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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
Coefficients Std error t- value p-value
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
Table Showing Average Excess Portfolio Return and Portfolio Betas for the
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.
Critical value for ttest with 5-Degrees of freedom at 95 % level (2.57)
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.
4.10. Test of Non-Linearity (2002-2004)
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
Coefficients Std error t- value p-value
00.12526 0.04608 2.718 ** 0.0419
10.10488 0.04577 2.292 0.0705
Coefficients Std error t- value p-value
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
Table Showing Average Excess Portfolio Return and Portfolio Betas for the
Sub period (2003 -2005) (N = 755)
4.13. Estimation of Security Market Line (2003-2005)
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.
Critical value for ttest with 5-Degrees of freedom at 95 % level (2.57)
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)
Constant BetaStandard
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
Coefficients Std error t- value p-value
0 0.16826 0.02357 7.138 *** 0.0008
1 0.06585 0.02329 2.826 ** 0.0368
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4.14. Test of Non-Linearity (2003-2005)
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)
Constant BetaStandard
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.
4.17. Estimation of Security Market Line (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.
Critical value for ttest with 5-Degrees of freedom at 95 % level (2.57)
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)
Critical value for t-test with 4-Degrees of freedom at 95% level (2.7765)
Coefficients Std error t- value p-value
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
4.20. Testing CAPM through Portfolios
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)
4.21. Estimation of Security Market Line (2005-2007)
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.
Critical value for ttest with 5-Degrees of freedom at 95 % level (2.57)
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.
Coefficients Std error t- value p-value
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.
4.24. Testing CAPM through Portfolios
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.
4.25. Estimation of Security Market Line (2006-2008)
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)
Critical value for ttest with 5-Degrees of freedom at 95 % level (2.57)
4.26. Test of Non-Linearity (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.
Coefficients Std error t- value p-value
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,
4.28. Testing CAPM through Portfolios
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
Coefficients Std error t- value p-value
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.
4.29. Estimation of Security Market Line (2007-2009)
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)
Critical value for ttest with 5-Degrees of freedom at 95 % level (2.57)
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)
Critical value for t-test with 4-Degrees of freedom at 95% level (2.7765)
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
Coefficients Std error t- value p-value
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
Beta Constant F Value R2
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
Beta Constant F Value R2
P value
Beta Constant F Value R2
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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Table Showing Consolidated Results for Different Study Periods by Using 10 Securities
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 Showing Consolidated Results for Different Study Periods by Using 10 Securities
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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