% market capitalization stocks in the field of

consumer durable in the Sector Series

BSE CG

Consumer goods index is a part of the BSE sectoral Indices.CG Index

comprises the companies occupying 90% market capitalization in the field of

consumer goods.

BSE

METAL

BSE metal index was launched to track the performance of major metal

companies in India

Each stocks & industry indices consist of 996 observations of the daily closing prices for the

chosen period. For the period 2005 to 2008 the data are taken from BSE website

(http://www.bseindia.com/)

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On the basis of available information on closing prices the rate of return on a particular asset is

computed by using the following formula:

Rit = (Pi, t – Pi, t-1)/Pt-1

Where, Pi, t = Daily closing price of asset i in the time period t,

Pi, t-1 = Daily closing price of asset i in the time period t–1,

Rit = Daily rate of return of asset i in the time period t

The weekly data on 91 days Treasury bill were used as proxy of risk free rate of return & BSE 30

(SENSEX) were used as a proxy for price of market portfolio. The 91 days Treasury bill were

used as risk free asset since it is backed by government of India, thus considered as one of the

safest asset in the country. The data for 91 days Treasury bill are taken from the Reserve Bank of

India‘s website (http://www.rbi.org.in/). Along with SENSEX, the study also used the BSE 100,

BSE 200 & BSE 500 as market proxy to examine the CAPM relationship for the selected stocks

for different market portfolios. The descriptions of selected market indices (especially SENSEX)

given in the following table:

TABLE-3:

DESCRIPTIONS OF SELECTED MARKET INDICES:

MARKET

INDEX

NAME Description

SENSEX

BSE Sensex stands for Bombay Stock Exchange Sensitive Index. It is an index

composed of the 30 largest and the most actively traded stocks in the market.

These companies holds around one fifth of the market capitalization of the BSE.

Sensex is regarded as the pulse of share market, the dips and rise of the Indian

share market can be identified through the Sensex. Free-float Market

Capitalization method is applied for the calculation of the Sensex. Using this

methodology, the market capitalization of a particular company is determined by

multiplying the price of its stock to the total number of shares issued by the

company.

BSE 100

BSE 100 index is called as BSE National Index as it works as broad-based index

reflecting the stock market at national level. It is an index composed of 100

companies from "Specified" and the "Non-Specified" list of the five major stock

exchanges, viz. Mumbai, Calcutta, Delhi, Ahmadabad and Madras.

BSE 200

BSE 200 index comprises of the 200 selected companies and their equity shares

from the specified and non specified lists of the major exchanges. Companies

are short listed on the basis of their current market capitalization and certain

fundamental factors like the market performance of the company

BSE 500

BSE 500 comprising 500 scrips. The index represents about 93% of the total

market capitalizations, ideally said to represent the total market.

The study uses daily asset returns from 10 companies listed on the Bombay Stock Exchange for

the period of January 2005 to December 2008. In order to obtain better estimates of the value of

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the beta coefficient, the study utilizes daily stock returns, because by doing so the study can

capture the day to day variations in asset prices.

7. TESTS FOR VALIDITY OF CAPITAL ASSET PRICING MODEL:

7.1. METHODOLOGY:

The study starts analysis by empirical model developed by Sharpe (1964) and Lintner (1966) in

which a relationship for expected return is written as:

E (R i) =R f βi [E (R M) R f]…………………………………………………. (2)

Where, E (R i) is expected return on i th asset, R f is risk free rate, E (R M) is expected return on

market portfolio & β is the measure of risk or market sensitivity parameter defined as:

βi = …………..………………………………………….……(3)

This equation (3) measures the sensitivity of asset return to variation in market return.

In risk premium form CAPM equation can be written as:

E (R i) R f = βi [E (R M) R f] ………………………………………..…………. (4)

Here, [E (R i) R f] is the excess return on ith asset & [E (R M) R f] is the excess return on

market portfolio over the risk-free rate. Equation (4) says that the expected excess return on any

asset is directly proportion to its β.

Now for estimation of individual asset βs the study uses the CAPM equation in risk premium

form with an intercept term:

R it R f t=αi βi [R Mt R ft] +uit……………………………….……..... (5)

Where, R it= the return on stock i (i=1, 2…… 10) at the period t (t=1, 2 …….995)

R ft= the rate of return on a risk-free asset at the period t

R Mt= the rate of return on proxy of market portfolio at the period t

uit= the corresponding random disturbance term in the regression equation.

uit iid N(0, σu2) & uit is independent of RMt.

The intercept term (αi) sometimes called ‗Jensen's alpha‘. i is the risk-adjusted performance

measure that represents the average return on a portfolio over and above that predicted by the

CAPM. i.e. it measures the degree to which a particular asset earning significant returns after

accounting for its market risk , as measured by beta. If the asset is earning a fair return for the

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given portfolio‘s systematic risk, then would be zero. Jensen‘s alpha allows the statistical test,

whether the ith asset gives significantly greater (or less) return than would be expected using the

CAPM. Jensen's measure is one of the ways to help determine if an asset is earning the proper

return for its level of risk. If the value is positive, then the asset is earning excess returns. In other

words, a positive value for Jensen's alpha means the asset has "beat the market".

It is assumed that the ex-post distribution from which returns are drawn is ex-ante perceived by

the investor. It follows from multivariate normality, that Equation (2) directly satisfies the

Gauss-Markov regression assumptions. Therefore for empirical testing of CAPM is carried out

on the basis of the equation:

i= γ1+ γ2 β i+ei………………………………………………………..… (6)

Where, I = Expected rate of return on ith asset = , for all i, i=1,2,……….10

Rit= rate of return from ith asset at the period t,

T=total number of data point (=995 in this study)

The coefficient γ1 is the premium associated with beta risk and an intercept term γ2 has been

added in the equation. The equation (6) also known as Security Market Line (SML).

