Validity of CAPM by Using Portfolios:
Evidence from Indian Capital Market
K.M. Yaseer1 & K.P. Shaji2
1Department of Commerce, PG Department of
Commerce Govt. College Madapally, University of�
Calicut , India
2Urban and Rural Development Finance
Corporation, Thiruvananthapuram, India
Correspondence: K.M. Yaseer,
Department of Commerce, PG Department of Commerce Govt. College Madapally,
University of� Calicut , India
Received: May 20, 2018������������ ��������������������� �Accepted: May 28, 2018����������� ����� �����Online Published: July 25, 2018
Abstract
This article tests the validity of Capital Asset
pricing Model and compares the results of 16 periods including 14 sub periods
which comprises 3 years each for the prediction of the expected returns in the
Indian capital Market. The tests were conducted on portfolios having different
security combinations. By using Black Jenson and Scholes methodology (1972) the
study tested the validity of the model for the whole and different sub periods.
The study used daily data of the BSE 100 index for the period from January 2001
to December 2010. Empirical results mostly in favor of the standard CAPM model.
However, the result does not find conclusive evidence in support of CAPM
Keywords: Capital
Asset pricing Model, Beta, systematic risk, Security market line.
I. Introduction
Globalization
and international investments to Indian capital market over the past decade
made investment arena tougher and investment decisions complex. Today the
market is highly volatile and the investor should be cautious and should
identify an appropriate tool to evaluate the risk and return involved in his
investment decisions. Normally rational investor will expect high return for
bearing risk and the rate of return on the investment should commensurate with
the riskiness of the assets. Capital Asset Pricing Model (CAPM) was developed
by Sharpe (1964), Lintner (1965), and Mossin (1966) and it has been used widely
for determining the risk return relationship in asset management. The core
assumption of this model is that contribution of an asset to the variance of
the market portfolio is the asset�s systematic risk and beta can explain the
asset�s risk. In other words, rate of return and the risk premium, which will
be proportional to assets market risk or beta quantifies the amount of risk
that cannot be diversified away.
This
study has four testable objectives. It checks the empirical validity of the
CAPM in Indian stock market and ascertains
the relationship between return of securities and market return. It also
compared whether expected rate of return is linearly related with systematic
risk and the difference in results while using different security combinations.
This study is unique in the sense that it is difficult to find a study, which
tested the validity of CAPM in Indian capital market by using different
portfolio combination. The analysis was conducted for the whole study period
and for different sub periods by using two different set of portfolios and
failed to find irrefutable evidence in validating CAPM. The size of the
sample and the number of companies used to construct the portfolio is one of
the important limitations.
2. Review of Literature
CAPM is the widely applauded model
to explain the risk return relation. Large number of studies has been carried
out to elucidate the relationship between return and factors which affect
return and this has been tested with individual security return and portfolio
return. Generally
portfolio betas are more precise when compared to the individual security beta
and researchers like Black and et.al (1972), Friend and Blume (1973) etc,
followed portfolio approach to examine CAPM. In1973 Fama and Mac.Beth tested
the linearity between expected return and pre ranked historic beta of assets
and included squared beta as an additional variable to the basic Capital Asset
Pricing Model and found a positive relation between return and risk.
Results of various empirical tests
revealed that there is a mixed feeling on the applicability of CAPM in
predicting risk return relationship. Studies conducted by (Fama and Mac Beth
1973), (Gibbons and Ferson, 1985) are generally in favor of CAPM. At the same
time there is substantial criticism against the CAPM since the mid of 1975 and
many empirical studies uncovered various anomalies that were clearly in
conflict with the model�s predictions. (Ross, 1976) introduced the concept of a
multi factor model with the theoretical foundation and presented a number of
state variables to explain the expected. (Roll, 1977) argued that one cannot
empirically test the CAPM because the construction of the market portfolio as
per the theory is impossible. (Basu, 1977) found that when stocks are sorted on
earnings-price ratios (E/P), the expected returns on high E/P stocks are higher
when compared to the return predicted by the Capital Asset Pricing Model.
Similarly (Stattman, 1980) tested the effect of book value on stock return,
(Banz, 1981) the size effect. (Bhandari, 1988) the effect of leverage and
showed the inefficiency of beta to explain the market returns.�� In 1992 by using the cross-sectional
regression Fama and French examined the validity of CAPM and found that size,
book to market, debt equity and earning price should consider in the
explanation of expected stock return. Further, Chan et.al (1991) challenged the
validity of CAPM. (Bark, 1991) tested the risk-return
relationship for assets by using the CAPM with Fama and Macbeths� two-stage
approach and found Sharpe-Linter-Mossin CAPM frame work is not adequate in the
Korean stock market. (Yue, 1997) tested CAPM with multivariate testing based on
Gibbon�s methodology in Hong Kong market and their results rejected both the
Sharpe- Lintner CAPM and Black CAPM at an extremely low level. (Harris et al.,
2003), (Fan, 2004), (Malin and et. al, 2004) UK, France and German markets
rejected CAPM. (Michailidis et.al, 2006) found that their study do not support the
theory�s basic hypothesis of CAPM in Greek securities market but explained the
excess returns.
Pettengill et. al (1995) found valid relationship between beta and returns by
using a modified methodology of Fama and MacBeth (1973). (Rahman et al., 2006) in Bangladesh market, (Andor et al.,
1999) Hungarian capital market also found positive relationship between beta
and ex-post return, concluded that CAPM valid for these markets. Besides this (Majumdar et
al., 2007) neither support nor reject (mixed result) the Capital Asset Pricing
Model.�
In
Indian context few studies were conducted for analyzing risk- return relationship
and studies by (Madhusoodanan, 1997), (Srinivasan,
1988) have generally supported CAPM. Studies by (Rao and Bhole, 1990),
(Vaidyanathan, 1995), (Sehgal, 1997), (Sehgal, 2003), (Mohanthy, 2002),
(Manjunatha, et.al 2006) questioned
the validity of CAPM in Indian context.
