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Testing the Empirical Validity of CAPM in Shorter PeriodsEvidence

from Indian Capital Market

DR D. LAZAR* and YASEER K.M

Abstract:

Capital asset pricing Model (CAPM) provides an equilibrium linear relationship between risk and expected

return of an asset. The purpose of this study is to examine the risk return relationship with the CAPM frame

work by Using Black, Jensen and Scholes (1972) Methodology. The study is conducted for seven sub periods

comprising of three years each .The total period covers 9 years and used data from the year 01-01-2001 to 31-

12-2009, which includes the recession period. The study used the data of 70 companies which are the part of

BSE100 and tested the validity of CAPM, test of SML, test of Non- linearity. Further the study compared the

relationship between beta and portfolio return. The analysis gives mixed result and we couldnt find conclusive

evidence in support of CAPM in the selected study periods.

Key words: CAPM, Intercept, Security Returns, Beta, Portfolio Returns, SML, Black Jensen and Scholes

Methodology (1972)

1. Introduction

Indian Capital Market has a long tradition and is one of the oldest in Asia and the history

records back to nearly 200 years ago. The first stock exchange in India is the Bombay stock

exchange which begins its operation in organized form from the year 1875. Indian capital

market growing and so far it is one of the developed markets in the world. The growth of the

capital market in India witnessed unique changes in the last two decades and there was an

unprecedented growth, in terms of the number of companies listed, total market

capitalisation, number of brokers and also in the number of participants. In India, Capital

market is one of the most important parts of the financial system and the stock exchanges

plays an important role in the economic growth and the growth in the stock market is

symbolised as a barometer of economic growth. Currently there are 23 stock exchanges and

one over the counter exchange operating in India. Out of which the National Stock

Exchanges (NSE) and the Bombay Stock Exchange (BSE) are the biggest in number of

companies listed and also in the market capitalization.

*Dr. Daniel Lazar, Pondicherry University, India.,[email protected]
mailto:[email protected]:[email protected]:[email protected]:[email protected]

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The capital market is an interface, where investors can buy and sell stocks and other selected

financial instruments. In India the growth of technology brought indefinite opportunities and

opened an arena for investors particularly in the capital market. Today a cursory glance

provides wildering collection of securities from the market and also a numerous number of

financial instruments and the stock market becomes an investment avenue for FIIs,

Institutional investors as well as individual investors. Today the investment arena is very

complex and the capital market is over flooded with many financial instruments and large

number of securities. Further the Indian market is highly volatile and selecting suitable

securities became a quite complex exercise. The investors are risk averse and he expects

additional return for the risk he bears. The market is highly complex, highly volatile and

unpredictable and a simple mistake and lack of attention may lead to loss of money. The

investor should be very alert and a suitable model which will help the investor to pick the

best investment option or one which is helpful for analysing the various alternatives will be

useful in decision making. Today investors and analysts are practicing different techniques

and models to find out the best investment opportunity which will help reduce the risk and

bag more return. CAPM is one of the important and widely used models for investment

analysis. This model can be used to evaluate any investment project and it provides an

equilibrium linear relationship between risk and expected return of an asset.

Every investment is characterised by risk and return and the element of risk is always akin

with every investment. The investment returns measure the financial results and may be

historical or prospective. The return may be in the form various types of yield and capital

appreciation, that the return is the sum of the benefits received (interest, dividend etc) while

he own the asset and the change in value of the asset in the form of capital gain or loss, which

is realised at the time of disposal of the asset. Risk is a mix of threat and opportunities which

literally means the possibility of danger. The risk is defined as the potential for variability

in return (Rao, Ramesh.K.S, 1989). Number of factors will affect the risk return relation and

the various factors which are external that affects large number of securities simultaneously

are known as systematic risk and is denoted as beta () .These types of risks are mostly

uncontrollable and One can examine the individual stock return to the overall market return by

comparing how an individual company stock reacts to overall market fluctuation. CAPM is one of the

models widely used throughout the world to explain the risk return relationship and the theory

postulate that there is a linear relationship between beta and return. But the literature shows that the

model gives different results for different market and thereby it is crucial to test the validity of this

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before applying to the field concerned. This study is attempt to test the empirical validity of the one

factor basic CAPM model in Indian Capital market by using three years data.

This study is organized as follows. Section 2 deals with the review of previous empirical work,

section 3 with methodology and the empirical work and results are explained in section4 and thesection 5for summary and conclusion.

2. Previous research

The modern portfolio theory explains that there is a clear trade of between risk and return

.The Markowitz portfolio selection model helps one to plot the efficient frontier of risky

assets and provides a useful framework for selecting an optimal combination of risky funds.

But this model however does not provide guidance with respect to the risk-return relationshipfor individual assets. The Capital asset pricing Model which was contributed by Jack

Treynor(1961, un published), William Sharpe (1964), John Lintner (1965), and Jan Mosssin

(1966), explains the equilibrium relationship between the expected return on risky assets .The

model provide a mechanism to assess the role of a particular asset in the overall portfolio risk

and return and it uses the result of capital market theory to derive the relationship between

expected return for the risky assets.

The literature showed that large number of studies has been conducted to test the applicability

of the model in different markets and found different results for different markets. The

empirical validity of this model was widely challenged in the late of Seventies, Eighties and

Nineties by roll, Fama French etc. But at the same time there are number of studies which are

in favor and supported the usage one factor model CAPM in developing and emerging

markets. Literature showed that Sauer and Murphy (1992) are definite about the applicability

of CAPM in describing risk return relation in the German Stock Market data. Similarly the

studies conducted by Black and fisher (1993), Daniel and Titman(1997), Gyorgy Andoret.al

(1999) for the Hungarian capital market.Ming-Hsiang Chen (2003) established that empirical

performance of the CAPM is encouraging and the CAPM outperforms the CCAPM in terms

of goodness of fit . Similarly Daniel Suh (2009)opined that in a highly volatile market

Parameter estimates of the CAPM are generally superior to those of the Fama French three

factor model

At the same time the studies conducted by roll (1977), Harris and et al.(2003)argued againstCAPM, Nopbhanon Homsud and et. al. (2009) found that Fama French model explain risk in

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stock return better than the traditional one factor Capital Asset Pricing model. Yan Li and

Liyan Yang( 2008) found that the conditional CAPM fails miserably to explain the size

effect, the value effect, and the momentum effect. Pablo Rogersand et.al (2007) found that

the results of their study propose and supported the explanatory power of Fama French

model. Cudi Tuncer Gursoy and Gulnara Rejepova (2007): found that their test result

weakens the validity of single index CAPM model in Turkey market over the analysis period.

Further Grigoris Michailidis and et.al(2006): Xi Yang, Donghui Xu (2006), Medvedev A.

(2004) Arduino Cagnetti (2001). Elsas Rand et.al (2000) etc tested CAPM and found

evidence against CAPM. Besides this Jan Bartholdy and Paula Peare (2004),Samit Maunder

and Frank W. Bacon (2007) neither support nor reject the Capital Asset Pricing Model

pIn Indian context, only few studies were conducted for analyzing risk return relationship in

Indian capital market and studies by Varma (1988), Srinivasan (1988) have generally

supported CAPM. The studies by Rao and Bhole (1990), Palaha(1991), Vaidyanadathan

(1995), Sehgal (1997) Sehgal (2001,2003), Mohanthy (2002) Mallikarjunappa and et.al

(2006) questioned the validity of CAPM in Indian context.

From the literature it is clear that there is a mixed opinion about the validity of one factor

CAPM model. But the fact is that only few researches were conducted to test the applicability

of the one factor capital asset pricing Model in Indian capital market by using daily data.

Therefore the present study is proposed to test validity of the one factor Capital Asset Pricing

Model by using daily data of 70 companies listed in BSE100. Index

3. Scope of the study

The present study will test the suitability of the CAPM frame work in Indian context by using

daily data of 70 companies. Since Indian capital market is one of the fastest developing

markets in the world, it is very important to suggest how far the western portfolio theories are

suitable to explain the differential return on financial assets in Indian capital market and also

to suggest the suitability of the model which will help the investors, fund managers and the

analysts. Further the study period also covers the recession period were we can see abnormal

fluctuation in the stock market and the period comprises from 01-01-2008 to 31-03-2009.This

will help the investors and fund managers to understand the applicability of this model in

such situations.

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3.1. Objectives of the study

The primary objective of the study is to test the empirical validity of the CAPM frame work

in Indian context by using Blacketal(1972) methodology. The main objectives of the study

are described below.1. To revisit the empirical validity of CAPM frame work in Indian capital market by

using portfolios having different number of Securities.