The validity of CAPM is examined in this study by testing two implications of the relationship

between expected return and market beta given in Equation (6).

First expected returns are linearly related to their betas and no other variable has marginal

explanatory power.

Second the beta premium is positive, meaning that expected return on market portfolio

exceeds the expected return on assets whose returns are uncorrelated with the market

return.

To test the linearity of the risk-return relationship, the study include a quadratic term of β i in the

standard model given in Equation (6), and the model takes the following form,

i=γ1+ γ2 β i+ γ3 β i2 + e i…………………………………..……..…...… (7)

To test the hypothesis that the risk associated with residuals has no effect on the expected asset

return, residual risk, δui2 of each asset is added as an additional explanatory variable:

i=γ1+ γ2 β i+ γ4 (δui2) + ei………………………………………...……... (8)

The next hypothesis that has to be tested is that, difference in expected return across assets are

entirely explained by difference in market betas, other variables should add nothing to the

explanation of expected return. In this study, it is tested by adding predetermined explanatory

variables in the form of beta-square to test linearity and residual standard deviation to test that

beta is the only essential measure of risk. The model becomes:

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i=γ1+ γ2 β i+ γ3 β i2 + γ4 (δui

2) + e i…………………….………..…...…. (9)

If coefficients of the additional variables are not statistically different from zero, this outcome

will be consistent with the CAPM hypothesis.

7.2. HYPOTHESIS TESTING:

The parameters of the equations from (5) to (9) need to be tested in order to test the CAPM

hypothesis in Indian context.

For the equation (5) the null hypotheses are:

The ith asset is nether underperforming the market nor beating the market;

The market risk or systematic risk associated with the ith asset is not significantly

different from zero.

i.e. H0: αi=0 & βi=0, for all i, i=1, 2…….10

The alternative hypothesis against these null hypotheses are, H1: αi 0 & βi 0. Therefore these

tests are basically two tailed test.

The study will reject the H0 if the estimated value of alphas &/or betas are either significantly

higher or smaller than zero. To test these hypotheses the study uses the following 2 test statistics

for alpha & beta respectively:

tα=0 = tT-2…………………………………...…………………………………(10)

tβ=0 = tT-2……………………………………………………………………...(11)

Where, are the least square estimates of α & β respectively, and & are the

corresponding standard errors. Now if absolute value of tα=0 & tβ=0 are much higher than tT-2, 0.025

then the data cast considerable doubt on the null hypothesis H0: αi=0 & βi=0; whereas, if absolute

value of tα=0 & tβ=0 are less than tT-2, 0.025 then data are in support of the null hypothesis at 5%

level of significance.

The form of model has selected to test the validity of CAPM known as excess return market

model. In excess return market model β measure the contribution of an asset to the variability of

the market index portfolio. The hypothesis of interest is to test if the asset has the same level of

risk as the market return against the alternative that the risk is different from the market.

That is, test the null hypothesis, H0: β=1 against the alternative, H1: β 1.

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The data cast a doubt on this hypothesis if the estimated value of β is significantly different from

1. The hypothesis can be tested using standard t-test:

tβ=1 = tT-2…………………………………………………..………………….(12)

The null hypothesis is rejected at 5% level of significance if |tβ=1|> tT-2, 0.025

Note that, it is a two tailed test. Next to get more appropriate idea about the stock betas (that is,

whether they are more or less risky than the market portfolio), the study consider one-tailed test.

The null hypothesis for this is, the null hypothesis is H0: β=1 against the alternatives, H0: β>1 &

H0: β<1.

To test that hypothesis the test statistic will not change, but the critical value of t statistic will

change. Now the study will accept the alternative hypothesis H0: β>1 at 5% level of significance

if, tβ=1> tT-2, 0.05 & at the same time the alternative hypothesis of H0: β<1 will be accepted at 5%

level of significance if, tβ=1< tT-2, 0.05

Where tT-2, 0.05 is one side 5% critical value of student-t distribution with t-2 degrees of freedom.

Next for the rest of the estimated equations, objective of the study is to test whether parameters

are significantly different from zero or not. So next the objective of the study will be to test the

null hypothesis, H0: γi=0 against the alternative, H1: γi 0. For that reason the appropriate test

statistic is,

tγi=0 = tn-(NUMBER OF PARAMETERS)……………………………………….…….(13)

Where, i=1, 2, 3, 4 & n=1, 2......10

The estimated parameters allow the study to test a series of hypotheses regarding the CAPM. The

tests are:

a. H0:γ2>0, that is, there is a positive price of risk in the capital market.

b. H0:γ3=0, that is, there are no nonlinearities in the security market line.

c. H0:γ4=0, that is, residual risk does not affect return.

7.3. EMPIRICAL RESULTS AND INTERPRETATION OF THE FINDINGS:

The empirical validity of CAPM is examined in this study by using daily data of 10 individual

stocks & 10 industry or sectoral indices available at Bombay Stock Exchange during the period

January 2005 to December 2008. The first part of the testing required the estimation of betas for

individual stocks by using daily observations on rate of returns for the period 2005 to 2008. In

the next part of this sub-section the study will test the validity of CAPM using different market

indices. And finally, in the final part of this sub-section the study will test the validity of CAPM

15

for different sectors using SENSEX as market proxy index. Useful remarks can be derived from

the results for the assets used in this study.

7.3.1. TESTS FOR CAPM ON DIFFERENT STOCKS:

TABLE-4:

ESTIMATES OF STOCK ALPHA & BETA COEFFICIENT USING SENSEX AS

PROXY FOR MARKET INDEX (EQUATION 5):

NOTE: Standard errors are in parenthesis; t0.025, 993 1.960; t0.05, 993 1.645

The range of the estimated stock betas is between 0.271 the minimum and 1.322 the maximum

with a standard deviation of 0.319 (table 4). All the beta coefficients for individual stocks are

statistically significant at 5% as well as 1% level of significance.