While examining the literature it is
clear that most of the studies in India used monthly or yearly data and only
few studies used daily and weekly data to test the validity of Capital Asset
Pricing Model. There is dearth of studies in Indian context and is planned to
examine the CAPM by using daily data of 70 companies listed in BSE100-index
with two different combinations of portfolios.
3. Objectives of the Research
The
main objectives of the study is to revisit the empirical validity of CAPM frame
work in Indian stock market by using different set of portfolios . The study
will use Black et.al (1972)
methodology and Fama and Mac Beth (1973) methodology to test the non linearity.
�
To
examine the empirical validity of the �CAPM� in Indian stock market.
�
To
establish the relationship between
return of securities and market return in Indian stock market.
� To check whether
expected rate of return is linearly related with systematic risk.
� To compare the
result of portfolios with different security combinations.
4. Source and Period of Data
The
sample for the study covers nine years daily data of 70 companies of BSE 100
stock Index, a broad-based index, launched in 1989 for the period from
01-01-2001 to 31-12-2009�� The data used
in this study were sourced from of Prowess- a data base of CMIE and the
websites Reserve Bank of India (RBI). The study considers 91 day Treasury bill
rate as the proxy for the risk free assets, will better reflects the short term
changes in the financial market.
5. Methodology for Testing 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 analyzed systematically.� The present study also follows a similar
approach will follow portfolio technique and use time series regression of
excess portfolio return on excess market return and also cross sectional
regression in risk premium form and is expressed by the equation below. In the
first step, betas (systematic risk) of individual securities are measured and
the beta coefficients of individual securities were calculated for the whole
period and for the sub 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 below.
�������������������� �������������������������� Rit- Rft = a i +bi (Rmt
�Rft) + 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, BSE 30 index is taken as the best proxy for the
market portfolio. eit is
the beta of stock i, eit
is the error term of regression equation at time t.�
In
the second stage, for the formation of portfolios individual beta for each
stock is arranged on ascending order and stocks were grouped in to portfolios
having 10 and 5 stocks each according to their beta value .The first portfolio
comprises the first 10/5 securities with lowest beta, the next portfolio with
the next 10/5 securities and same method is followed for the formation of other
portfolios and there by last portfolio is formed with securities having the
highest beta. Then portfolio betas are calculated by using the following model.
rpt = ap + bp rmt
+ ept�� ������������������� ----------------------
������������������������������������� �����(2)
Where
rpt
is the average excess portfolio return on time t, bp is the estimated portfolio beta, and, e
pt is the error term in the regression equation at time t.
to
estimate the ex post security market line for each testing period the portfolio
return are regressed against portfolio betas. The model is
���������
rp =� λ0 +
λ1 bp + ep��� �����
��������� ----------------------
������������� ������������������(3)
Where
rp = is the average excess return of the portfolio P, bp is the beta of
the portfolio P, and ep is the error term in the regression equation
Further
the study will also tested the non- linearity between the total portfolio
return and betas by using the following equation.�
����������
rp =� λ0� +�
λ1bp� +�
λ2b2p
+� ep����������������������� �������� -------------------� �����������(4)
6. CAPM in Different Periods.
To test the validity of CAPM, the
study considered whole period data that is (2001-2009) and then the entire test
period is divided in to seven different sub periods comprising three years
each. The details are shown in Table1 below.
Table 1. Different Portfolio
Formation Periods and Testing Periods
|
Period |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
Period Range |
01-09 |
01-03 |
02-04 |
03-05 |
04-06 |
05-07 |
06-08 |
07-09 |
|
Portfolio Formation |
2001 |
2001 |
2002 |
2003 |
2004 |
2005 |
2006 |
2007 |
|
Testing period |
2009 |
2003 |
2004 |
2005 |
2006 |
2007 |
2008 |
2009 |
6.1. CAPM in the Whole Study Period
(2001-2009) with Portfolios Having Ten Securities
|
Port folio |
Portfolio
Return(rp) |
Intercept |
Beta |
Standard Error |
R2 |
F value |
P Value of Beta
at 99% |
|
P1 |
0.11130 |
0.07971*** |
0.47233 |
0.76289 |
0.54509 |
2688.93 |
0.0000 |
|
P2 |
0.11554 |
0.06680*** |
0.72892 |
0.97319 |
0.63685 |
3935.33 |
0.0000 |
|
P3 |
0.12702 |
0.06868*** |
0.87242 |
0.79571 |
0.78981 |
8432.46 |
0.0000 |
|
P4 |
0.13047 |
0.06646*** |
0.95720 |
0.90286 |
0.77844 |
7884.51 |
0.0000 |
|
P5 |
0.19971 |
0.12924*** |
1.05378 |
0.91577 |
0.80541 |
9288.38 |
0.0000 |
|
P6 |
0.16271 |
0.08401*** |
1.17683 |
1.09133 |
0.78425 |
8156.95 |
0.0000 |
|
P7 |
0.18238 |
0.09388*** |
1.32345 |
1.20891 |
0.78931 |
8406.92 |
0.0000 |
|
Avg Rf |
0.01626 |
Average��� rm = (Rm-Rf) |
0.06687 |
***significant
at 99 % level. |
|||
The study investigated the
applicability of CAPM and the data used in this study consists 5259 days
observations of 70 stocks listed in the BSE 100 Index. The results for the
whole period by using the model (2) are shown in Table 2 below. Portfolio 1(P1)
with lowest beta earned the minimum return of (0.1113) and the portfolio 5 with
the beta (1.0538) gives the maximum return (0.1997). During the study period
the average risk free return is (0.0163) and the average excess return on the
market is (0.0669).The CAPM postulates that higher risk beta is associated with
higher
Table 2.Test Results for Whole Study Period (2001 � 2009) (N= 5259) rate of return
and the result of the study partially supports this argument since portfolio6
and portfolio7 with highest beta bags less return than portfolio 5.