2. To check whether higher or lower risk generate higher or lower rate of return.

3. To ascertain the relationship between return of securities and market return

4. To check whether expected rate of return is linearly related with systematic risk.

3.2. Source and Period of Data

In this study the test is organized to examine the suitability of CAPM models in Indian

context by considering daily data of 70 companies which are the part of BSE 100 stock

Index,a broad-based index, launched in 1989 as the base year 1983-84. The sample for the

study covers nine years daily data for a period from 01-01-2001 to 31-12-2009 and the data

used in this study were sourced from RBI , SEBI, BSE websites and Prowess- a data base of

CMIE., (Center for Monitoring Indian Economy) a leading private sector economic research

data provider in India. The study will consider 70 actively traded stocks listed in the BSE100

index including financial institutions. Brown and Warner (1985) suggest that the daily price

are better for auto correlation in event methodology and is felt that quarterly , monthly and

weekly data do not provide a very meaningful relationship between risk and return and hence

daily data is used in this study. Further the study considers 91 day Treasury bill rate as the

proxy for the risk free assets, which is available in weekly format in the Reserve Bank of

India site. The 91 day Treasury bill is specifically chosen because it will better reflects theshort term changes in the financial market and also a number of studies used the same

3.3. Research Method

Since the main objective of the study is to examine the suitability of CAPM in Indian context,

it is proposed to collect nine years data of actively traded companies of BSE 100. The

average percentage daily return of shares is put to use for the study to calculate the return and

risk of the companies. Share prices returns in Prowess are calculated by considering all

benefits accrued / losses incurred by the share holder by way of change in price on the

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exchange, benefits received or losses incurred due to bonus issues, rights issues, and adhoc

gains/losses. The return calculation also ensures that any split or consolidation event which

happens has no effect on the return, except in the event of the prices changing due to market

activity, return is calculated on closing prices. Here the data has been analyzed in two stages,

in the first stage the daily percentage return has been used for all the scrip throughout the

study period. In the second part of the analysis attempts are made to work out to test the

applicability of Capital Asset Pricing Model in Indian context

3.4. Methodology for the basic Capital Asset Pricing Model

Black, Jensen and Scholes (1972) introduced a time series test of the CAPM and the

relationship between risk and return has been analysed systematically. They carried out thestudy by using 1931-1965 data of all the NYSE stocks and they form portfolios and regressed

them on beta. They had tested whether the relationship is linear and also whether any firm-

specific volatility of a securitys return has an impact on the return of securities.

Mallikarjunappa (2007), Valeed A Ansari (2000), in their studies in Indian capital market and

Xi Yang (2006) Chinese stock market Grigoris Michailidis (2006) in Greek market etc. used

the same methodology. The present study also follows a similar methodology followed by the

Black and etal (1972).Further the study will also us Fama Macbeth (1973) methodology to

test the Non-Linearity.

3.5 Testing CAPM with portfolios having 10 Securities

This study will test the CAPM model for the period from 2001 to 2009 and used the same

method followed by the Black, Jenson and Scholes in (1972). This methodology use portfolio

technique and also time series regression of excess portfolio return on excess market return

and also cross sectional regression in risk premium form, which can be express by theequation below. The study will also use Fama and Macbeth methodology to test the non

linearity .

For this, in the first step betas (also known as the systematic risk) of individual

securities are measured and the beta coefficients of individual securities were

calculated for the seven portfolio formation periods. A time series regression between

the daily percentage return against the market return is used to get the beta coefficient

of each security in the sample and the model is shown bellow.

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Rit- Rft= i +i (RmtRft) + eit ---------------------- (1)Where: Rit is the rate of return on asset i (or portfolio) at time t, Rft is the risk-free rate at

time t, Rmt is the rate of return on the market portfolio at time t. i is the beta of stock i, eit

is the is the error term in the regression equation at time t. The equation can also expressed

as

rit = i + i rmt + eit ---------------------- (1A)Where:

RitRft = r it and RmtRft = r mt

r it is the excess return of stock i

r mt is the average risk premium and the i is the intercept

The study will use the percentage daily return of security return on index (BSE 100) and the

risk free return. The daily return of securities and the market for the period are regressed by

taking the company return as dependent variables and the market return as the independent

variable.

In the second stage, the portfolios are constructed by using the calculated betas. For the

formation of portfolios the individual beta for each stock is the arranged on ascending order

and the stocks were grouped in to portfolios having 10 stocks each according to their beta

value .The first portfolio comprises the first 10 securities with the lowest beta, the next

portfolio with the next 10 securities. The same method is followed for the formation of other

portfolios and there by the last portfolio is formed with the securities having the highest beta.

In this stage the portfolio betas are calculated by using the following regression model.

rpt = p + p rmt + ept ---------------------- (2)Where

rptis the average excess portfolio return on time t,

p is the estimated portfolio beta, and

e pt is the error term in the regression equation at time t.

In the third step in order to estimate the ex post security market line for each testing period

the portfolio return are regressed against portfolio betas. The model for the calculation is

rp= 0 + 1p + ep ---------------------- (3)Where

rp=is the average excess return of the portfolio P

p is the beta of the portfolio P, and

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ep is the error term in the regression equation

The theory says that if the CAPM is true 0 should be equal to zero and the slope SML,1 is

the average risk premium of the market portfolio.

Further the study will also test the non- linearity between the total portfolio return and betas

by using the following equation.

rp= 0 + 1p + 2p + ep ------------------- (4)Here the theory says that if the CAPM is true, the portfolio returns and its betas are linearly

related with each other and2 will be equal to zero.

3.6 The Statistical test of the CAPM

The t -Test

Further the validity of the CAPM is statistically tested by using the t- test at different levels

of significance, say- 99%, 95%. (This study will not consider 90% confidence level for

interpretation even though some of the coefficients are significant at 90% level) the The t

test has been introduced by W.S Gosset and the distribution of the ratio t has been derived for

normally distributed population. It is most commonly applied when the test statistic would

follow a normal distribution and the analysis is commonly used to compare and evaluate the

difference in means between two groups. Theoretically, the t-test can be used even if the

sample sizes are very small and as long as the variables are normally distributed within each

group and the variation of scores in the two groups is not reliably different.

3.7 Why Black, Jenson and Sholes Methodology

Miller and Scholes (1972) diagnosed that while using individual stock betas, there is problem

because of the betas are measured with error and the measurement error in right hand variable

biases down regression coefficients. Fama and MacBeth (1973), Black, Jenson and Scholes

(1972) addressed this problem by grouping stocks in to portfolios. Portfolio betas are better

measured because the portfolio has lower residual variance. Further the individual betas vary

over the time as the size, leverage and risk of the business change. Secondly the individual

stock return is so volatile that you cannot reject the hypothesis that all average returns are the

same (Asset pricing: John H. Cochrane, Princeton University Press, USA, P- 434-435).There

by the present study planned to use this methodology.

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3.8Limitation of the studyThe size of the sample and the number of companies used to construct the portfolio is one of

the important limitations. Only seven portfolios are formed and tested in the present study

and this may affect the statistical result and may be biased in limited observations. Theliterature says that the CAPM tests realized in international scope use more than 30 years of

observations and the market portfolio plays an important role in the test results. But the

present study used 9 years data and conducted tested with return of only one index.

4. Testing CAPM in Different study Periods

In order to dress up the question of the validity of the CAPM in Indian context ,the test is

conducted by dividing the entire nine year period in to seven different sub periods comprising

three years each and the sub periods includes 2001-2003, 2002-2004, 2003-2005, 2005-2007,

2006-2008 and 2007-2009. The outline of the study is summarised in the Table 1 below.

Table .1

Table Showing the Different Portfolio Formation Periods and Testing Periods

In the first step of the empirical testing the systematic risk (beta), also known as the un

diversifiable risk which unanimously affects the prices of all securities in the market is

measured. The beta coefficient shows the risk associated with a security or portfolio and as

per the theory the investor should be bothered only about the systematic risk which cannot be

diversified away. The basic CAPM theory clearly argues that the efficient market is expected

to compensate only the systematic risk which is denoted by beta ().

In the first step, the beta coefficients of individual securities are calculated for the seven sub

periods. A time series regression model (1) is run between the daily percentage return

against the percentage market return is used to get the beta coefficient of each security in the

sampleRit - Rft = i + i ( Rmt- Rft) + eit -------- (1)

Period 1 2 3 4 5 6 7

Period Range01-03 02-04 03-05 04-06 05-07 06-08 07-09

Portfolio

Formation2001 2002 2003 2004 2005 2006 2007

Testing period 2003 2004 2005 2006 2007 2008 2009

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4.1 Period Wise Distribution of Beta

The betas for individual securities by using the above model were calculated for different

study periods. The result shows that the range of estimated beta for the sub period 1 is in

between 0.15575 minimum and the maximum 2.0056.The range of beta for the sub period 2is in between 0.16846 and 1.74350 and for the sub period 3, the beta lies between 0.166861

minimum and 1.68426 maximum .The range of beta for the period 4 shows that the minimum

beta is 0.27854 and the maximum is 1.62242 and the beta for the period 5 lies between

0.30657 minimum and 1.57201 maximum . For the sub period 6 the minimum beta is

0.28916 and the maximum 1.61827 and for the seventh sub periods the range of beta is in

between 0.04611 and 1.66231. Here we can see variation in the range of beta in different

Study periods.

4.2 Average Excess Portfolio Return and Beta

Different studies shows that combining securities in to portfolios will definitely helps to

diversify the risks due to the firm specific factors and will enhance the precision of estimates

of beta and the expected return on the portfolios. At this stage of the study, the portfolios are

constructed by using the calculated betas. The same procedure is repeated for the whole

sample period, for the adjusted period and also for different sub periods. The average excessreturn was calculated for each portfolio and the following regression model (2) is used to

calculate the portfolio beta.

rpt = p + p rmt + ept ------------- (2)On the basis of the regression results the CAPM is tested for different sub periods.