Stock name α coefficient β coefficient

t-value t-value t-value

( H0: αi=0) ( H0: βi=0) ( H0: βi=1)

ITC

-0.001 0.680 -0.500 11.866 -5.582

(0.001) (0.057)

NESTLE

0.001 0.271 1.347 8.286 -22.338

(0.001) (0.033)

INFOSYS

-0.001 0.800 -0.931 20.900 -5.230

(0.001) (0.038)

NIIT

-0.001 0.734 -0.503 10.482 -3.792

(0.001) (0.070)

RANBAXY

-0.001 0.646 -1.565 13.197 -7.238

(0.001) (0.049)

NOVRATIS

-0.001 0.311 -1.622 9.623 -21.364

(0.001) (0.032)

SBI

0.000 1.025 0.831 34.865 0.850

(0.001) (0.029)

ICICI

0.000 1.322 0.016 42.245 10.279

(0.001) (0.031)

CASTROL

0.000 0.425 0.522 11.747 -15.918

(0.001) (0.036)

HPCL

0.000 0.660 -0.572 15.929 -8.215

(0.001) (0.041)

16

Some of the very important observations from the table-4 are as follows:

The theory indicates that higher market risk (beta) is associated with a higher level of

return. However, the results of the study do not support this hypothesis. The beta

coefficients of the 10 stocks do not indicate that higher beta stocks are related with

higher returns. Consider the table 5:

TABLE-5:

VALUES OF AVERAGE STOCKS RETURNS AND CORRESPONDING BETAS:

Stock name β coefficient

MEAN

RETURN

NESTLE 0.271 0.001112

NOVRATIS 0.311 -0.000694

CASTROL 0.425 0.000694

RANBAXY 0.646 -0.001029

HPCL 0.660 -2.38E-05

ITC 0.680 -0.000111

NIIT 0.734 -0.000215

INFOSYS 0.800 -0.000198

SBI 1.025 0.00102

ICICI 1.322 0.000677

For example, ICICI stock is the highest beta stock (β=1.322), yields a lower return than

NESTLE stock (0.0007<0.0011), stock with the lowest beta value (β=0.271). These

contradicting results can be partially explained by the significant fluctuations of stock returns

over the period examined (standard deviation of ICICI stock is higher than that of NESTLE).

Now consider some of the important results that are coming out of the study:

The α-coefficients for all the stocks are not significantly different from zero at 5% as well

as 1% level of significance. So none of the selected firms have beaten the market for the

selected period of time.

The β values for all the stocks included in the study are significantly different from zero.

And more importantly, the beta values for the ICICI stock found to be significantly

greater than 1& that for the stock of SBI is found to be not significantly different from 1.

Therefore the study can conclude that, the ICICI stock is more risky than market

portfolio, & the level of risk associated the stock SBI is as large as or as small as the

market portfolio. Finally, the beta value for the rest of the stocks is significantly less than

one.

17

Next to estimate the SML the study needs to estimate the equation (6), that is: i=γ1+ γ2 β i+ei. The estimation result for this equation is given in the following table (table-6):

TABLE-6:

ESTIMATED SECURITY MARKET LINE USING SENSEX AS THE PROXY OF

MARKET PORTFOLIO (EQUATION 6):

Table 6 shows that, given the sample observations, SML do not hold in Indian context, since, the

coefficient γ1 & γ2 in equation (6) are not significantly different from zero. Hence, the results

shown that there is evidence against the CAPM (Table 5 and 6) in Indian capital market.

In order to test for linearity of relationship between asset returns and betas, the study needs to

estimate the equation (7). The estimated results are given in the following table (table-7):

TABLE-7:

TEST FOR NON-LINEAR RELATIONSHIP BETWEEN RETURN & BETA USING

SENSEX AS PROXY OF MARKET PORTFOLIO (EQUATION 7)

Coefficient γ1 γ2 γ3

Value 0.001 -0.004 0.003

p-values 0.317 0.257 0.203

R Square 0.249

F-statistic 1.162

As the table 7 shows, none of the coefficients in the equation (4) is significantly different from

zero. And, more importantly coefficient γ3 in this equation is not significantly different from

zero, & thus consistent with the hypothesis that the expected return-beta relationship is not non-

linear.

Coefficient γ1 γ2

Value 0.000 0.000

p-values 0.771 0.593

R Square 0.193

F-statistic 0.310

18

The next hypothesis that needs to be examined is that, there is no effect of residual variance on

expected return. For that reason the study needs to estimate the equation (8). The estimated result

is given in the following table (table-8):

TABLE 8:

TEST FOR NON-SYSTEMATIC RISKS RETURN RELATIONSHIP USING SENSEX

AS THE PROXY OF MARKET PORTFOLIO (EQUATION 8):

As the table 8 shows, none of the coefficients in the equation (8) is significantly different from

zero. And, more importantly coefficient γ4 in this equation is not significantly different from

zero, & thus consistent with the hypothesis that residual risk does not have any effect on stock

return. Therefore the study may conclude that residual risk has no affect on the expected return

of the selected stocks. Therefore in case of return calculation residual risk no longer appears to

be important (Table 8).