R-square
explains the relative amount of the variance in return of a particular
portfolio with the return on index.�
In
the case of portfolio 1, the R2 value is (0.54509), which indicates
less than adequate correlation with the market index. Were as in portfolio 5, R2
value is (0.80541), which indicates that above 80 per cent of the variation in
the scrip has been explained by the relationship with the index. The
positive constants suggest that the portfolios have earned higher returns than
the CAPM has predicted. Thus from the analysis it is clear that in most of the
cases β is a predictor of return in Indian capital market during the study
period but there no conclusive evidence in favor of CAPM.
6.1.1 Test of Non-Linearity
(2001-2009)
Test
for the non-linearity helps one to check whether there exists non-linearity
between portfolio return with beta. As per theory, if CAPM holds true λ0
and λ2 will be equal to zero and the λ1 will be
equal to the average risk premium. In this work the non-linearity has been
tested by using the regression model (4).The results of the estimated values
are summarized in the Table 3; it shows that the value of the constant λ0
is not significantly different from zero. Statistically the t - value is
(0.8377), which is less than (2.7765) at 5% significant level and thereby it is
consistent with the argument of CAPM.
Table
3. Test of Non-Linearity for the Whole Period (2001 - 2009)
|
|
Coefficients |
Std error |
t- value |
p-value |
|
λ0 |
0.08368�� |
0.09989� |
0.8377��� |
0.4493 |
|
λ1 |
0.02685��� |
0.23162���� |
0.1159��� |
0.9133 |
|
λ 2 |
0.03990�� |
0.12751�� |
0.3130��� |
0.7699 |
Critical value
for 4-Degrees of freedom (2.7765)
In
the case of λ1, the t- value is (0.1159) is smaller than
(2.7765), and it is not significantly different from zero. As per the CAPM, the
λ1 should be equal to the average risk premium; hence the
result is inconsistent with the CAPM hypothesis. In the case of λ2,
the value (0.3130) and the t-value is less than (2.7765) at 5% significance
level and thereby it is consistent with the CAPM hypothesis. Thus, it is clear
tha betas are linearly related with expected return. Hence CAPM cannot be
clearly rejected during the study period.
6.2. CAPM in Different Sub Periods
6.2.1 Consolidated
Test Results for Different Sub �Periods (Ten Securities)
CAPM is tested for different study
period by using portfolios having 10 securities. The results for different
study periods are summarized below in Tables 4 to 7. The findings are 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.
Study reveals that while using percentage return and portfolios with equal
weight, in most of the case beta explain the variation in portfolio returns, in
few periods lower beta earned more return than higher beta portfolios, which is
clear from table. 4.
Table 4. Consolidated Results for
Different Sub Periods by Using 10 Securities
�
|
Port folio |
Sub period 1 (20001-2003) |
Sub period 2 (2002-2004) |
||||||||||
|
Portfolio return |
Constant |
Beta |
R2 |
F� Value |
P value Beta |
Portfolio return |
Constant |
Beta |
F� Value |
R2 |
P value Beta |
|
|
P1 |
0.1358 |
0.1189*** |
0.34760 |
0.2715 |
279.90 |
0.0000 |
0.18812 |
0.1456*** |
0.40544 |
390.38 |
0.3402 |
0.0000 |
|
P2 |
0.1988 |
0.1709*** |
0.57192 |
0.3664 |
434.37 |
0.0000 |
0.13299 |
0.0651*** |
0.64687 |
1315.22 |
0.6347 |
0.0000 |
|
P3 |
0.1438 |
0.1084*** |
0.72707 |
0.5547 |
935.38 |
0.0000 |
0.27030 |
0.1820*** |
0.84115 |
1378.53 |
0.6455 |
0.0000 |
|
P4 |
0.1821 |
0.1415*** |
0.83370 |
0.5541 |
933.16 |
0.0000 |
0.20948 |
0.1071*** |
0.97486 |
1317.89 |
0.6352 |
0.0000 |
|
P5 |
0.2164 |
0.1702*** |
0.94681 |
0.5903 |
1081.92 |
0.0000 |
0.23339 |
0.1177*** |
1.10212 |
2776.67 |
0.7858 |
0.0000 |
|
P6 |
0.2196 |
0.1668*** |
1.08355 |
0.5961 |
1108.22 |
0.0000 |
0.27087 |
0.1415*** |
1.23187 |
2449.39 |
0.7639 |
0.0000 |
|
P7 |
0.1284 |
0.0514 |
1.57857 |
0.7688 |
2496.59 |
0.0000 |
0.27020 |
0.1172*** |
1.45715 |
2179.65 |
0.7422 |
0.0000 |
|
Avg Rf |
0.01681 |
Average�� rm = (Rm-Rf) |
0.04881 |
Avg Rf |
0.0142 |
Average rm = (Rm-Rf) |
0.10498 |
|||||
***
significant at 99%
Table� 5. Consolidated Results for Different Sub
Periods by Using 10 Securities
|
Port folio |
Sub period 3( 2003-2005) |
Sub period 4 (2004-2006) |
||||||||||
|
Portfolio return |
Constant |
Beta |
R2 |
F� Value |
P value Beta |
Portfolio return |
Constant |
Beta |
R2 |
F� Value |
P value Beta |
|
|
P1 |
0.19576 |
0.1312*** |
0.46072 |
0.39166 |
487.370 |
0.0000 |
0.19367 |
0.13865*** |
0.56299 |
0.53150 |
854.283 |
0.0000 |
|
P2 |
0.23213 |
0.1359*** |
0.69667 |
0.64385 |
1368.55 |
0.0000 |
0.13098 |
0.04788** |
0.81057 |
0.77784 |
2636.53 |
0.0000 |
|
P3 |
0.19582 |
0.0762*** |
0.84995 |
0.73712 |
2122.70 |
0.0000 |
0.18110 |
0.09071*** |
0.89768 |
0.78512 |
2751.36 |
0.0000 |
|
P4 |
0.24712 |
0.1152*** |
0.94406 |
0.70782 |
1833.88 |
0.0000 |
0.16977 |
0.07077*** |
0.97381 |
0.81428 |
3301.59 |
0.0000 |
|
P5 |
0.24341 |
0.0943*** |
1.06785 |
0.84625 |
4166.87 |
0.0000 |
0.13713 |
0.02389 |
1.1060 |
0.81169 |
3245.86 |
0.0000 |
|
P6 |
0.23194 |
0.0589** |
1.24122 |
0.74919 |
2261.24 |
0.0000 |
0.17221 |
0.04885* |