4.3. Testing CAPM in the First Sub Period (2001-2003)

In the first sub period the analysis is carried out on the data of 70 companies listed BSE 100

and covers the period 1st Jan - 2001 to 31st Dec 2003. For the first sub period, the study used

753 daily observations and the test is repeated with the same test procedures used for the

whole and adjusted periods. For this sub period it is also noted that, BSE 100 index was

(2023.82) in the beginning and it was (3074.87) at the end of the study period the total gain in

the index was (1051.05) points during this period.

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4.4 Testing CAPM through Portfolios

For the sub period 1st- Jan-2001 to 31stDec-2003, the test considers 753 observations and the

results are shown in the Table 2 below. From the table, it is clear that portfolio 1 (P1) with

lowest beta earned the minimum return of (0.135846) while the portfolio 6 (P6) with the

highest beta (1.08355) receives the maximum return (0.21964).But the portfolio seven with

higher beta bagged nearly half of the return than the portfolio 6 and hence the argument of

CAPM that higher risk beta is associated with higher rate of return is violated. Out of the

seven portfolios, both the beta and the return shows an increasing trend up to the portfolio 6

,but in portfolio seven, the return (0.128447) is decreasing while the beta (1.57857) shows an

increase from (1.08355).

The R2 value for the first six portfolios lies between (0.27150) and (0.596), which indicates

less than adequate correlation with the market index. But in portfolio 7, R2 value is (0.76875),

which indicates that above 76 per cent of the variation in the scrip has been explained by the

relationship with the index. Further from the Table 2, it is noted that the all the constant

except portfolio 7 are statistically significant and also have positive values. That means the

first six constants are statistically significant and the alpha coefficient is significantly

different from zero, there by reject the null hypothesis. Further the estimated betas of

portfolios are found to be statistically significant at 99% level; thereby we reject the null

hypothesis that the portfolio beta is not a significant determinant of portfolio return. Thus

from the analysis it clear that the can be used for predicting risk return relationship in

Indian stock market for the sub period 2001-2003

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Table 2

Table Showing Average Excess Portfolio Return and Portfolio Betas for the

Sub period (2001 -2003) (N = 753)

4.5. Estimation of Security Market Line (2001 - 2003)

The result for the first sub period is shown in the Table 3.and it is clear that the t-test rejects

the null hypothesis that 0 is not significantly different from zero. Here the calculated value

of the intercept is (0.17757) and it is significantly different from zero. Statistically, the result

shows that the t- value is greater than (2.57) at 95% confidence level and hence the o is

statistically inconsistent with CAPM. Further from table it is clear that 1 is negative

(0.0029) and it is nearly equal to zero and the Absolute t - value is less than (2.57), this

means that 1 is not significantly different from zero. But as per CAPM the 1 should be

greater than zero, there by the result is inconsistent with the CAPM hypothesis and the

CAPM is rejected during this period.

Port

folio

Portfolio

Return

(rp)

Constant BetaStandard

ErrorR

2F value

P Value

of beta

at 99%

P1 0.135846 0.11887 0.34760 0.82728 0.27150 279.895 0.0000

P2 0.198832 0.17091 0.57192 1.09264 0.36644 434.367 0.0000

P3 0.143898 0.10840 0.72707 0.94657 0.55466 935.384 0.0000

P4 0.1821840.14148

0.83370 1.62623 0.55408 933.163 0.0000

P5 0.216427 0.17020 0.94681 1.14613 0.59027 1081.92 0.0000

P6 0.219646 0.16675 1.08355 1.29599 0.59606 1108.22 0.0000

P7 0.128447 0.05138 1.57857 1.25793 0.76875 2496.59 0.0000

Avg Rf 0.01681 Average rm = (Rm-Rf) 0.04881

The value of constants of P1, P2, P3,

P4, P5, P6, are significant at 99 %

level but P7 is insignificant

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Table 3.

Table showing the result of the test of SML for Sub period (2001 - 2003)

*** shows significant at 99% level

Critical value for ttest with 5-Degrees of freedom at 95 % level (2.57)

4.6. Test of Non-Linearity (2001-2003)

The result of the test of non-linearity for the sub period 1 is summarised bellow in the Table

4.The result shows that the intercept (0.03810) of the model is not significantly different from

zero. Statistically the t- value is (0.5678), which is less than (2.7765) at 5% significant level

and thereby it is consistent with the argument of CAPM.

Table 4

Table showing the result of the test of Non-Linearity for the Sub period (2001 - 2003)

Critical value of ttest for 4-Degrees of freedom at 95% (2.7765)

In the case of 1, the t- value is (2.252), which is less than (2.7765), and it is significantly not

different from zero. As per the CAPM, the 1 should be equal to the average risk premium;

hence we can conclude that result is inconsistent with the CAPM hypothesis. In the case of

2, the value of coefficient is (0.17365) and the absolute t- value is less than (2.7765) at 5%

significance level, 2 is consistent with the CAPM hypothesis. Thus we can say that the betas

are linearly related with return and hence CAPM is can be accepted during the first sub

period but still the data showed weakness to fully explain the model.

4.7. Section IV: CAPM in Second Sub Period (2002-2004)

The data used in the second sub period consists of 759 daily observations of a sample of 70

companies listed in BSE 100. The second period covers the period from 01-01-2002 to 31-

12-2004. Further, in the beginning of this sub period BSE 100 index was (1557.22) points

and it was (3580.34) at the end. The total gain in the index was (2023.12) points during this

Coefficients Std error t- value p-value

0 0.17757 0.04133 4.296*** 0.0077

1 0.00291 0.04380 0.066 0.9495


0 0.03810 0.06711 0.5678 0.6005

1 0.33520 0.14884 2.252 0.0874

2 0.17365 0.07466 2.326 0.0806

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period, which shows that, there is an increase of 972 points in the index when compared with

the previous period. The various test results for the period is described below.

4.8.Testing CAPM through Portfolios

As per the Capital asset pricing theory, the higher risk beta is associated with higher rate of

return. But from the Table 5 it is clear that the portfolio 2 (P2) with lowest beta earned the

minimum return of (0.132295) and the portfolio 6(P6) earned more return than the other

portfolios. During the study period all the portfolios including the portfolio with lowest beta

earned more return than the average excess market return and also the risk free return. Further

the positive constants suggest that the portfolios have earned higher returns than the CAPM

has predicted

Table 5


Sub period (2002-2004) (N =759)

In the case of portfolio1, the value of R2 is (0.34023), and in all other case the R2 value is in

between (0.63) and (0.78) which indicates that above 63 to78 % of the variation in the scrip

has been explained by the relationship with the index. If we look further in to the results of

the test for alpha and the slope coefficients of portfolios, the result shows that the constant

(alpha) values are significantly different from zero, and thereby the null hypothesis is

rejected. Further the p value of slope coefficient are greater than the level of significance in

all the cases and thereby we reject the null hypothesis that beta does not significantly explain

the variation in portfolio return. Thus the conclusion from this analysis is that beta can

explain the portfolio return as suggested by CAPM during the second sub period.

Port -

folio

Portfolio

Return(rp)Constant Beta

Standard

ErrorR

2

F valueP Value

of beta

at 99%

P1 0.18812 0.14555 0.40544 0.77423 0.34023 390.375 0.0000

P2 0.13299 0.06508 0.64687 0.67298 0.63469 1315.22 0.0000

P3 0.27030 0.18199 0.84115 0.85477 0.64552 1378.53 0.0000

P4 0.20948 0.10713 0.97486 1.01318 0.63516 1317.89 0.0000

P5 0.23339 0.11769 1.10212 0.78913 0.78577 2776.67 0.0000

P6 0.27087 0.14154 1.23187 0.93917 0.76390 2449.39 0.0000

P7 0.27020 0.11722 1.45715 1.17759 0.74222 2179.65 0.0000

Avg Rf 0.014238Average rm =

(Rm-Rf)0.10498

The values of constants of P1, P2,

P3, P4, P5, P6, P7are significant at

99 % level

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4.9. Estimation of Security Market Line (2002-2004)

The Table 6 describes the result for the sub period 2 which compose the values of 0 and

1.From the table it is clear that the t- test rejects the null hypothesis that 0 is not

significantly different from zero. Here the calculated value of the intercept is (0.12526) and issignificantly different from zero. Statistically, the result shows that the t- value is greater than

(2.57) at 95 % confidence level and the o is significant. It means that the result is

statistically inconsistent with CAPM.

Table 6

Table showing the estimation of SML for Second Sub Period (2002 - 2004)

** Shows significant at 95% level.


Furtherthe value of the 1 is (0.10488) and the t- value is less than (2.57) this means that 1 is

not significantly different from zero .As per CAPM the 1 should be greater than zero, there

by the result is inconsistent with the CAPM hypothesis and the data shows its weakness to

fully explain the CAPM during this sub period.


The result of the non-linearity test for the sub period 2 is summarised bellow in the table

7.The result shows that the value of the intercept is (0.12757) and is not significantly

different from zero. Statistically the t- value is (1.015) and is less than the table value, hence

we accept the null hypothesis that 0 is not significantly different from zero. Thus it is

consistent with the argument of CAPM.

