Validity of CAPM by Using Portfolios: Evidence from Indian Capital Market

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 
 

Where: Ri t is the rate of return on asset i (or portfolio) at time t, Rf t is the risk-free rate at time t, Rm t 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. ei t is the beta of stock i, ei t 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. r pt =  p +  p r mt + e pt ---------------------- (2) Where r pt is 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.
to estimate the ex post security market line for each testing period the portfolio return are regressed against portfolio betas. The model is r p = λ 0 + λ 1  p + e p ----------------------(3) Where r p = is the average excess return of the portfolio P,  p is the beta of the portfolio P, and e p 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. r p = λ 0 + λ 1  p + λ 2   p + e p -------------------(4)

CAPM in Different Periods.
To test the validity of CAPM, the study considered whole period data that is (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(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.  Period (2001Period ( -2009

with Portfolios Having Ten Securities
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 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 R 2 value is (0.54509), which indicates less than adequate correlation with the market index. Were as in portfolio 5, R 2 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 λ 0 and λ 2 will be equal to zero and the λ 1 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. In the case of λ 1 , the t-value is (0.1159) is smaller than (2.7765), and it is not significantly different from zero. As per the CAPM, the λ 1 should be equal to the average risk premium; hence the result is inconsistent with the CAPM hypothesis. In the case of λ 2 , 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

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)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)).

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.  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

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. 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][2007][2008]

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.