1.20218 |
0.84072 |
3974.74 |
0.0000 |
|
P7 |
0.27509 |
0.0690** |
1.47422 |
0.79990 |
3026.13 |
0.0000 |
0.17639 |
0.02408 |
1.48129 |
0.84064 |
3972.28 |
0.0000 |
|
Avg Rf |
0.01366 |
Average�� rm = (Rm-Rf) |
0.13860 |
Avg Rf |
0.0142 |
Average rm = (Rm-Rf) |
0.10505 |
|||||
***
Significant at99%,** Significant at 95%,* Significant at90%
Table� 6. Consolidated Results for Different Sub
Periods by Using 10 Securities
|
Port folio |
Sub period 5 (2005-2007) |
Sub period 6� (2006-2008) |
|
||||||||||
|
Portfolio return |
Constant |
Beta |
R2 |
F� Value |
P value Beta |
Portfolio return |
Constant |
Beta |
R2 |
F� Value |
P value Beta |
|
|
|
P1 |
0.27919 |
� 0.0613 |
1.4924 |
0.8002 |
2997.27�� |
0.0000 |
0.05494 |
0.05317* |
0.4755 |
0.59363 |
1085.4 |
0.0000 |
|
|
P2 |
0.28746 |
� 0.0672 |
1.5099 |
0.7860�� |
2748.69�� |
0.0000 |
0.00965 |
�0.00700 |
0.7117 |
0.77526 |
2563.1 |
0.0000 |
|
|
P3 |
0.30661 |
0.0858 **�� |
1.5166�� |
0.7784�� |
2628.29�� |
0.0000 |
0.03012 |
�0.02690 |
0.8655 |
0.81634 |
3302.5 |
0.0000 |
|
|
P4 |
0.31259 |
0.0911** |
1.5203���� |
0.7617� |
2391.5 |
0.0000 |
�� -0.01330 |
�0.01678 |
0.9389 |
0.86496 |
4759.4 |
0.0000 |
|
|
P5 |
0.30497 |
� 0.0842 * |
1.5222���� |
0.7771� |
2608.02�� |
0.0000 |
0.05991 |
0.05603** |
1.0439 |
0.90513 |
7088.8 |
0.0000 |
|
|
P6 |
0.30914 |
�0.0865�
**� |
1.52323����� |
0.7822�� |
2686.45�� |
0.0000 |
0.06231 |
0.05787 |
1.1944 |
0.86683 |
4836.6 |
0.0000 |
|
|
P7 |
0.31722 |
0.0972** |
1.52382����� |
0.7717�� |
2529.03�� |
0.0000 |
0.12303 |
0.11767*** |
1.4412 |
0.87329 |
5120.82 |
0.0000 |
|
|
Avg Rf |
0.01724 |
Average�� rm = (Rm-Rf) |
�0.14487 |
Avg Rf |
0.01939 |
Average� rm = (Rm-Rf) |
0.00372 |
|
|||||
*** Significant at99%,� ** Significant at95%, Note: The Values of
Constant, F, Pand R2 are adjusted to 4 digits.
Table 7. Consolidated Results for
Different Sub Periods by Using 10 Securities
|
Port folio |
Sub period 7 (2007-2009) |
||||||
|
Portfolio return |
Constant |
Beta |
R2 |
F� Value |
P value Beta |
||
|
P1 |
0.08502 |
0.06672� ** |
0.393851 |
0.53903 |
860.651 |
0.0000 |
|
|
P2 |
0.04054 |
0.00929 |
0.67844 |
0.73441 |
2035.23 |
0.0000 |
|
|
P3 |
0.08185 |
0.04320 |
0.82771 |
0.79910 |
2927.60 |
0.0000 |
|
|
P4 |
0.08081 |
0.03690 |
0.93784 |
0.83494 |
3723.10 |
0.0000 |
|
|
P5 |
0.11927 |
0.06948 ** |
1.04698 |
0.84949 |
5719.99 |
0.0000 |
|
|
P6 |
0.16448 |
��
0.10719*** |
1.23770 |
0.87192 |
5010.55 |
0.0000 |
|
|
P7 |
0.12786 |
����� 0.05648 |
1.47794 |
0.88429 |
5624.87 |
0.0000 |
|
|
Avg Rf |
0.04611 |
Average������� rm = (Rm-Rf) |
0.04611 |
|
|||
6.2.2 Test of Non �Linearity
The test for the non- linearity
(Table 8-10) reveals that, for whole and adjusted period result support CAPM
hypothesis. In addition high value of estimated correlation coefficient between
the intercept and the slope indicates that the model explains excess returns
Table 8.Consolidated Results for
Different Study Periods by Using 10 Securities
|
Coefficient |
Whole Period (2001-2009) |
Sub Period 1(2001-2003) |
Sub Period 2(2002-2004) |
||||||
|
Constant |
t -value |
P value |
Constant |
t- value |
P value |
Constant |
t-� value |
P value |
|
|
l0 |
0.0837 |
0.8377 |
�0.4493 |
0.03810 |
�0.5678 |
�0.6005 |
0.12757 |
1.0150 |
0.3674 |
|
l1 |
0.0269 |
0.1159 |
0.9133 |
0.33520 |
�
2.252 |
�
0.0874 |
0.0991 |
0.3444 |
0.7479 |
|
l2 |
0.0399 |
0.3130 |
0.7699 |
−0.1736 |
−2.326 |
�
0.0806 |
0.0030 |
0.0201 |
0.9849 |
***
Significant at 99 %level,������� **�� Significant at 95% level
Table 9. Consolidated Results for
Different Study Periods by Using 10 Securities
|
Coefficient |
Sub Period 3(2003-2005) |
Sub Period 4(2004-2006) |
Sub Period 5 (2005-2007) |
||||||
|
Constant |
t- value |
P value |
Constant |
t-� value |
P value |
Constant |
t-� value |
P value |
|
|
l0 |
0.1839 |
2.6050 |
0.0597 |
�
0.2984 |
�
2.766 |
�0.0505 |
�
60.2641 |
�
1.055 |
0.3509 |
|
l1 |
0.0298 |
0.1946 |
0.8552 |
−0.2699 |
−1.244 |
0.2815 |
−80.6609 |
−1.065 |
0.3469 |
|
l2 |
0.0186 |
0.2389 |
0.8229 |
�
0.12792 |
�1.224 |
�0.2881 |
�
27.1154 |
�
1.080 |
�0.3410 |
Table 10. Consolidated Results for
Different Study Periods by Using 10 Securities
|
Coefficient |
Sub Period 6 (2006-2008) |
Sub Period 7(2007-2009) |
||||
|
Constant |
t-� value |
P value |
Constant |
t-� value |
P value |
|
|
l0 |
� 0.2037 |
�2.393 |
0.0750 |
�0.0647 |
� 0.7213 |
0.5106 |
|
l1 |
−0.4595
|
������������ −2.485 |
0.0678 |
−0.0185
|
−0.0924 |
0.9308 |
|
l2 |
� 0.2826 |
���� 2.975** |
�0.0410 |
�0.0529 |
� 0.5030 |
0.6414 |
***
Significant at 99 %level,������� **�� Significant at 95% level
6.3 CAPM Frame Work in Indian Capital Market
(Portfolios with Five Securities)
In this section an attempt is made
to test the empirical validity of the CAPM by using portfolios having five
securities. The theory says that through
diversification one can strategically reduce the risk by allocating available funds
in many securities by forming balanced portfolios. Further, this test
will also help us to compare the results with our studies with same set of data
and also to check whether number of securities in a portfolio has any influence
on measuring the efficiency and validity of CAPM.