Finally to examine the hypothesis that, no other variables other than stock‘s beta have any

influence on stock returns the study estimate the equation (9). The estimated result is given as

follows (table-9):

TABLE 9:

TEST FOR EFFECTS OF OTHER VARIABLES ON STOCK RETURN USING SENSEX

AS THE PROXY OF MARKET PORTFOLIO (EQUATION 9):

Since the analysis on the entire 4-year period did not yield strong evidence in favor of the CAPM

the study examined whether a similar approach on yearly data would provide more supportive

evidence. All models were tested separately for each year. But still the result did not support the

CAPM hypothesis (Tables 10, 11, 12 & 13).

Coefficient γ1 γ2 γ4

Value 0.000 0.000 -0.674

p-values 0.682 0.589 0.238

R Square 0.222

F-statistic 0.999

Coefficient γ1 γ2 γ3 γ4

Value 0.001 -0.003 0.002 -0.383

p-values 0.427 0.550 0.482 0.586

R Square 0.289

F-statistic 0.811

19

TABLE-10:

ESTIMATED SML USING SENSEX AS THE PROXY OF MARKET PORTFOLIO

(YEARLY SERIES, EQUATION 6)

YEAR COEFFICIENT VALUE t-value p-value

2005 γ1 0.00 -0.34 0.74

γ2 0.00 0.55 0.60

2006 γ1 0.00 -0.35 0.74

γ2 0.00 0.69 0.51

2007 γ1 0.00 0.72 0.49

γ2 0.00 1.36 0.21

2008 γ1 0.00 0.18 0.86

γ2 0.00 -1.93 0.09

TABLE 11:

TEST FOR NON-LINEAR RELATIONSHIP BETWEEN RETURN & BETA USING

SENSEX AS THE PROXY OF MARKET PORTFOLIO (YEARLY SERIES, EQUATION

7)

YEAR COEFFICIENT VALUE t-value p-value

2005 γ1 0.00 1.52 0.17

γ2 -0.01 -1.89 0.10

γ3 0.01 2.09 0.08

2006 γ1 0.00 -0.42 0.69

γ2 0.01 0.42 0.69

γ3 0.00 -0.35 0.74

2007 γ1 0.00 1.10 0.31

γ2 0.00 -0.54 0.61

γ3 0.00 0.85 0.42

2008 γ1 0.00 0.55 0.60

γ2 -0.01 -1.02 0.34

γ3 0.00 0.54 0.60

20

TABLE 12:

TEST FOR NON-SYSTEMATIC RISK RETURN RELATIONSHIP USING SENSEX AS

THE PROXY OF MARKET PORTFOLIO (YEARLY SERIES, EQUATION 8)

YEAR COEFFICIENT VALUE t-value p-value

2005 γ1 0.000 0.097 0.926

γ2 0.001 0.722 0.493

γ4 -1.120 -2.032 0.082

2006 γ1 -0.001 -0.261 0.802

γ2 0.002 0.649 0.537

γ4 -0.192 -0.115 0.912

2007 γ1 0.001 0.708 0.502

γ2 0.001 0.954 0.372

γ4 -0.099 -0.303 0.771

2008 γ1 0.001 1.030 0.337

γ2 -0.002 -1.709 0.131

γ4 -2.176 -1.350 0.219

21

TABLE 13:

TEST FOR EFFECTS OF OTHER VARIABLES ON STOCK RETURN USING SENSEX

AS THE PROXY OF MARKET PORTFOLIO (YEARLY SERIES, EQUATION 9):

The findings of this study are not supportive of the theory‘s basic hypothesis that higher risk

(beta) is associated with a higher level of return.

The inclusion of the square of the beta coefficient to test for nonlinearity in the relationship

between returns and betas indicates that the findings are according to the hypothesis and the

expected return-beta relationship is not non-linear. Additionally, the tests conducted to

investigate whether the CAPM adequately captures all-important aspects of reality by including

the residual variance of stocks indicates that the residual risk has no effect on the expected return

on portfolios.

The lack of strong evidence in favor of CAPM compels the study of yearly data to test the

validity of the model. But still the findings did not support the CAPM hypothesis.

YEAR COEFFICIENT VALUE t-value p-value

2005 γ1 0.00 1.23 0.26

γ2 -0.01 -1.23 0.27

γ3 0.01 1.41 0.21

γ4 -0.77 -1.35 0.23

2006 γ1 0.00 -0.39 0.71

γ2 0.01 0.41 0.70

γ3 -0.01 -0.34 0.74

γ4 -0.28 -0.16 0.88

2007 γ1 0.00 1.89 0.11

γ2 -0.01 -1.52 0.18

γ3 0.01 1.72 0.14

γ4 -0.63 -1.49 0.19

2008 γ1 0.00 0.63 0.55

γ2 0.00 -0.23 0.82

γ3 0.00 -0.13 0.90

γ4 -2.32 -1.13 0.30

22

The results of the tests conducted on data from the BSE for the period of January 2005 to

December 2008 do not appear to clearly accept the CAPM. These results can be explained in two

ways.

1. Measurement and model specification errors arise due to the use of a proxy instead of the

actual market portfolio. This error biases the regression line estimated slope towards zero.

2. Estimation error arises due to non-existence of any risk free asset in the market.

The tests may provide evidence against the CAPM but that does not necessarily constitute

evidence in support of any alternative model.

23

7.3.2. TESTS FOR CAPM ON DIFFERENT STOCKS USING DIFFERENT MARKET

INDICES:

Now assuming, the study provide evidence against the CAPM due to errors arise from the use of

a proxy instead of the actual market portfolio, the study re-estimate the equation (5) & (6) using

3 different market indices, namely: BSE100, BSE200, BSE500.