Table 7Table showing the result of the test of Non-Linearity for the Sub period (2002 - 2004)

Critical value for t-test with 4-Degrees of freedom at 95% level (2.7765)

In the case of 1, the t- value is (0.3444) which is less than (2.7765), and it is not significantly

different from zero. Hence we can conclude that result is inconsistent with the CAPM


00.12526 0.04608 2.718 ** 0.0419

10.10488 0.04577 2.292 0.0705


0 0.12757 0.12565 1 .015 0.3674

1 0.09918 0.28795 0.3444 0.7479

2 0.00307 0.15287 0.0201 0.9849

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hypothesis because the value 1 should be equal to the average risk premium. In the case of

2, the value is (0.00307) and the t- value is less than (2.7765), at 5% significance level, we

can say that it is consistent with the CAPM hypothesis. From the analysis it is clear that the

value of the 2 is not significantly different from zero .Thus we cannot clearly reject the

CAPM is during the second sub period.

4.11. Section V: CAPM in Third Sub Period (2003-2005)

The study investigated the applicability of CAPM and the data used in this study consisted 70

stocks listed in the BSE 100 Index over the period 01-01-2003 to 31-12-2005. For the third

sub period, the study used 755 daily observations and the test is repeated with the same

methodology and test procedures used for the whole period and adjusted period. For this sub

period, it is also noted that BSE 100 index was (1664.67) in the beginning and it was

(4953.28) at the end .The total gain in the index during this period was (3288.61) points.

4.12. Testing CAPM through Portfolios

For the third sub period, the test considers 755 observations over the period 01-01-2003 to 31-

12-2005. From the Table 8, it is clear that beta of the portfolio increases from portfolio 1 to

portfolio 7, but we cannot see such trend in portfolio return. Beta of the portfolio 3 (P3) and

portfolio 6 (P6) earns less when compared to portfolio two and portfolio 4 & 5(P4 & P5) which

shows that the result contradicts the CAPM. The R2 value for the first portfolios is (0.39166),

which indicates less than adequate correlation with the market index. But in portfolio 2 to 7, R2

value is in between (0.64385) and 0.84625) which indicates that 64 to 84 per cent of the

variation in the scrip has been explained by the relationship with the index.

If we further look in to the Table 8, it is noted that the values of constants are significant at

different level (P6 & P7 at 90% level and all others at 99%level) and also have positive values,which suggests that, we reject the null hypothesis that the alpha is not significantly different

from zero. Further all the estimated betas of portfolios are found to be statistically significant at

the 99% level, and we reject the null hypothesis that the portfolio beta is not a significant

determinant of portfolio return. Thus from the analysis it is clear that the can predict the risk

return relationship in the Indian market during the sub period 2003-2005

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Table 8


Sub period (2003 -2005) (N = 755)


From the Table 9, it is clear that the t-test rejects the null hypothesis that 0 is not

significantly different from zero. Here the calculated value of the intercept is (0.16826) and it

is significantly different from zero.

Table 9Table showing the result of the test of SML for the Sub period (2003 - 2005)

** Shows significant at 95% level.*** Shows significant at 99% level.


Statistically, the result shows that the t- value is greater than (2.57) at 95% confidence level

and the p value is significant at 99% level, hence the result do not support the CAPM. Further

looking in to the table it is clear that the slope (1) is significantly different from zero. Here

the t- value is greater than (2.57) at 95% confidence level. As per the CAPM, 1 should be

equal to the average risk premium, which should be greater than zero and it is concluded that

the result is consistent with the CAPM. Hence the CAPM is accepted for the third sub period

by rejecting Ho that 0 = 0

Port-

folio

Portfolio

Return

(rp)


ErrorR

2

F valueP Value of

beta

at 99%P1 0.19576 0.13121 0.46072 0.78158 0.39166 487.370 0.0000

P2 0.23213 0.13598 0.69667 0.70528 0.64385 1368.55 0.0000

P3 0.19582 0.07629 0.84995 0.69089 0.73712 2122.70 0.0000

P4 0.24712 0.11524 0.94406 0.82561 0.70782 1833.88 0.0000

P5 0.24341 0.09436 1.06785 0.61953 0.84625 4166.87 0.0000

P6 0.23194 0.05893 1.24122 0.97754 0.74919 2261.24 0.0000

P7 0.27509 0.06909 1.47422 1.00364 0.79990 3026.13 0.0000

Avg Rf 0.01366 Average m = (Rm-Rf) 0.13860

The values of constants of P1, P2, P3,

P4, P5 are significant at 99 % level; theconstants of P6 and P7 are significant at

90 %Level


0 0.16826 0.02357 7.138 *** 0.0008

1 0.06585 0.02329 2.826 ** 0.0368

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The results of the estimated values for the test of non - linearity is summarised in the Table

10. The result shows that the intercept is (0.18392) and 0 is not significantly different from

zero. Statistically the t- value is (2.605), which is less than (2.7765) at 5% significant level

and there by the null hypothesis is accepted and is consistent with the CAPM hypothesis.

Table 10

Table showing the test of Non-Linearity for the Sub period (2003 - 2005)Critical value for t-test with 4-Degrees of freedom at 95% level (2.7765)

In the case of 1, the t- value is (0.02979) is smaller than (2.7765), and it is not significantly

different from zero. As per the CAPM, the 1 should be equal to the average risk premium.

Hence we can conclude that result is inconsistent with the CAPM hypothesis. The value 2 is

(0.01858) and the t- value is less than (2.7765), at 5% significance level that means it is not

significantly different from zero. Hence, we can say that it is consistent with the CAPM

hypothesis. Hence the CAPM is accepted but the data shows weakness to fully explain the

postulates of CAPM.

4.15. Section VI CAPM in Fourth Sub Period (2004 -2006)

This sub period considered the daily data for the period from 01-01-2004 to 31-12-2006 and

the dataset consists of 755 daily observations of 70 companies which have been the part of

BSE 100 index. In the beginning of the test period the BSE 100 index was (3074.87) points

and it was (6982.56) at the end. The total gain in the index was (3907.69) points during this

period,

4.16. Testing CAPM through portfolios

For the fourth sub period 755 observations are used and the result shows that portfolio 1 (p1)

with lowest beta (0.56299) received maximum return when compared to the other portfolios

especially P5, P6, and P7 which are having beta values above one. Here all the portfolios

Coefficients Std error t -value p-value

0 0.18392 0.07060 2.605 0.0597

1 0.02979 0.15312 0.1946 0.8552

2 0.01858 0.07777 0.2389 0.8229

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including the portfolio 2, with lowest beta bags more return than the average excess market

return and also the risk free return.

Table 11

Table Showing Average Excess Portfolio Return and Portfolio Betas for Sub Period

(20042006)(N = 755)

The CAPM explains that, higher risk is associated with higher rate of return and the result ofthe study does not find any support for this argument because ,we cannot find any positive

correlation (-0.09531) between beta and the average portfolio excess return. Here all the

portfolios including the portfolio 2, with lowest beta received more return than the average

excess market return and also the risk free return.

In the case of portfolio 1, the R2 value is (0.53150), which indicates less than adequate

correlation with the market index. But for other portfolios, the R2 value is above (0.777) to

(0.957), which indicates that above 77 % to 95% of the variation in the scrip has been

explained by the relationship with the index. All the values of the constants except p5 and p7

are statistically significant and all are positive. It indicates that, the alpha coefficients are

significantly different from zero and hence we reject the null hypothesis that the intercept is

not significantly different from zero. Further the positive constants suggest that the portfolios

earned higher returns than the CAPM has predicted. All the p values of estimated betas are

found to be statistically significant at the 99% level; thereby we reject the null hypothesis that

the portfolio beta is not a significant determinant of portfolio return. Thus from the analysis

Port -

folio

Portfolio

Return

(rp)


ErrorR

2

F valueP Value

of beta

at 99%

P1 0.19367 0.13865 0.56299 0.78490 0.53150 854.283 0.0000

P2 0.13098 0.04788 0.81057 0.64327 0.77784 2636.53 0.0003

P3 0.18110 0.09071 0.89768 0.69737 0.78512 2751.36 0.0000

P4 0.16977 0.07077 0.97381 0.69060 0.81428 3301.59 0.0000

P5 0.13713 0.02389 1.1060 0.79109 0.81169 3245.86 0.0000

P6 0.17221 0.04885 1.20218 0.77701 0.84072 3974.74 0.0000

P7 0.17639 0.02408 1.48129 0.95771 0.84064 3972.28 0.0000

Avg

Rf0.01496

Average

rm = (Rm-Rf)0.10505

The constants of P1, P3, P4, are significant

at 99 % level; P2 at 95 % Level and P6 at

90% significant level. P5,P7 are

insignificant

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we can say that the is a predictor of return for the Indian market during the sub period

2004-2006.


The estimated result of the SML for the sub period 4 is shown in the Table 12 below. Fromthis it is clear that the t-test rejects the null hypothesis that 0 is not significantly different

from zero. Here the calculated value of the intercept is (0.17341) and it is significantly

different from zero. Statistically, the result shows that the t- value is greater than (2.57) at

95% confidence level; hence the o is statistically inconsistent with CAPM.