While analyzing table 11, it is
clear that out of the14 portfolios, with the increase in beta we cannot see any
increasing trend in the average portfolio excess return; rather it comes up and
down. Results also supplement that, all portfolios including portfolio with
lowest beta earned more than the average excess market return and the risk free
return. Further the positive constants suggest that, the portfolios earned
higher returns than the CAPM has predicted. Further from the Table11, it can be
noted that the all constants�� has
positive values. Thus the result indicates that, the alpha coefficients are
significantly different from zero and hence we reject the null hypothesis.
Further all estimated betas 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�� β is a predictor of return during the
whole study period (2001-2009).
Table 11.Results
of the Whole Study Period (2001 � 2009)
|
Port folio |
Portfolio Return(rp) |
Constant |
Beta |
Standard Error |
R2 |
F value |
P� Value 99% |
|
P1 |
0.08861 |
0.06414 |
0.36583 |
0.92121 |
0.33020 |
1106.26 |
0.0000 |
|
P2 |
0.13393 |
0.09521 |
0.57899 |
1.09383 |
0.46691 |
1965.43 |
0.0000 |
|
P3 |
0.12553 |
0.07899 |
0.69593 |
1.38381 |
0.44153 |
1774.18 |
0.0000 |
|
P4 |
0.10556 |
0.05461 |
0.76191 |
1.05857 |
0.61823 |
3633.93 |
0.0000 |
|
P5 |
0.13207 |
0.07543 |
0.84704 |
1.06828 |
0.66276 |
4410.18 |
0.0000 |
|
P6 |
0.12198 |
0.06193 |
0.89781 |
1.09352 |
0.67816 |
4728.54 |
0.0000 |
|
P7 |
0.13557 |
0.07309 |
0.93429 |
1.14146 |
0.67682 |
4699.57 |
0.0000 |
|
P8 |
0.12536 |
0.05982 |
0.98011 |
1.22015 |
0.66855 |
4526.25 |
0.0000 |
|
P9 |
0.18670 |
0.11754 |
1.03411 |
1.11044 |
0.73053 |
6083.59 |
0.0000 |
|
P10 |
0.21272 |
0.14094 |
1.07345 |
1.30458 |
0.67912 |
4749.29 |
0.0000 |
|
P11 |
0.18653 |
0.10890 |
1.16086 |
1.68331 |
0.59786 |
3336.14 |
0.0000 |
|
P12 |
0.13889 |
0.05912 |
1.19280 |
1.29372 |
0.72657 |
5962.97 |
0.0000 |
|
P13 |
0.18345 |
0.10019 |
1.24502 |
1.51927 |
0.67734 |
4710.72 |
0.0000 |
|
P14 |
0.18131 |
0.08756 |
1.40188 |
1.44521 |
0.74628 |
6600.44 |
0.0000 |
|
Avg
Rf |
0.01626 |
Average rm
=(Rm-Rf) |
0.06687 |
significant
at 99% level |
|||
6.4 Consolidated result for the sub periods
(Five securities)
In
the second Phase test is repeated with five securities by using same
methodology and procedure by constructing 14 portfolios for different sub
periods and results for different study periods are summarized below in Table
12 to 15.�
6.5 Through Portfolios having five securities
each.