The estimation results are given in the following tables:

TABLE-14:

ESTIMATES OF STOCK ALPHA & BETA COEFFICIENTS USING BSE100 AS THE

PROXY OF MARKET PORTFOLIO (EQUATION 5):

Standard errors are in parenthesis. t0.025, 993 1.960; t0.05, 993 1.645

Stock

name α coefficient β coefficient

t-value t-value t-value

( H0: αi=0) ( H0: βi=0) ( H0: βi=1)

ITC

-0.001 0.692 -0.474 12.118 -5.388

(0.001) (0.057)

NESTLE

0.001 0.284 1.366 8.741 -22.015

(0.001) (0.033)

INFOSYS

-0.001 0.764 -0.845 19.603 -6.059

(0.001) (0.039)

NIIT

-0.001 0.758 -0.484 10.867 -3.469

(0.001) (0.070)

RANBAX

Y

-0.001 0.659 -1.541 13.533 -6.994

(0.001) (0.049)

NOVRATI

S

-0.001 0.347 -1.635 10.873 -20.498

(0.001) (0.032)

SBI

0.001 1.033 0.927 35.525 1.132

(0.001) (0.029)

ICICI

0.000 1.292 0.137 39.818 9.000

(0.001) (0.032)

CASTRO

L

0.000 0.458 0.543 12.828 -15.178

(0.001) (0.036)

HPCL

0.000 0.708 -0.561 17.462 -7.189

(0.001) (0.041)

24

TABLE-15:

ESTIMATES OF STOCK ALPHA & BETA COEFFICIENTS USING BSE200 AS THE

PROXY OF MARKET PORTFOLIO (EQUATION 5):

Stock

name α coefficient β coefficient

t-value t-value t-value

( H0: αi=0) ( H0: βi=0) ( H0: βi=1)

ITC

0.000 0.706 -0.431 12.200 -5.074

(0.001) (0.058)

NESTLE

0.001 0.292 1.399 8.876 -21.480

(0.001) (0.033)

INFOSYS

-0.001 0.762 -0.763 19.144 -5.993

(0.001) (0.040)

NIIT

-0.001 0.782 -0.447 11.071 -3.091

(0.001) (0.071)

RANBAX

Y

-0.001 0.674 -1.495 13.651 -6.614

(0.001) (0.049)

NOVRATI

S

-0.001 0.367 -1.610 11.419 -19.679

(0.001) (0.032)

SBI

0.001 1.043 1.055 35.184 1.457

(0.001) (0.030)

ICICI

0.000 1.292 0.285 38.416 8.685

(0.001) (0.034)

CASTRO

L

0.000 0.479 0.588 13.302 -14.457

(0.001) (0.036)

HPCL

0.000 0.729 -0.502 17.792 -6.620

(0.001) (0.041)

Standard errors are in parenthesis

25

TABLE-16:

ESTIMATES OF STOCK ALPHA & BETA COEFFICIENTS USING BSE500 AS THE

PROXY OF MARKET PORTFOLIO (EQUATION 5):

Standard errors are in parenthesis

TABLE 17:

ESTIMATED SML FOR STOCK RETURNS USING BSE100 AS THE PROXY OF

MARKET PORTFOLIO (EQUATION 6):

Coefficient γ1 γ2

Value 0.000 0.000

p-values 0.766 0.600

R Square 0.036

F-statistic 0.297

Stock name α coefficient β coefficient

t-value t-value t-value

( H0: αi=0) ( H0: βi=0) ( H0: βi=1)

ITC

0.000 0.724 -0.426 12.315 -4.705

(0.001) (0.059)

NESTLE

0.001 0.304 1.404 9.111 -20.821

(0.001) (0.033)

INFOSYS

-0.001 0.762 -0.745 18.739 -5.858

(0.001) (0.041)

NIIT

-0.001 0.809 -0.444 11.300 -2.669

(0.001) (0.072)

RANBAXY

-0.001 0.689 -1.490 13.753 -6.214

(0.001) (0.050)

NOVRATIS

-0.001 0.389 -1.619 11.989 -18.795

(0.001) (0.032)

SBI

0.001 1.053 1.068 34.658 1.743

(0.001) (0.030)

ICICI

0.000 1.297 0.307 37.255 8.523

(0.001) (0.035)

CASTROL

0.000 0.499 0.594 13.707 -13.737

(0.001) (0.036)

HPCL

0.000 0.748 -0.496 18.019 -6.079

(0.001) (0.041)

26

TABLE-18:

ESTIMATED SML FOR STOCK RETURNS USING BSE200 AS THE PROXY OF

MARKET PORTFOLIO (EQUATION 6):

Coefficient γ1 γ2

Value 0.000 0.000

p-values 0.773 0.613

R Square 0.033

F-statistic 0.277

TABLE-19:

ESTIMATED SML FOR STOCK RETURNS USING BSE500 AS THE PROXY OF

MARKET PORTFOLIO (EQUATION 6):

Coefficient γ1 γ2

Value 0.000 0.000

p-values 0.781 0.626

R Square 0.031

F-statistic 0.257

Some of the very important conclusions that can be drawn from the above results are as follows:

1. For all the 4 most popular market indices the security market line does not hold.

2. The study getting almost similar results for whatever market index being used; such as:

a. The α-coefficients for all the stocks are not significantly different from zero.

b. The β values for all the stocks included in the study are significantly different from

zero.

c. The β-coefficient of ICICI stock is significantly greater than 1 at 5% level of

significance.

d. The β-coefficient of SBI is not significantly different from 1 at 5% level of

significance.

e. Finally, the beta values for the rest of the stocks are significantly less than one.

27

7.3.3. TESTS FOR CAPM ON DIFFERENT SECTORS:

So far the study was based on 10 selected stocks. But it may not reflect the market as a whole.

That is why instead of stocks of individual firms the study has used the 10 sectoral indices

(mentioned earlier in section-3) to examine the validity of CAPM relationship for the market as a

whole. The estimation results for equations (5), (6), (7), (8) & (9) are given in the following 5

tables, namely table 20, 21, 22, 23, 24 respectively.