Table 12Table showing the result of the test of SML for the Sub period (2004- 2006)

*** Shows significance at 99% level.


Further from table it is clear that1 is negative (0.00748) and it is nearly equal to zero and

the absolute t- value is less than (2.57), this means that 1 is not significantly different from

zero. But as per CAPM the 1 should be greater than zero, there by the result is inconsistent

with the CAPM hypothesis and the model is fully rejected during the sub period.

4.18.Test of Non-Linearity (2004-2006)

While testing the non-linearity, as per the CAPM the 0 and 2 will be equal to zero and the

1 should be equal to the average risk premium. The results of the estimated values are

summarised bellow in the Table 13.

Table 13Table showing the result of the test of Non-Linearity for the Sub period (2004- 2006)



0 0.17341 0.03639 4.765 *** 0.0050

1 0.00748 0.03494 0.2141 0.8389

Coefficients Std error t -value p-value

0 0.29847 0.10790 2.766 0.0505

1 0.26997 0.21703 1.244 0.2815

2 0.12792 0.10452 1.224 0.2881

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The result shows that the intercept of the model is greater than the risk free interest rate and

the constant 0 is significantly different from zero. Statistically the t- value is (2.766), which

is greater than (2.7765) at 5% significant level and there by the null hypothesis is rejected and

hence inconsistent with the argument of CAPM. The absolute t- value for the 1 is (1.244)

which is less than (2.7765) and the value is not significantly different from zero. As per the

CAPM, 1 should be equal to the average risk premium; hence we can conclude that result is

inconsistent with the CAPM hypothesis. The t- value of 2 (1.224) is less than (2.7765) and

hence value is not significantly different from zero, which is consistent with the CAPM. Thus

the CAPM couldnt clearly be rejected during the sub period.

4.19. Section VII: CAPM in the Fifth Sub Period (2005 -2007)

This sub period considered the daily data for the period from 01-01-2005 to 31-12-2007 and

the dataset consists of 750 daily observations of 70 companies which have been the part of

BSE 100 index. It is also noted that in the beginning of this study period the BSE 100 index

was at (3580.34) points and at the end of the study period it is (11154.28) resulting a total

gain of (7573.94) points throughout the period


The study in the sub period 5 used 750 observations and the data covers the period from 1-

01-2005 to 31-03-2007.The estimates of the study is reported in the table 14 below. The table

reveals that all the constants are positive. During this period the portfolios bags higher rate of

return when compared with the other study periods. Further The CAPM postulates that higher

risk beta is associated with higher rate of return and the result of the study partially support

this argument because we can see high positive correlation between beta and average excess

return on portfolios. Further it is also interesting to note that all the beta values are in between

(1.49240) and (1.52382).Out of the seven portfolios, the beta shows an increasing trend, P7

with high beta (1.5203) earned more return than others and the R2 explains that 76.17% of the

variation in the scrip has been explained by the relationship with the index. In the case of

portfolio 1, the R2 value is (0.8002), which indicates that adequate correlation with the

market index. If we further look in to the Table 14, it is noted that the constants of P1 and P2

are of statistically insignificant but all others are significant at 95 and 90% level. Further the

positive constants suggest that the portfolios have earned higher returns than the CAPM has

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predicted. All the p values of estimated betas are found to be statistically significant at 99%

level; thereby we reject the null hypothesis that the portfolio beta is not significant

determinant of portfolio return. Thus from the analysis we can say that beta can predict the

risk return relation in the Indian capital market during the sub period 2005-2007.

Table 14

Table Showing Average Excess Portfolio Return and Portfolio Betas for the Sub Period

(20052007)(N = 750)


The result for the fifth sub period is shown in the Table 15 and it is clear that the t-test rejects

the null hypothesis that 0 is not significantly different from zero. Here the value of the

intercept is (1.41536) and it is significantly different from zero. Statistically, the result

shows that the t- value is greater than (2.57) at 95% confidence level and hence the o is

statistically inconsistent with CAPM.

Portf

olio

Portfolio

Return (rp)Constant Beta

Standard

ErrorR

2

F valueP Value of

beta

at 99%P1 0.27919 0.06130 1.49240 1.07047 0.8002 2997.27 0.0000

P2 0.28746 0.06720 1.50999 1.13101 0.7860 2748.69 0.0000

P3 0.30661 0.08589 1.51668 1.16175 0.7784 2628.29 0.0000

P4 0.31259 0.09113 1.52038 1.22087 0.7617 2391.53 0.0000

P5 0.30497 0.08421 1.52228 1.17057 0.7771 2608.02 0.0000

P6 0.30914 0.08654 1.52323 1.15407 0.7822 2686.45 0.0000

P7 0.31722 0.09722 1.52382 1.18991 0.7717 2529.03 0.0000

Avg

Rf0.01724

Average rm =

(Rm-Rf)0.14487

The value of constants P3, P4, P6 andP7 are significant 95 % level and P5, at

90% significant level. P1 ,P2 are

insignificant

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Table 15Table showing the result of the test of SML for the Sub period (2005 - 2007)

*** Shows significance at 99% level.


Further from table it is clear that1 is (1.13347) and it is significantly different from zero.

Here the t- value is greater than (2.57) which means that it is consistent with CAPM

hypothesis

4.22.Test of Non-Linearity (2005-2007)The results of the estimated values for the test of non - linearity are summarised in the table

16. The result shows that the intercept (60.2641) of the model is 0 is significantly different

from zero. Statistically the t- value is (1.055), which is less than (2.7765) at 5% significant

level and thereby we cannot reject the null hypothesis. Thus it is consistent with the CAPM

hypothesis.In the case of 1, the absolute t- value is (1.065) is smaller than (2.7765), since

it is not significantly different from zero. As per the CAPM, the 1 should be equal to the

average risk premium; hence we can conclude that result is inconsistent with the CAPM

hypothesis.

Table 16

Table showing the test of Non-Linearity for the Sub period (2005- 2007)

Critical value for t-test with 4-Degrees of freedom at 95% level (2.7765)The value 2 is (27.1154) and the t- value is less than (2.7765) at 5% significance level that

means it is not significantly different from zero. Hence, we can say that it is consistent with

the CAPM hypothesis. Hence, the relationship is linear but the data is weak to explain the

CAPM during the study period.


0 1.4153 0.32306 4.381 *** 0.0071

1 1.13347 0.21316 5.317 *** 0.0031

Coefficients Std error t - value p-value

0 60.2641 57.1167 1.055 0.3509

1 80.6609 75.7428 1.065 0.3469

2 27.1154 25.1092 1.080 0.3410

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4.23. Section VIII: CAPM in the Sixth Sub Period (2006 -2008)

The data used in the seventh sub period consists of 745 daily observations of a sample of 70

companies listed in BSE 100. This sub period covers the data from 01-01-2006 to 31-12-

2008. It is also noted that in the beginning of this study period the BSE 100 index was at

(4953.28) points and at the end of the study period it is (4988.04) resulting a total gain of

(34.76) points. Further it is noted that the period includes a part of the recession period.


The table 17 deals with the test results for the constant alpha and the beta coefficient of the

portfolio for the sub period 01-01-2006 to 31-12-2008.In the case of portfolio return the

portfolio 4 earns the least return (-0.01330) and the value of the constant is also negative.

Further the value of the R2 shows high correlation between the market return and the

portfolio return .For all the portfolios the value of R2 is in between (0.593) and (0.905), which

indicates that adequate correlation with the market index. ie is 59% to 90% of the variation in

the scrip has been explained by the relationship with the index. The table shows that most of

the constants are insignificant and thereby we cannot reject the null hypothesis.

Table 17Table Showing Average Excess Portfolio Return and Portfolio Betas for the

Sub period (2006-2008)

Port -

folio

Portfolio

Return (rp)Constant Beta

Standard

ErrorR

2

F valueP Value

of beta

at 99%

P1 0.05494 0.05317 0.47559 0.82658 0.59363 1085.42 0.0000

P2 0.00965 0.00700 0.71177 0.80501 0.77526 2563.14 0.0000

P3 0.03012 0.02690 0.86554 0.86240 0.81634 3302.58 0.0000

P4 -0.01330 0.01678 0.93899 0.77934 0.86496 4759.44 0.0000

P5 0.05991 0.05603 1.04399 0.70999 0.90513 7088.83 0.0000

P6 0.06231 0.05787 1.19443 0.98340 0.86683 4836.66 0.0000

P7 0.12303 0.11767 1.44127 1.15324 0.87329 5120.82 0.0000

Avg Rf 0.01939 Average rm = (Rm-Rf)0.00372

The value of constants of P7 is

significant at 99% level P5 at 95 %

Level and P1 at 90% significant level.P2,P3,P4,P6 are insignificant

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Further the positive constants suggest that the portfolios have earned higher returns than the

CAPM has predicted. All the p values of estimated betas are found to be statistically

significant at the 99% level; thereby we reject the null hypothesis that the portfolio beta is not

significant determinant of portfolio return. Thus the analysis do not gives a firm result in

support of CAPM.