Table 12. Consolidated Results for
Different Sub Periods by Using 5 Securities
|
Port folio |
Sub period 1 (20001-2003) |
Sub period 2 (2002-2004) |
||||||||||
|
Portfolio return |
Constant |
Beta |
R2 |
F� Value |
P value Beta |
Portfolio return |
Constant |
Beta |
F� Value |
R2 |
P value Beta |
|
|
P1 |
0.19742 |
0.18649*** |
0.224016 |
0.05953 |
47.543 |
0.0000 |
0.17171 |
0.13756*** |
0.32533 |
0.15175 |
135.43 |
0.000 |
|
P2 |
0.07307 |
0.05011*** |
0.47042 |
0.32234 |
357.22 |
0.0000 |
0.20452 |
0.15354*** |
0.48554 |
0.28184 |
297.09 |
0.000 |
|
P3 |
0.11733 |
0.09139*** |
0.53131 |
0.35932 |
421.19 |
0.0000 |
0.09170 |
�0.02911 |
0.59613 |
0.46562 |
659.59 |
0.000 |
|
P4 |
0.28033 |
0.25043*** |
0.61253 |
0.19548 |
182.48 |
0.0000 |
0.17428 |
�0.10105*** |
0.69761 |
0.52564 |
838.85 |
0.000 |
|
P5 |
0.14339 |
0.11568*** |
0.56765 |
0.67610 |
1567.61 |
0.0000 |
0.23518 |
�0.15026*** |
0.80884 |
0.54483 |
906.11 |
0.000 |
|
P6 |
0.17951 |
0.14242*** |
0.75989 |
0.43036 |
567.39 |
0.0000 |
0.30542 |
�0.21372*** |
0.87345 |
0.48309 |
707.48 |
0.000 |
|
P7 |
0.17044 |
0.13072*** |
0.81355 |
0.43529 |
578.89 |
0.0000 |
0.29151 |
�0.19444*** |
0.92460 |
0.42010 |
548.40 |
0.000 |
|
P8 |
0.19392 |
0.15224*** |
0.85385 |
0.48513 |
707.62 |
0.0000 |
0.12744 |
�0.01982 |
1.02513 |
0.54577 |
909.55 |
0.000 |
|
P9 |
0.20621 |
0.16085*** |
0.92927 |
0.49174 |
726.60 |
0.0000 |
0.21617 |
�0.10394*** |
1.06901 |
0.67917 |
1602.54 |
0.000 |
|
P10 |
0.22664 |
0.17956*** |
0.96435 |
0.45395 |
624.35 |
0.0000 |
0.25062 |
�0.13144*** |
1.13524 |
0.64087 |
1350.90 |
0.000 |
|
P11 |
0.23548 |
0.18411*** |
1.05245 |
0.44146 |
593.58 |
0.0000 |
0.29870 |
�0.17431*** |
1.18485 |
0.59285 |
1102.28 |
0.000 |
|
P12 |
0.20380 |
0.14939*** |
1.11465 |
0.54388 |
895.50 |
0.0000 |
0.24304 |
0.10877** |
1.27889 |
0.69318 |
1710.29 |
0.000 |
|
P13 |
0.20038 |
�0.13433 |
1.35309 |
0.57866 |
1031.42 |
0.0000 |
0.24396 |
�0.10043*** |
1.36722 |
0.66184 |
1481.60 |
0.000 |
|
P14 |
0.05651 |
−0.0315 |
1.80405 |
0.60889 |
1169.21 |
0.0000 |
0.29643 |
0.13401** |
1.54707 |
0.63798 |
1334.06 |
0.000 |
|
Avg Rf |
0.01681 |
Average�� rm = (Rm-Rf) |
0.04881 |
Avg Rf |
� 0.0142 |
Average rm = (Rm-Rf) |
0.10498 |
|||||
*** Significant at 99%, **
Significant at 95%� .
Table 13. Consolidated Results for Different Sub Periods by Using 5
Securities
|
Port folio |
Sub period 3 (20003-2005) |
Sub period 4 (2004-2006) |
||||||||||
|
Portfolio return |
Constant |
Beta |
R2 |
F� Value |
P value Beta |
Portfolio return |
Constant |
Beta |
F� Value |
R2 |
P value Beta |
|
|
P1 |
0.24929 |
0.20095*** |
0.34627 |
0.05431 |
43.47 |
0.0000 |
0.28197 |
���
0.23574*** |
0.44003 |
0.24059 |
238.56 |
0.0000 |
|
P2 |
0.20172 |
0.12413*** |
0.55581 |
0.33865 |
387.63 |
0.0000 |
0.10538 |
0.03384 |
0.68098 |
0.54276 |
893.85 |
0.0000 |
|
P3 |
0.20792 |
0.11751*** |
0.64766 |
0.52264 |
828.82 |
0.0000 |
0.14888 |
0.06619 |
0.78709 |
0.59590 |
1110.41 |
0.0000 |
|
P4 |
0.25831 |
0.15440*** |
0.74439 |
0.45755 |
638.53 |
0.0000 |
0.11308 |
0.02567 |
0.83205 |
0.68855 |
1664.72 |
0.0000 |
|
P5 |
0.23397 |
0.12034*** |
0.81396 |
0.57012 |
1003.95 |
0.0000 |
0.17716 |
��
0.08494** |
0.87792 |
0.65463 |
1427.33 |
0.0000 |
|
P6 |
0.15640 |
0.03245 |
0.88791 |
0.60786 |
1173.46 |
0.0000 |
0.18503 |
��
0.08919** |
0.91237 |
0.67145 |
1538.93 |
0.0000 |
|
P7 |
0.18686 |
0.05801 |
0.92303 |
0.61339 |
1201.05 |
0.0000 |
0.20167 |
���� 0.10168*** |
0.95182 |
0.63368 |
1302.60 |
0.0000 |
|
P8 |
0.30750 |
0.17265*** |
0.96590 |
0.54568 |
909.245 |
0.0000 |
0.13786 |
�0.03367 |
0.99184 |
0.74699 |
2223.26 |
0.0000 |
|
P9 |
0.21573 |
0.07267** |
1.02480 |
0.67206 |
1551.36 |
0.0000 |
0.12929 |
�0.01800 |
1.05944 |
0.81215 |
3255.66 |
0.0000 |
|
P10 |
0.27128 |
0.11611*** |
1.11157 |
0.70056 |
1771.07 |
0.0000 |
0.14496 |
�0.02424 |
1.14913 |
0.63506 |
1310.39 |
0.0000 |
|
P11 |
0.23793 |
0.06852* |
1.21355 |
0.72147 |
1960.87 |
0.0000 |
0.09773 |
−0.0250 |
1.16838 |
0.79510 |
2922.04 |
0.0000 |
|
P12 |
0.22874 |
0.05149 |
1.26967 |
0.60091 |
1139.83 |
0.0000 |
0.24669 |
���� 0.11720*** |
1.23260 |
0.70469 |
1796.91 |
0.0000 |
|
P13 |
0.30853 |
0.11609*** |
1.37849 |
0.64444 |
1372.07 |
0.0000 |
0.12800 |
−0.01909 |
1.40033 |
0.77133 |
2539.94 |
0.0000 |
|
P14 |
0.24079 |
0.02146*** |
1.57112 |
0.72060 |
1952.39 |
0.0000 |
0.22479 |
�0.06110 |
1.55817 |
0.76394 |
2436.99 |
0.0000 |
|
Avg Rf |
0.01366 |
Average�� rm = (Rm-Rf) |
0.13960 |
Avg Rf |
�0.01496 |
Average rm = (Rm-Rf) |