TABLE-20:

ESTIMATES OF SECTOR SPECIFIC ALPHA & BETA COEFFICIENTS USING

SENSEX AS PROXY OF MARKET PORTFOLIO (EQUATION 5):

Stock name α coefficient β coefficient

t-value t-value t-value

( H0: αi=0) ( H0:

βi=0)

( H0:

βi=1)

AUTO

0.000 0.774 -1.668 50.168 -14.609

(0.000) (0.015)

POWER

0.000 1.035 0.900 60.970 2.083

(0.000) (0.017)

BANKEX

7E-05 1.106 0.194 59.225 5.675

(0.000) (0.019)

FMCG

0.000 0.634 0.975 33.476 -19.293

(0.000) (0.019)

HC

0.000 0.586 -1.139 38.447 -27.175

(0.000) (0.015)

IT

0.000 0.842 -1.109 38.690 -7.255

(0.000) (0.022)

OIL & GAS

0.000 1.028 1.030 63.701 1.737

(0.000) (0.016)

CD

-3E-05 0.843 -0.058 30.977 -5.778

(0.001) (0.027)

CG

0.001 1.025 1.534 57.184 1.378

(0.000) (0.018)

METAL

0.000 1.177 -0.997 49.363 7.410

(0.000) (0.024)

t0.025, 993 1.960; t0.05, 993 1.645

28

TABLE-21:

ESTIMATED SML FOR DIFFERENT SECTORS USING SENSEX AS PROXY OF

MARKET PORTFOLIO (EQUATION 6):

COEFFICIENT VALUE t-value p-value

γ1 0.000 -0.288 0.781

γ2 0.001 1.112 0.298

TABLE-22:

TEST FOR NON-LINEAR RELATIONSHIP BETWEEN SECTORAL RETURNS &

BETAS USING SENSEX AS PROXY OF MARKET PORTFOLIO (EQUATION 7)

COEFFICIENT VALUE t-value p-value

γ1 -0.001 -0.429 0.681

γ2 0.004 0.478 0.647

γ3 -0.002 -0.382 0.714

TABLE-23:

TEST FOR NON-SYSTEMATIC RISK RETURN RELATIONSHIP FOR DIFFERENT

SECTORS USING SENSEX AS PROXY OF MARKET PORTFOLIO (EQUATION 8)

COEFFICIENT VALUE t-value p-value

γ1 -6E-05 -0.106 0.919

γ2 0.001 0.856 0.420

γ4 0.001 1.418 0.199

TABLE-24:

TEST FOR EFFECTS OF OTHER VARIABLES ON RETURN FOR DIFFERENT

SECTORS USING SENSEX AS PROXY OF MARKET PORTFOLIO (EQUATION 9):

COEFFICIENT VALUE t-value p-value

γ1 -0.001 -0.203 0.846

γ2 0.002 0.261 0.803

γ3 -0.001 -0.187 0.858

γ4 0.001 1.269 0.252

29

The estimated alpha values for all the selected sectors are not significantly different from zero.

So, the study concludes that, none of the sector have beaten the market for the selected sample

time period. On the other hand, the beta values for all the selected industries are significantly

positive & among them the beta values for the POWER, BANKEX, OIL & GAS and METAL

industries are significantly greater than one.

The estimated results shows evidence against CAPM, because, the estimated coefficients for the

security market line, i.e. equation (6), are not significantly different from zero. At the same time,

all the other null hypotheses corresponding to the equation (7), (8) & (9), (i.e. there are no

nonlinearities in the security market line, and residual risk does not affect return) are also

accepted by the given data set.

7.4. INTERPRETATION OF RESULT:

So the results of these studies indicate that the Capital Asset Pricing Model probably cannot

explain the risk return relations in the Indian capital market. There could be several reasons for

the empirical data not supporting the model. One of the short coming of this kind of ex-post

(after the fact) test of CAPM is the difficulty in defining the market portfolio. The assumptions

of CAPM imply that the market portfolio reflects the universally preferred combination of risky

assets. The market portfolio in CAPM should ideally include all assets. Naturally for testing

purposes only a reasonable proxy for the market portfolio has to be used (like, SENSEX,

BSE100, BSE200, BSE500 etc.). Thus if the market proxy is not properly defined tests of CAPM

may give misleading results. However in this study to address this problem, 4 different market

indices are being used. Thus the possibility that the results are distorted due to problems in the

construction of the market index appears to be quite low and other more probable causes need to

be explored. Such as, unlike stock markets in the developed countries the Indian capital market is

relatively new and growing. The inadequacies in the infrastructure may be one of the reasons

behind the inefficiency of Indian capital market.

In this context the study conducted by Fama & French (1992) on returns data has few

implications. The results of the study do not support the positive risk return hypothesis of

CAPM. The author found that the size and the book value to market of equity explain the cross

sectional variation in average returns during the period. However the authors are not sure

whether the two factors, size and book to market of equity, can be regarded as a proxy of risk.

Thus it can be seen that there have been less empirical support to CAPM in the very recent

studies abroad and the ability of beta to reflect the risk of a security is doubtful. Moreover the

efficient market assumptions behind CAPM is likely to be less valid in India compared to the

developed country markets, where the securities trading is much more efficient in terms of

greater transparency in transactions, faster and easier availability of information related to the

market, shorter settlement periods, less transaction cost, greater liquidity and depth of the market

etc.

Some of the more important factors which may cause CAPM to be ineffective in the Indian

context and has the potential to reduce the efficiency level of the India Capital Market are:

30

(a) NON DIVERSIFIED PORTFOLIO HOLDING:

Various studies on Indian capital market shown that, the average investor in India holds very few

stocks 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. And therefore, holding small

number of securities or undiversified portfolios can add to market inefficiency.