From the Table 18, we can see that, the value of the intercept is (0.03215) statistically; the

result shows that the absolute t- value is less than (2.57) at 95% confidence level, and the o

is not significantly different from zero. Thus the result is consistent with the CAPM. As per

CAPM 1 should be equal to the average risk premium and here the t- value is (1.657), whichis less than the table value is not significantly different from zero and should be greater than

zero. Hence it is concluded that the result is inconsistent with the CAPM and hence there is

mixed result and we dont have conclusive evidence in support of CAPM in the sixth sub

period.

Table 18Table showing the result of the test of SML for the Sub period (2006- 2008)



The result for the sub period 6 is summarised bellow in the Table 19. The result shows that

the intercept (0.20379) of the model 0 is significantly different from zero. Statistically the t-value is (2.393), which is less than (2.7765) at 5% significant level and thereby we cannot

reject the null hypothesis. Thus it supports the argument of CAPM. In the case of 1, the

absolute t- value is (2.485) which is less than (2.7765) and it is not significantly different

from zero. As per the CAPM, the 1 should be equal to the average risk premium and hence

we can conclude that result is inconsistent with the CAPM hypothesis.


0 0.03215 0.04977 0.6461 0.5467

1 0.08270 0.04992 1.657 0.1585

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Table 19Table showing the result for the test of Non-Linearity for the Sub period (2006- 2008)

** Shows significant at 95% level.Critical value for t-test with 4-Degrees of freedom at 95% level (2.7765)

In the case of 2, the value is (0.28262) and the t- value is greater than (2.7765) at 5%

significance level, we can say that it is inconsistent with the CAPM hypothesis. From the

analysis it is clear that the value of the 2 is significantly different from zero .Thus we cannot

say that the betas are linearly related with each other and hence CAPM is rejected during the

sixth sub period.

4.27. Section IX: CAPM in the Seventh Sub Period (2007 -2009)

In the seventh sub period the analysis is carried out on the data of 70 companies listed BSE

100 and covers the period from 01-01-2007 to 31-12-2009, the study used 738 daily

observations and the test is repeated with the same test procedures used for other test period.

In the beginning of the test period the BSE 100 index was (6982.56) points and it was

(9229.71) at the end. The total gain in the index was (2247.15) points during this study

period,


The study in the sub period 7 used 738 observations and the data covers the period from 1-

01-2007 to 31-03-2009.Further the study period includes the period which is excluded for

defining the adjusted period due to the high fluctuation in the capital market. It will be

interesting to check the result during this period and the various estimates are reported in the

Table 20 below. The table reveals that all the constants are positive and all the portfolios

except the portfolio 2 (P2) bags higher return than the average excess market return


0 0.20379 0.08517 2.393 0.0750

1 0.45958 0.18494 2.485 0.0678

2 0.28262 0.09500 2.975** 0.0410

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Table 20

Table Showing Average Excess Portfolio Return and Portfolio Betas for

Sub Period (20072009)(N = 738)

The CAPM postulates that higher risk beta is associated with higher rate of return but from

the result we cannot see any upward trend in the portfolio return. In the case of portfolio 1,

the value of R2 is greater than (0.73441) and in the case portfolio7 it (0.88429) the maximum,

which shows that adequate correlation with the market index. If we further look in to the

Table 20, it is noted that most of the constants are insignificant and al1 are positive, which

suggests that we cannot reject the null hypothesis that the alpha is not significantly different

from zero. Further the estimated betas of portfolios are found to be statistically significant at

the 99% level; thereby we reject the null hypothesis that the portfolio beta is not a significant

determinant of portfolio return. Thus the analysis gives a mixed result and we cannot clearly

accept the CAPM for this sub period 2007-2009 and apart from other period it may be due to

the recession effect.


The estimated result of the SML for the sub period 7 is shown in the Table 21 below. The

table shows that the t-test accept the null hypothesis that 0 is not significantly different from

zero. Here the calculated value of the intercept is (0.02385) and it is not significantly

Port -folio

Portfolio

Return(rp)

Constant Beta StandardError

R2 F value

P Value of

betaat 99%

P1 0.08502 0.06672 0.393851 0.82383 0.53903 860.651 0.0000

P2 0.04054 0.00929 0.67844 0.92283 0.73441 2035.23 0.0000

P3 0.08185 0.04320 0.82771 0.93873 0.79910 2927.60 0.0000

P4 0.08081 0.03690 0.93784 0.94318 0.83494 3723.10 0.0000

P5 0.11927 0.06948 1.04698 0.88599 0.84949 5719.99 0.0000

P6 0.16448 0.10719 1.23770 1.07297 0.87192 5010.55 0.0000

P7 0.12786 0.05648 1.47794 1.20925 0.88429 5624.87 0.0000

Avg Rf 0.01702Average rm =

(Rm-Rf)0.04611

The values of constants of P6 are

significant at 99% level P1, P5 at 95 %

significance level .P2, P3, P4, P7are

insignificant.

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different from zero. Statistically, the result shows that the t- value is less than (2.57) at 95%

confidence level and hence it is insignificant, thus consistent with CAPM.

Table 21

Table showing the estimation of SML for the Sub Period (2007- 2009)


Further from table it is clear that1 is (0.08072) and the t- value is greater than (2.57). Hence,

1 is significantly different from zero. As per CAPM the 1 should be greater than zero, there

by the result is inconsistent with the CAPM hypothesis. Thus the CAPM is rejected in the

seventh sub period.

4.30. Test of NonLinearity (2007-2009)

Test for the non-linearity is used to check whether there exists non- linearity between

portfolio return with beta. As per theory, if CAPM holds true 0 and 2 will be equal to zero

and the 1 will be equal to the average risk premium.

Table 22Table showing the result of the test of Non-Linearity for the Sub period (2007- 2009)


The results of the estimated values for the sub period 7 are summarised bellow in the Table

22. The result shows that the intercept (0.06469) of the model is not significantly different

from zero. Statistically the t- value is (0.7213), which is less than (2.7765) at 5% significant

level and there by the null hypothesis is accepted and is consistent with the argument of

CAPM.The absolute t- value for the 1, is (0.0924) which is less than (2.7765), and the value

of intercept is not significantly different from zero. As per the CAPM, the 1 should be equal

to the average risk premium; hence we can infer that result is inconsistent with the CAPM

Coefficients Std error t-value p-value

0 0.02385 0.03514 0.6789 0.5274

1 0.08072 0.03516 2.296 0.0701


0 0.06469 0.08969 0.7213 0.5106

1 0.01859 0.20112 0.0924 0.9308

2 0.05287 0.10512 0.5030 0.6414

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hypothesis. The t- value of 2 is (0.503), which is less than (2.7765) and the value is not

significantly different from zero. Thus we can say that beta is linearly related with return.

Hence, we cannot fully reject CAPM during this sub period.

5. Summary and Conclusion

This study examined the empirical validity of CAPM, which was questioned in home security

market as well as throughout the world markets. The present study used daily return of 70

securities listed in BSE 100 index. The CAPM is tested for different study period through

different methods by using portfolios having 10 securities. The results of the different tests

for different study periods are summarized below in Table 23.-29. The Form the table,

following conclusion can be derived.

1. The test for portfolios based on percentage return with equally weighted portfolios

having 10 securities mostly in support of CAPM but do not give a conclusive

evidence in favor of CAPM

2. For the sub periods, the test gives mixed result and in some period the test clearly

rejects the CAPM hypothesis and in few sub periods it partially supports the CAPM

hypothesis.

3. In almost all the cases the constant have positive values, which suggest that the

portfolio bagged more return than the CAPM has predicted.

4. In analyzing the risk - return relationship, for most of the cases the R2 shows a high

value over .65 (approximate), which shows that above 65% of the variation, has been

explained by the relationship with index.

5. From the analysis, it is found that, generally higher beta provides higher return to the

investor , in most of the case beta explain the variation in portfolio returns.( it does

not mean it is fully true in 100% cases)

6. Test for SML and Non linearity support CAPM but do not give conclusive evidence

in favor of CAPM in different sub periods.

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I. Through PortfoliosTable 23

Table Showing Consolidated Results for Different Study Periods by Using 10 Securities

Port folioSub period 1 (20001-2003)

Constant F Value R2

P value Beta

P1 0.1189 279.90 0.2715 0.0000

P2 0.1709 434.37 0.3664 0.0000

P3 0.1084 935.38 0.5547 0.0000

P4 0.1415 933.16 0.5541 0.0000

P5 0.1702 1081.92 0.5903 0.0000

P6 0.1668 1108.22 0.5961 0.0000

P7 0.0514 2496.59 0.7688 0.0000

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Table Showing Consolidated Results for Different Study Periods by Using 10 SecuritiesTable 24

I. Through PortfoliosTable 25

Note: The Values of Constant, F, and R2

are adjusted to 4 digits.