0.10505 |
|||||
*** Significant at 99%, **
Significant at 95%� * significant at 90
Table 14. Consolidated Results for
Different Sub Periods by Using 5 Securities
|
Port folio |
Sub Period 5 (2005-2007) |
Sub period 6 (2006-2008) |
||||||||||
|
Portfolio return |
Constant |
Beta |
R2 |
F� Value |
P value Beta |
Portfolio return |
Constant |
Beta |
F� Value |
R2 |
P value Beta |
|
|
P1 |
0.18841 |
0.12317*** |
0.45032 |
0.27014 |
276.86 |
0.0000 |
0.04525 |
0.04382 |
0.382707 |
0.37697�� |
449.574�� |
0.0000 |
|
P2 |
0.05039 |
−0.0449 |
0.65794 |
0.45728 |
630.24 |
0.0000 |
0.06464 |
0.06252 |
0.568486 |
0.52345�� |
816.136 |
0.0000 |
|
P3 |
0.09877 |
−0.0093 |
0.74606 |
0.55341 |
926.918 |
0.0000 |
-0.00058 |
−0.0030 |
0.674543 |
0.62702� |
1249.06 |
0.0000 |
|
P4 |
0.16718 |
0.05084 |
0.80304 |
0.61659 |
1202.75 |
0.0000 |
0.01988 |
0.01709 |
0.749013 |
0.68243� |
1596.64 |
0.0000 |
|
P5 |
0.27100 |
���
0.14695*** |
0.85632 |
0.63024 |
1274.93 |
0.0000 |
-0.0127 |
−0.0158 |
0.841287 |
0.68243� |
1596.65� |
0.0000 |
|
P6 |
0.30328 |
���
0.17368*** |
0.89459 |
0.51774 |
803.03 |
0.0000 |
0.07296 |
0.06965* |
0.889805 |
0.72932 |
2001.94�� |
0.0000 |
|
P7 |
0.17761 |
0.04330 |
0.92708 |
0.71130 |
1842.96 |
0.0000 |
-0.05857 |
−0.0619 |
0.918755 |
0.74232�� |
2140.44 |
0.0000 |
|
P8 |
0.19412 |
0.05283 |
0.97526 |
0.68251 |
1608.00 |
0.0000 |
0.03197 |
0.02840 |
0.959227 |
0.78576�� |
2725.07� |
0.0000 |
|
P9 |
0.16470 |
0.01685 |
1.02056 |
0.85017 |
4244.59 |
0.0000 |
0.02223 |
0.01848 |
1.00811 |
0.80510� |
3069.29� |
0.0000 |
|
P10 |
0.19538 |
0.03938 |
1.07679 |
0.73240 |
2047.21 |
0.0000 |
0.09760 |
0.09358** |
1.07988 |
0.83894� |
3870.42� |
0.0000 |
|
P11 |
0.21096 |
0.04895 |
1.11830 |
0.76155 |
2389.04 |
0.0000 |
0.07970 |
0.07545* |
1.14211 |
0.80342� |
3036.71� |
0.0000 |
|
P12 |
0.22037 |
0.04218 |
1.23002 |
0.69938 |
1740.26 |
0.0000 |
0.04492 |
0.04028 |
1.24674 |
0.78747� |
2753.06� |
0.0000 |
|
P13 |
0.23825 |
0.02799 |
1.45135 |
0.69469 |
1701.98 |
0.0000 |
0.15627 |
0.15127*** |
1.34516 |
0.79343�� |
2853.99� |
0.0000 |
|
P14 |
0.32012 |
0.09764** |
1.53569 |
0.75221 |
2270.75 |
0.0000 |
0.08980 |
0.08408 |
1.53739 |
0.80657�� |
3098.32�� |
0.0000 |
|
Avg Rf |
0.01724 |
Average�� rm = (Rm-Rf) |
0.144872 |
Avg Rf |
0.01939 |
Average rm = (Rm-Rf) |
0.00372 |
|||||
***
Significant at 99%, ** Significant at 95% * significant at 90
Table 15. Table Showing Consolidated
Results for Different Sub Periods by Using 5 Securities
|
Port folio |
Sub Period 7 (2007-2009) |
|||||
|
Portfolio return |
Constant |
Beta |
R2 |
F� Value |
P value Beta |
|
|
P1 |
0.08810** |
���
0.07446** |
0.29498 |
0.30900 |
329.13 |
0.0000 |
|
P2 |
0.08176 |
0.05897 |
0.49271 |
0.49339 |
718.79 |
0.0000 |
|
P3 |
0.06897 |
0.04041 |
0.61765 |
0.54659 |
887.28 |
0.0000 |
|
P4 |
0.01236 |
−0.02181 |
0.73922 |
0.60759 |
1139.59 |
0.0000 |
|
P5 |
0.10275 |
0.06578 |
0.79951 |
0.61307 |
1168.77 |
0.0000 |
|
P6 |
0.06021 |
0.02063 |
0.85599 |
0.74569 |
2158.11 |
0.0000 |
|
P7 |
0.08465 |
0.04232 |
0.91536 |
0.70034 |
1720.14 |
0.0000 |
|
P8 |
0.07589 |
0.03148 |
0.96031 |
0.80335 |
3006.82 |
0.0000 |
|
P9 |
0.15860 |
��
0.11175** |
1.01291 |
0.78123 |
2628.33 |
0.0000 |
|
P10 |
0.07721 |
0.02722 |
1.08105 |
0.81452 |
3232.01 |
0.0000 |
|
P11 |
0.11063 |
0.05557 |
1.19049 |
0.86458 |
4698.93 |
0.0000 |
|
P12 |
0.21823 |
���� 0.15881*** |
1.28490 |
0.76514 |
2397.79 |
0.0000 |
|
P13 |
0.11196 |
��������� 0.04916 |
1.35803 |
0.85806 |
4449.48 |
0.0000 |
|
P14 |
0.13770 |
0.06381 |
1.59784 |
0.79477 |
2850.37 |
0.0000 |
|
Avg Rf |
0.01702 |
Average�� rm = (Rm-Rf) |
0.046245 |
|||
***
Significant at 99%, ** Significant at 95%�
* significant at 90
Findings
reveals that beta can explain the variation in portfolio return while using
equally weighted portfolios and it is found that in most of the cases the
return on portfolio increases with increase in beta, but we cannot see this
trend in all the portfolios as similar to the previous results
6.7 Test of Non �Linearity
The test for non-linearity shows
that in each case the beta square coefficient was insignificantly different
from zero, which tells that there exists a linear relationship between expected
return and beta. Thus the findings are according to the CAPM hypothesis. But in
most of the cases, it is found that the tests in the sub periods were also
consistent with the above hypothesis and indicate evidence in supporting the
CAPM but did not provide conclusive evidence in favor of CAPM.