(b) LIQUIDITY:

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

position in the exchange is highly unsatisfactory. The trading in the exchanges in India is highly

concentrated on a few stocks. 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 stocks 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 the stock

market. Low liquidity can also result in inefficient pricing of stocks and price setting

behavior by investors (non price taker).

(c) 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. In specific cases it can carry out investigations on alleged insider trading.

Greater transparency in transactions will make insider trading more difficult to hide. However

the task of detecting insider trading is a difficult one. Even in developed countries, where there

are elaborate systems to prevent insider trading in existence, insider trading allegedly take place.

The best way to reduce the possibility of insider trading is to reduce the scope of making profit

through it. This can be achieved by ensuring speedy availability of price sensitive information to

the public.

In a market dominated by insider trading, the investors cannot have homogeneous expectations

as assumed in CAPM. Moreover the very presence of insider trading implies that market price do

not reflect all information (otherwise insider trading will not be profitable), i.e., market is not

perfectly efficient.

31

(d) 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. But, in the present context this problem has reduced.

Besides problems of office space and inadequate technology the present number of brokers in the

exchanges is also not sufficient to provide proper services to the vast investor population.

Moreover as the number of brokers is small, they almost have an assured volume of business. As

the brokers now do not have to compete with each other much to get business there is no

incentive for them to improve the quality of the investor service. The cost of the service provided

by them also tends to be high. The monopoly of the brokers increases the transaction cost of

investors.

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.

8. TEST FOR STABILITY OF STOCK BETAS:

Even though the study provides evidence against the CAPM hypothesis, beta of a security has

been the most important tool for investment management among both academicians and

practitioners. Beta has occupied center stage in both risk measurement and risk management. It is

one of the most widely used measures of risk. Beta has wide ranging application in financial

economics. Beta measures the systematic risk (non-diversifiable risk). The use of Beta financial

decision-making models is a dynamic measure of the performance of the business that is referred

to as the ex ante measure. Further, the stability of beta is of great concern as it is a very important

tool for almost all investment decisions and plays a significant role in the modern portfolio

theory. Portfolio managers effectively control the risk of their portfolio by determining and

varying the weighted average beta of the securities they hold. However, if the individual stock

betas can change dramatically over two successive time periods it will be very difficult for them

to get a correct estimate of the risk of their portfolio, because it will then indicates uncertain

systematic risk exposure.

In this section the aim of the study to examine the stability of the stock betas under some special

circumstances. Such as:

The Sensex on January 08, 2008 touched all time peak of 21,078 before closing at

20,873. After that peak day the SENSEX fall slowly. In the third week of January 2008,

the Sensex experienced huge falls along with other markets around the world. On January

21, 2008, the Sensex saw it‘s highest ever loss of 1,408 points at the end of the session.

The Sensex recovered to close at 17,605.40 after it fall to the day's low of 16,963.96, on

high volatility as investors panicked following a price fall in global counterparts. Now the

study will try to examine the stability of stock betas against this particular scenario.

32

The next interesting study would be to check the stability of stock betas over the market

cycle. i.e. to examine whether stock betas are stable over short term up-turn & down-turn

movement in stock market return.

To examine these, study proceeds as follows:

8.1. METHODOLOGY:

For the test for stability of stock betas the dummy variable technique has used.

Now the objective of this study is to check the assumption that, the estimated value of β are

assumed not to vary over time. Therefore the hypothesis of study is that the stock betas are

invariant of time. Study has considered SENSEX as the appropriate proxy for market index.

To examine the effect of stock market crash on beta stability the re-estimation equation (5) need

to be done by introducing two kinds of dummies (slope dummy & intercept dummy variables) in

equation (5). The new regression equation can be written as follows:

R it R f t= αi + βi [R Mt R ft] +λ1D1+ ф1D1(R Mt R ft) +u1it …………………. (14)

Where, D1=1, between time period January 2005 to 8th January 2008

0, between time periods 9th January 2008 to December 2008

Now, if the parameter ф1 is significantly different from zero, then the conclusion can be made

that, there is a significant effect of stock market crash on stability of stock betas. Otherwise there

will be no such effect of stock market crash on systematic risk of individual stocks.

The next interesting study regarding stock beta concerns the stability of stock β over the market

cycle. For that reason study assumes that market is in ‗up cycle‘ if (R M R f)> 0, & in otherwise

cases the study will assume that the market is in ‗down cycle‘.

Now to examine the stability of stock β over the market cycle, the study will re-estimate the

equation (5) using a new dummy variable D2 as follows:

R it R f t=αi +βi [R Mt R ft] +λ2D2+ ф2D2(R Mt R ft) +u2it………………….. (15)

Where, D2=1, if (R M R f)> 0

0, if (R M R f) 0

The dummy variable D2 divide the sample into ―up market‖ movements & ―down market‖

movements. The regression that allows the β to differ depending on market cycle is then given

by the equation (15).

33

So, the effect of market cycle on stock β can be examined by the significance of the parameters

ф1 & ф2 respectively.

8.2. HYPOTHESIS TESTING:

The hypotheses that are needed to be tested in this study are:

Stability of the systematic risk of a stock is not affected by stock market crash.

Up cycle & down cycle movement in the stock market have no influence on systematic

risk.