Port

folio

Sub period 2 (2002-2004) Sub period 3( 2003-2005) Sub period 4 (2004-2006)

Constant F Value R2

P value

Beta Constant F Value R2

P value


P value

Beta

P1 0.1456 390.38 0.3402 0.0000 0.1456 390.38 0.3402 0.0000 0.13865 854.28 0.5315 0.0000

P2 0.0651 1315.22 0.6347 0.0000 0.0651 1315.22 0.6347 0.0000 0.04788 2636.53 0.7778 0.0003

P3 0.1820 1378.53 0.6455 0.0000 0.1820 1378.53 0.6455 0.0000 0.09071 2751.36 0.7851 0.0000

P4 0.1071 1317.89 0.6352 0.0000 0.1071 1317.89 0.6352 0.0000 0.07077 3301.59 0.8143 0.0000P5 0.1177 2776.67 0.7858 0.0000 0.1177 2776.67 0.7858 0.0000 0.02389 3245.86 0.8117 0.0000

P6 0.1415 2449.39 0.7639 0.0000 0.1415 2449.39 0.7639 0.0000 0.04885 3974.74 0.8407 0.0000

P7 0.1172 2179.65 0.7422 0.0000 0.1172 2179.65 0.7422 0.0000 0.02408 3972.28 0.8406 0.0000

Port

folio

Sub period 5 (2005-2007) Sub period 6 (2006-2008) Sub period 7 (2007-2009)

Constant F Value R2

P value


P value


P value

Beta

P1 0.0613 2997.27 0.8002 0.0000 0.0532 1085.42 0.5936 0.0000 0.0667 860.65 0.5390 0.0000

P2 0.0672 2748.69 0.7860 0.0000 0.0070 2563.14 0.7753 0.0000 0.0093 2035.23 0.7344 0.0000

P30.0859 2628.29 0.7784 0.0000 0.0269 3302.58 0.8163 0.0000 0.0432 2927.60 0.7991 0.0000

P4 0.0911 2391.53 0.7617 0.0000 0.0168 4759.44 0.8650 0.0000 0.0369 3723.10 0.8349 0.0000

P5 0.0842 2608.02 0.7771 0.0000 0.0560 7088.83 0.9051 0.0000 0.0695 5719.99 0.8495 0.0000

P6 0.0865 2686.45 0.7822 0.0000 0.0579 4836.66 0.8668 0.0000 0.1072 5010.55 0.8719 0.0000

P7 0.0972 2529.03 0.7717 0.0000 0.1177 5120.82 0.8733 0.0000 0.0565 5624.87 0.8843 0.0000

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II. Test of Security Market LineTable 26

*** Significant at 99 %level** Significant at 95% level

Table 27

*** Significant at 99 %level

CoefficientsSub Period1(2001-2003) Sub Period 2 (2002-2004) Sub Period 3( 2003-2005) Sub Period 4 (2004-2006)

Constant t- value P valueConstant

t -

valueP value

Constant t- value P value Constant t- value P value

0.17764.2960

***0.0077

0.12526 2.718

**0.0419

0.168267.138 *** 0.0008 0.1734

4.765

***0.0050

0.0029 0.066 0.9495 0.10488 2.292 0.0705 0.06585 2.826** 0.0368 0.00748 0.2141 0.8389

Coefficients

Sub Period 5 (2005-2007) Sub Period 6 (2006-2008) Sub Period 7 (2007-2009)

Constant t- value P value Constant t- value P value Constant t- value P value

1.4153 4.381*** 0.0071 0.03215 0.6461 0.5467 0.02385 0.6789 0.5274

1.13347 5.317*** 0.0031 0.08270 1.657 0.1585 0.08072 2.296 0.0701

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III. Test of NonLinearity


Table 28

Coefficient

Sub Period 1(2001-2003) Sub Period 2(2002-2004) Sub Period 3(2003-2005)

Constant t- value P value Constant t- value P value Constant t- value P value

0.03810 0.5678 0.6005 0.12757 1.0150 0.3674 0.1839 2.6050 0.0597

0.33520 2.252 0.0874 0.0991 0.3444 0.7479 0.0298 0.1946 0.8552

0.1736 2.326 0.0806 0.0030 0.0201 0.9849 0.0186 0.2389 0.8229

III. Test of NonLinearityTable 29

Coefficient

Sub Period 4(2004-2006) Sub Period 5 (2005-2007) Sub Period 6 (2006-2008) Sub Period 7(2007-2009)

Constant t- value P value Constant t- value P value Constant t- value P value Constant t- value P value

0.29847 2.766 0.0505 60.2641 1.055 0.3509 0.2037 2.393 0.0750 0.0647 0.7213 0.5106

0.26997 1.244 0.2815 80.6609 1.065 0.3469 0.4595 2.485 0.0678 0.0185 0.0924 0.9308

0.12792 1.224 0.2881 27.1154 1.080 0.3410 0.2826 2.975** 0.0410 0.0529 0.5030 0.6414

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The sub period 6 & 7 which covers the recession period generally in Support of CAPM but in

the sub period 1 and 4 the test of non linearity shows that beta is not linearly related with

expected return.The findings of the study shows that, the test in the Indian market by using

70 securities listed in the BSE 100 index is mostly supportive in different test periods to the

hypothesis of Capital Asset Pricing Model, which says that higher beta provides higher return

to the investor and the study reveals that while using percentage return and portfolios with

equal weight, in most of the case beta explain the variation in portfolio returns.

Regarding the security market line, The CAPM predicts that 0 (the intercept) should be

equal to zero and the 1 (the slope of SML) should be equal to the average risk premium. The

result for the SML for the whole period support the CAPM but for the adjusted period the 0

is inconsistent with CAPM and thereby we cannot say that CAPM is fully accepted for the

adjusted period. The result for the different sub periods by using portfolios with 10 securities

mostly rejected CAPM. Five out of Seven test results clearly reject the CAPM hypothesis

while two partially support CAPM hypothesis. From the above result, we cannot give

conclusive evidence in favor of CAPM.

The test for non- linearity between beta and stock return is tested by including beta square

coefficient. As per CAPM the portfolio return and its betas are linearly related with each

other when the 0 and 2 is equal to zero. The test for the non - linearity tells that, for the

whole and adjusted period the result is in support of the CAPM hypothesis. For the adjusted

period we cannot give conclusive evidence in support of the CAPM hypothesis, but the

model supports the non linearity of the CAPM factors in most of the cases, which explains

the beta estimates. Further the high value of the estimated correlation coefficient between the

intercept and the slope indicates that the model explains excess returns. However in most of

the case, the intercept have value near to zero, weakens above explanation.

In short most of the test result supports the CAPM and is in favor of the model but we cannot

see conclusive evidence in support of CAPM to wrap up the question of the validity of

CAPM in Indian context

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Reference

1. Andor Gyorgy, Ormos Mihly and SzAbo Balazs, 1999, Empirical Testing ofCapital Asset Pricing Model(CAPM) In the Hungarian Capital Market,Periodica

Polytechnica, Ser. Soc. Man. Scl.Nol.7, Vol. 1, PP. 4761.

2. Ansari, Valeed A (2000). Capital Asset Pricing Model: Should We Stop Using It ,Vikalpa, Vol.25(1), PP-55-64.

3. Bark, Hee-Kyung K (1991). Risk, Return, and Equilibrium in the Emerging Markets:Evidence from the Korean Stock Market, Journal of Economics and Business, Vol

43(4), pp-353-362.

4. Bartholdy Jan, Peare, Paula, 2004, Estimation Of Expected Return: CAPM Vs FamaAnd French, Working Paper Series no 176, Centre For Analytical Finance,

University of Aarhus.

5. Bello, Zakri.Y, 2008, A Statistical Comparison of the CAPM to the Fama-FrenchThree Factor Model And the Caharts Model, Global journal of Finance and

Banking Issues, Vol.2, pp14-24.

6. Black, F., Jensen, M. C. and Scholes, M. (1972), The Capital asset pricing model:Some empirical tests, Studies in the Theory of Capital Markets, New York: Praeger.

pp-79-121.

7. Black, Fischer (1993). Beta and Return, Journal of Portfolio Management, Vol.20(1), 8-18.

8. Brav, Alon, Lehavy, Reuven, Michaely, Roni, 2005 Using Expectations to TestAsset Pricing Models, FinancialManagement, Vol. 34, No. 3, PP. 31-64.

9. Cagnetti Arduino,2001 ,Capital Asset Pricing Model and Arbitrage Pricing Theory -in the Italian Stock Market: an Empirical Study, http://www.ssrn.com/.

10.Chan, Cheong ,Yue , 1997 Multivariate testing of the capital asset pricing model inthe Hong Kong stock market,Applied Financial Economics, Vol.7: 3, PP.311 - 316.

11.Chen, Ming-Hsiang, 2003, Risk and return: CAPM and CCAPM, The QuarterlyReview of Economics and Finance, Vol.43, PP.369393.

12.Cheng, Tsung-Chi, Neng, Hung, Tsai Lai,Pei-Fen,2005, On the Two-Stage Estimationof Fama-French Three Factor Models: Evidence from Taiwan,

http://www.airitilibrary.com/.

13.Cochrane, John H. (2001)Asset Pricing. New Jersey: Princeton University Press.

14.Connor, Gregory and Sehgal,Sanjay, 2001, Tests of the Fama and French Model inIndia, http://www.ifa.com/.

15.Daniel, Kent and Titman, Sheridan (1997). Evidence on the Characteristics of Cross

Sectional Variation in Stock Returns,Journal of Finance, Vol.52(1), pp.1-33.