Table 16. Consolidated Results for
Different Study Periods by Using 5 Securities
|
Coefficient |
Whole Period (2001-2009) |
Sub Period 1(2001-2003) |
Sub Period 2(2002-2004) |
||||||
|
Constant |
t -value |
P value |
Constant |
t- value |
P value |
Constant |
t-� value |
P value |
|
|
l0 |
�0.0823 |
�0.7274 |
0.4822 |
0.0614 |
�0.8831 |
0.3961 |
�
0.11708 |
�1.08700 |
0.3005 |
|
l1 |
�0.1659 |
�0.6458 |
0.5316 |
�0.3015 |
�2.0410 |
0.066 |
�
0.12597 |
�
0.51670 |
0.6156 |
|
l2 |
−0.0332 |
−0.2383 |
�
0.816 |
−0.1613 |
�−2.266** |
0.0446 |
−0.01167 |
−0.0906 |
0.9294 |
**
Significant at 95 %level,** Significant at 95 %level
|
Coefficient |
Sub Period 3(2003-2005) |
Sub Period 4(2004-2006) |
Sub Period 5 (2005-2007) |
||||||
|
Constant |
t- value |
P value |
Constant |
t-� value |
P value |
Constant |
t-� value |
P value |
|
|
l0 |
�0.24430 |
���� 2.8490** |
0.0158 |
�0.450307 |
������ 3.383*** |
��
0.0061 |
�0.1325 |
0 .76954 |
0.4578 |
|
l1 |
−0.06528 |
−0.3534 |
0.7305 |
−0.588368 |
−2.200 |
��� 0.0501 |
−0.0087 |
−0.0253 |
0.9803 |
|
l2 |
�0.05308 |
�
0.5643 |
0.5839 |
�0.281998 |
�
2.175 |
��� 0.0524 |
�0.0730 |
0.43605 |
0.6713 |
Table 17. Consolidated Results for
Different Study Periods by Using 5 Securities
***
Significant at 99 %level, ** Significant at 95 %level
Note: Some
of the coefficients in tables are significant at 90% level
Table 18. Consolidated Results for
Different Study Periods by Using 5 Securities
|
coefficient |
Sub
Period 6 (2006-2008) |
Sub
Period 7 (2007-2009) |
||||
|
Constant |
t-� value |
P
value |
Constant |
t-� value |
P
value |
|
|
l0 |
�0.1067 |
�1.0370 |
0.3222 |
�0.0777 |
�� 1.073 |
0.3064 |
|
l1 |
−0.2344 |
−1.0620 |
0.3110 |
−0.0457 |
−0.2867 |
0.7797 |
|
l2 |
� 0.1637 |
�1.4520 |
0.1743 |
�0.06414 |
� 0.7770 |
0.4536 |
The
test for non-linearity for the whole period shows that in each case the beta
square coefficient was significantly different from zero, which tells that
there exists a linear relationship between expected return and beta. Thus the
findings are according to the CAPM hypothesis.�
Further it is found that the tests in the sub periods were also
consistent with the above hypothesis and indicate evidence in supporting the
CAPM but did not provide conclusive evidence, or not fully in favor of the CAPM
in all the tests. This leads to the conclusion that some of the results is
inconsistent with the theory and hence against the CAPM. The test for portfolios based on percentage return with
equally weighted portfolios having 5 securities does not give conclusive
evidence in support of CAPM. In some periods, the test clearly rejects the CAPM
hypothesis and in few periods it partially supports the CAPM hypothesis.
Further in some of the sub periods the constants are insignificant and reject
the CAPM hypothesis. The study also found that, during the study period most of
the portfolios, including the portfolio with lowest beta earned more than the
average excess market return and the positive constants suggest that the
portfolios earned higher return than the CAPM has predicted. The fluctuation in
the market seems to influence the return of the portfolios. During the period
of recession, some of the portfolios found to report a negative return (during
the sub period 2006-2008)
7. Summaries and Conclusion
Investment decision is one of the
key areas in finance and the risk return relationship is one of the most
discussing facts in investment decisions.�
This study tested the empirical validity of CAPM, and non-linearity
between risk return. The result of the study is mostly in support and favor of
the CAPM and is in support Ansari (2000) who suggests that the evidence is not
sufficient to drop the use of the model. While comparing the test with ten
securities and five securities it is found that the CAPM rejected in more tests
when portfolios are formed with 10 securities and it shows almost similar
result but there is difference in rejection period. This leads to the
conclusion that portfolio combination may have importance in pricing and it
should be established with more empirical tests. In short the result reveals that
the CAPM not conclusively validated during the study period and this do not
means that the data fully reject CAPM. present study reveals that beta can
explain the variation in portfolio return while using equally weighted
portfolios and it is found that, in most of the cases the return on portfolio
increases with increase in beta, but we cannot see this trend in all the
portfolios.
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