These hypotheses can be tested using the following null hypotheses:

1. H0: ф1 = 0, against the alternative H1: ф1 0

2. H0: ф2 = 0, against the alternative H0: ф2 0

The test statistics are t-statistics:

1. tф1=0= tT-4………………………………………………………..……….(16)

2. tф2=0= tT-4…………………………………...………………..…………..(17)

34

8.3. RESULT:

The estimated results are given in the following tables (table 25 & 26)

TABLE-25:

ESTIMATES OF THE COEFFICIENTS α, β, λ & ф, USING SENSEX AS THE PROXY

OF MARKET PORTFOLIO :( EQUATION-14)

Stock name α coefficient β coefficient λ coefficient ф coefficient

ITC

0.001 0.566 -0.002 0.272

(0.346) (7.371) (-0.806) (2.348)

NESTLE

0.001 0.201 0.000 0.159

(0.473) (4.590) (0.078) (2.409)

INFOSYS

0.001 0.732 -0.002 0.167

(0.628) (14.287) (-1.361) (2.159)

NIIT

-0.003 0.921 0.004 -0.447

(-1.251) (9.848) (1.328) (-3.169)

RANBAXY

0.000 0.600 -0.003 0.119

(0.237) (9.138) (-1.213) (1.200)

NOVRATIS

-0.001 0.233 -0.001 0.180

(-0.541) (5.405) (-0.439) (2.755)

SBI

0.001 1.003 -0.001 0.054

(0.718) (25.406) (-0.410) (0.905)

ICICI

0.001 1.513 -0.001 -0.434

(0.737) (36.900) (-0.452) (-7.019)

CASTROL

0.002 0.383 -0.002 0.106

(1.297) (7.904) (-1.276) (1.445)

HPCL

0.002 0.664 -0.003 0.004

(0.990) (11.953) (-1.458) (0.044)

t-ratios are in parenthesis; t0.05, 991 1.645; t0.025, 991 1.960

35

TABLE-26:

ESTIMATES OF THE COEFFICIENTS α, β, λ & ф USING SENSEX AS THE PROXY

OF MARKET PORTFOLIO :( EQUATION-15)

t-ratios are in parenthesis

t0.05, 991 1.645

t0.025, 991 1.960

Stock name α coefficient β coefficient λ coefficient ф coefficient

ITC

-0.004 0.537 0.007 0.026

(-2.015) (4.864) (2.314) (0.165)

NESTLE

0.003 0.384 -0.003 -0.136

(2.496) (6.104) (-1.550) (-1.479)

INFOSYS

-0.005 0.585 0.005 0.260

(-3.411) (7.964) (2.454) (2.426)

NIIT

0.004 1.001 -0.003 -0.453

(1.421) (7.416) (-0.768) (-2.307)

RANBAXY

-0.001 0.743 0.002 -0.283

(-0.330) (7.873) (0.757) (-2.058)

NOVRATIS

-0.002 0.327 0.003 -0.171

(-1.370) (5.261) (2.029) (-1.890)

SBI

-0.001 0.963 0.004 -0.017

(-1.277) (16.999) (2.431) (-0.206)

ICICI

0.000 1.295 -0.001 0.092

(-0.084) (21.446) (-0.556) (1.044)

CASTROL

0.002 0.536 -0.001 -0.210

(1.496) (7.691) (-0.343) (-2.073)

HPCL

0.002 0.806 -0.001 -0.273

(1.161) (10.099) (-0.431) (-2.348)

36

8.4. INTERPRETATION OF RESULT:

The results shows that except beta value for SBI stock all other stock‘s beta values are affected

either by stock market crash or by market up cycle & down cycle movement or by both. The

reason may be that throughout the study period the beta value for SBI stock is not significantly

different from one. i.e. the SBI stock is as good or as bad as market portfolio, it is neither more

sensitive than market portfolio nor less sensitive than market portfolio.

For the other stocks the beta value is not stable. The stock market crash has effect on the stability

for the betas of the stocks like ITC, NESTLE, INFOSYS, NIIT, NOVRATIS, and ICICI. 4 out of

these 6 firm‘s beta values are found to be negatively affected by stock market crash. These 4

firms are: ITC, NESTLE, INFOSYS, NOVRATIS. And for the other 2 firms (NIIT, ICICI) the

studies have found that, there is a positive effect of stock market crash on their beta values.

On the other hand, the beta values for the firms like INFOSIS, NIIT, RENBAXY, NOVRATIS,

CASTROL, and HPCL are affected by up-cycle & down-cycle movement in stock market. As far

as movement of beat value is concern, for the stocks of the firm INFOSYS beta value is found to

be influenced positively by up-turn movement of stock market. On the other hand the beta values

for the stocks of NIIT, RENBAXY, NOVRATIS, CASTROL, and HPCL are affected negatively

by up-turn movement (as defined earlier) in the stock market.

The findings of these studies are sample specific, due to short period covered & smaller number

of companies are included in the sample. This study does not claim generalization of the results.

37

9. CONCLUSION:

The first part of the study shows, the Capital Asset Pricing Model probably cannot explain the

risk return relationship in the Indian capital market. Some of the important factors which have

the potential to reduce the efficiency level of the India Capital Market, & thus may cause CAPM

to be ineffective in the Indian context are:

Non diversified portfolio holding

Liquidity problem

Insider trading problem

Inadequate infrastructure.

Still beta of a security considered as one of the most important tool for investment management

among both academicians and practitioners. The final part of the study shows that, the stock

betas are not stable over time, they may change over time. The reason behind those changes may

be anything. The study shows that, the recent stock market crash (January 2008) & up-turn &

down-turn movement in market rate of return have some influence on stability of stock betas.

Since this beta variability indicates uncertain systematic risk exposure, portfolio managers

should consider it as a form of risk to be controlled. And obviously, the objective of the portfolio

managers should be to minimize the beta variability. To minimize beta variability in small

portfolios, however, a different strategy is required.

Minimization of portfolio beta variability cannot be achieved by combining stocks which,

individually, have low beta variability. Rather, the strategy of a portfolio manager should be to

hold a large, well diversified portfolio that used to have the stationary beta.

38

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