7/27/2019 345 Daniel

36/39

16.Fama, Eugene F and French, Kenneth R (1992). The Cross-section of ExpectedStock Returns,Journal of Finance, Vol.47 (2), pp.427-465.

17.Fama, Eugene F and French, Kenneth R (2004). The CapitalAsset Pricing Model:Theory and Evidence,Journal of Economic Perspectives, Vol.18 (3), pp. 25-46.

18.Fan, Stephen C, , 2004,Have we misinterpreted CAPM for 40 years? a theoreticalproof, Working Paper Series, http://www.ssrn.com/.

19.Fletcher Jonathan, Kihanda, Joseph, 2005, An examination of alternative CAPM-based models in UK stock returns,Journal of banking and finance, Vol.29, pp.2995-

3014.

20.Glabadanidis, Paskalis, 2009, A Dynamic Asset Pricing Model with Time VaryingFactor and Idiosyncratic Risk, Journal of Financial Econometrics, Vol. May 6,

pp.1-18.

21.Grauer, Robert R., Janmaat, Johannus A. b , 2010, Cross -sectional tests of theCAPM and FamaFrench three-factor model,Journal of Banking & Finance, Vol.34

,pp. 457470

22.Gursoy Cudi Tuncer, Rejepova , Gulnara , 2007, Test of Capital Asset Pricing ModelIn Turkey,Dogus Universitesi Dergisi, Vol.8 (1), pp.47-58 ,

23.Hamao, Yasushi , 1988,An Empirical Examination Of The Arbitrage Pricing TheoryUsing Japanese Data,Japan And The World Economy,Vol 1, pp.45-61.

24.Harris, Robert S; Marston, Felicia C; Mishra, Dev R and OBrien, Thomas J (2003).Ex Ante Cost of Equity Estimates of S&P 500 Firms: The Choice between Global

and Domestic CAPM,Financial Management, Vol. 32(3), pp51-66.

25.Homsud, Nopbhanon , Wasunsakul, Jatuphon , Phuangnark, Sirina, and Joongpong ,Jitwatthana, 2009, A Study of Fama and French Three Factors Model and Capital

Asset Pricing Model in the Stock Exchange of Thailand, International Research

Journal of Finance and Economics ,Issue 25.

26.Hsiang, Ming Chen, 2003, Risk and return: CAPM and CCAPM The QuarterlyReview of Economicsand Finance, Vol. 43, pp.369393.

27.Jagannathan, R., Wang, Z., 1996, The conditional CAPM and the cross-section ofexpected returns,Journal of Finance, Vol.51, pp.353.

28.Javid, Attiya Y. 2009, Test of higher moment capital asset pricing model in case ofpakistani equity markrt, European journal of Economics, Finance and

Administrative Sciences.Vol(15) pp.144-162.

29.Koch Stefan and Westheide Christian, The Conditional Relation between Fama-French Betas and Return, G August 4, 2008

30.Kothari, S P; Shanken, J and Sloan, R P (1995). Another Look at the Cross -section

of Expected Stock Returns,Journal of Finance, Vol. 50(1), PP185-224.

7/27/2019 345 Daniel

37/39

31.Lewellen, Jonathan, Nagel, Stefan, 2006, The conditional CAPM does not explainasset-pricing anomalies,Journal of Financial Economics ,Vol.82, pp.289314,

32.Li, Yan and Yang, Liyan, 2009, Under conditioning and Over conditioning: Testingthe Conditional CAPM and the Conditional Fama-French Three-Factor Model

ttp://www.ssrn.com/,

33.MacKinlay, A. Craig, 1995, Multifactor models do not explain deviations from theCAPM, USA Journal of Financial Economics, Vol.38, pp. 3-28.

34.MacKinlay, A. Craig, 1987,Mackinlay, C.A. 1995, Multifactor models do notexplain deviations from the CAPM,Journal of Financial Economics, vol. 38, pp. 3

28

36.Madhusoodanan, T P (1997). Risk and Return: A New Look at the Indian StockMarket,Finance India, Vol.11 (2), pp.285-304.

37.Majumdar, Samit, Bacon, Frank .W, 2007, Multi Factor Pricing Model: AnAlternative Approach to CAPM,ASBBS E-Journal, Volume 3, No. 1.

38.Malin Mirela , Veeraraghavan, Madhu, 2004, On the Robustness of the Fama andFrench Multifactor Model: Evidence from France, Germany, and the United

Kingdom International Journal of Business and Economics, , Vol. 3, No. 2, pp.155-

176 .

39.Manjunatha, T; Mallikarjunappa, and Begum, Mustiary(2007). Capital Asset PricingModel: Beta and Size Tests, AIMS International Journal of Management, Vol1 (1),

pp.71-87.

40.Michailidis, G, Tsopoglou, S., Papanastasiou, D. and Mariola, E. (2006)Testing theCapital Asset Pricing Model (CAPM): The Case of the Emerging Greek Securities

MarketInternational Research Journal of Finance and Economics, Vol.4, PP.78-91.

41.Mohanty, Pitabas (2002). Evidence of Size Effect on Indian Stock Returns, Vikalpa,27(2), pp.27-37.

42.Pettengill, G., Sundaram, S., & Mathur, I. (1995). The conditional relation betweenbeta and returns, Journal of Financial and Quantitative Analysis, Vol.30, pp.101-

116.

43.Rahman, Moztafizur,Baten,Azizul, Alam,Ashraf-Ul, 2006, An Empirical Testing OfCapital Asset Pricing Model In Bangladesh, Journal of Applied Sciences

Vol.6(3),pp.662-667.

44.Reinganum, Marc R., 1981, A New Empirical Perspective on the CAPM, Journalof Financial and Quantitative Analysis, Vol. XVI, No.4.

45.Roll, R. (1977). A critique of the asset pricing theorys tests, Journal of FinancialEconomics, Vol.4, PP.129-176.

7/27/2019 345 Daniel

38/39

46.S.Shijin, Kumar, Arun G. and Sanghamitra B,2007, Relationship between Size, Valueand Market Risk: Some Evidence, International Journal of Investment Management

and Financial Innovations,p-

47.Samit Majumdar ,Frank W. Bacon, 2007 , Multi Factor Pricing Model:An Alternative

Approach To CAPM ,ASBBS E-Journal, Volume 3, No. 1.

48.Sauer, A. and A. Murphy, 1992, An Empirical Comparison of Alternative Models ofCapital Asset Pricing in Germany, Journal of Banking and Finance, PP.16-47

49.Srinivasan, S (1988). Testing of Capital Asset Pricing Model in IndianEnvironment,Decision, Vol.15(1), pp.51-59.

50.Suh, Daniel The Correlations and Volatilities of Stock Returns: The CAPM beta andthe FamaFrench Factors, http :// ssrn.com/1364567

51.Terregrossa, S J (2001). Robust Informational Tests on the CAPM, AppliedEconomics, Vol.8(2),pp. 121-124.

52.Wong,Kie Ann and Meng Siong Lye, 1990, Market Values, Earnings Yields AndStock Returns Evidence From Singapore,Journal of Banking and Finance, Vol.14

(2-3) :3 ,pp.I l-326.

53.Yalwar, Y B (1988). Bombay Stock Exchange: Rates of Return and Efficiency,Indian Economics Journal, Vol.35(4), pp.68-121.

54.Yang, Xi and Donghui Xu . 2006. Testing the CAPM modelA Study of theChinese Stock Market, Master Thesis Essay. Sweden: UMEA School of Business.

55.Yonezawa ,Yasuhiro Hin, Tio Kia, 1992,An empirical test of the CAPM on the

stocks listed on the Tokyo Stock Exchange,Japan and the World Economy,vol.4 ,

pp.145-161,

Books &websites

1. Asset Pricing,Princton Universty Press, John.H. Cochrane,P-434,4352. Economic Outlook for 2010-113. Fundamentals of Financial Management, Rao, Ramesh.K.S, p-389, 1989

4. Investments a Global Perspective, jack C. Francis and Roger Ibbotson, prentice Hall ,New Jersey5. Asset Pricing, John.H. Cochrane, Princton University Press,P-434,435.6. Investments, William.F.Sharpe and et.al, prentice hall India Pvt. Limited, 1996.7. Investments, ZVI Bodie and et.al.Tata McGraw hill publishing company, Newdeli,

2008.

8. Rao, Ramesh.k.s Fundamentals of Financial Management, page 389, 1989sey,2002.9. S.Kevin, Security analysis and portfolio Management, 2008.10.Security analysis and portfolio Management, S.Kevin, PHI L Ltd, New Delhi, 2008.11.Statistics-Handbook of Statistics on Indian Economy.12.http://benmcclure.mp/.

13.http://bseindia.com/about/abindices/bse30.asp# reconstitution.14.http://www.crisil.com/.

7/27/2019 345 Daniel

39/39

15.http://www.essays.se/about/empirical+test+of+CAPM/.16.http://www.imf.org.17.http://www.rbi.org.in/.18.http://www.sebi.gov.in/.19.http://www.wikipedia.org.

20.https://cdbmsi.reservebank.org.in/cdbmsi/servlet/login/.21.https://sebi.ac.in/ monthly bulletins.

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