Empirical Test of Capital Asset Pricing Model in Indian Financial Market
By:
Cristian Selawa
10436030
Thesis Supervisor:
Dr. K.B.T.
Thio
The capital asset pricing model (CAPM) is one of the major findings in the world of financial economics. However, the validity of CAPM has been continuously debated. The present study investigates the CAPM validity in Indian Stock market, in particular, Bombay Stock Exchange (BSE) by using 6 years data periods. The methodology introduced Black, Jansen and Scholes which is used to do the investigation. The major finding in the present study is that CAPM performances in Indian stock market shows ambiguity of the usefulness. The values of the intercept in the tests are zero in sub period 1 and sub period 3, however it is not the case in the other sub periods. The security market line and non-linearity test are performed to validate the relationship between risk and return and in most cases the results in supporting the CAPM argument. However, a conclusive conclusion cannot be drawn to explain the validity of CAPM.
1. Introduction
Indian financial market is one of the oldest financial markets in the world. Founded in 1892, the result on the activities of the stock market has been giving a significance contribution to India’s economic growth since then (King, 1993). O’neil (2008) categorizes India as one of the biggest emerging market in the world, followed by Brazil, Russia and China in the group named BRIC. Emerging market countries are high-growth developing countries, Cavusgil (1987). The economy characteristics of emerging country are different with the developed country. As stated by Quelch and Arnold (1998), emerging market countries have an absolute level of economic development compare to developed countries. Also, Miller (1998) finds that emerging market has more opportunities to do market expansion. The fact that big opportunity exists in emerging country attracts investors to do business there, in this case India. Based on its importance, it develops an interesting subject to evaluate Indian financial market as one of the main channel of investor doing business in India. The market value capitalizations of Indian financial market is over one billion dollar, make India stands on the eleventh position on the largest market capitalization country in the world with more than three thousand companies listed. National Stock Exchange of India (NSE) and Bombay Stock Exchange (BSE) are the major Indian stock markets. The trading activities from BSE and NSE cover almost seventy percent of total stock trading in India. Considering the circumstances, it is important for investors, both from demand and supply side, to agree on the price of the stocks. Therefore, pricing of stock is an important element of the trading activity and brings significant consequences to the market.
Risk-return relationship has been categorized as one of the prominent factor to evaluate stock prices. In 1964, Sharpe and Lintner built Capital Asset Pricing Model (CAPM) to accommodate the evaluation of the stock prices and to explain the risk-return relationship factor into the model. The general equation of CAPM:
m f
i f i r r r r Where: iβι : relative risk of share i M
r : expected return of the market portfolio
rf : risk-free interest rate
The main idea of CAPM is that the higher the risk associated with the stock (that is represent by βι ) has to be accompanied by the higher returns of the stock in order to compensate the
risk. Also, the separation theorem has to be highlighted in the model. It is shown in the model that the capital market contains two elements of risk, the unsystematic risk and systematic risk. CAPM argues that the unsystematic risk can be eliminated through diversification, leaving only systematic risk becomes the sole prominent factor of the determination of the expected return on stocks.
The present study aims to test the theory of CAPM in Indian financial market by trying to explain four objectives of the study listed in section 3.1. In general, the study is arranged in the following manner. The first chapter is the introduction of the present case. The second section provides the discussion of the previous findings of CAPM. The third and fourth sections provide the scope of the study and the methodology used in testing the CAPM. Finally, the fifth and the sixth sections provide the result of the test and conclusion of the study.
2. Literature Review 2.1 The Birth Of CAPM
CAPM was founded by Sharpe and Lintner in 1964, developing the modern portfolio theory that was preliminary founded by Markowitz in 1952. The modern portfolio theory suggests that there is an obvious relationship between risk and return. It is stated that risky asset has more return compare to less risky asset. In addition, Markowitz portfolio selection model provides guidance to plot the efficient frontier of risky assets and selecting an optimal set of risky assets. However, Markowitz model does not observe the relationship between risk and return for individual risky asset. Furthermore, the Markowitz model has been criticized because the model elaborates abstract economics concept, for example, utility. From the practical economics point of view, the concept of utility elaborates into the model is impossible to be done because quantifying the number of utility people expect to have and measuring the degree of risk aversion are unattainable.
The CAPM was originated by the extension of the Markowitz model to help explains the equilibrium of risk-return relationship for individual risky asset. (Lintner, 1965) CAPM was built under four strong assumptions about the market, the first one is that individual investor can invest any part of its capital in certain risk-free asset that earn interest at common positive rate. The second assumption is that investor can invest any fraction of its capital in any or all of a given finite set of risky securities. The third assumption is that the risky asset securities are traded in a single purely competitive market, no transactions costs and taxes and at given market prices. And the last assumption is that any investor may borrow funds to invest in risk assets.
The first empirical test of CAPM was conducted by Lintner (1965) and Douglas (1968). The investigation was conducted using the NYSE (New Stock Exchange) data. The result is not aligned with the theory of CAPM, in which the study finds that the intercept of the security market line is not equal to the risk-free asset, and also there is a deviation of the regression coefficient that is not equal to the average risk premium as the theory of CAPM suggests. However, the study conducted by Douglas and Lintner suffers measurement error. The error can be shown by the correlation between estimated betas and firm specific risk that are not normal (very high). In addition, the existing of the skewness of the investigated stock distribution is also contradicting the CAPM argument. Furthermore, Fama and MacBeth (1973) tested the CAPM by different methodology by applying the combination of time series and cross sectional regression into the framework to inspect the risk premium value in the second-stage regression. By making twenty portfolio consisted of high to low beta stocks, the cross sectional regression are used to find the coefficient of the beta. The results obtained from the study was that the beta was not statistically significant different from zero. Also, the value of the beta remained insignificant for the following sample period and the intercept of the SML was greater than the risk free rate. However, as opposed to lintner, the study conducted by Fama and MacBeth concluded that stocks yields were not disturbed by the residual risk. The CAPM empirical test analysis has also been done in Japan Stock market. By using the same method applied by Black, Scholes and Jansen (1972) but without forming the portfolio stages, and using the data of monthly changing price of stock from period 1956 to 1976, Maru and Yonezawa (1984) found that CAPM is valid, by looking at market risk and firm-specific risk that can explain the yields of Japanese stock. In addition, Gunnlaugsson (2007) did the study of CAPM validity in Icelandic stock market. He took the sample data of monthly price change of 100 stocks from January 1999 to May 2004 and implemented the methodology introduced by Black (1927). The result indicated that the CAPM is valid that can be represent by the beta coefficient that explain the average stock yields. Also, the evidence that strong correlation between beta and stock returns exists in this particular study. In addition, it is stated that the unsystematic risk is statistically insignificant having the correlation with the securities returns, as CAPM predicted. Fama and French (1992) come with strong argument stated that CAPM is miss-specified. They argue that beta does not replicate the cross-section of the expected yield, however, through elaboration between the size and book-to-market variable can help to explain the variations of the securities average returns. They introduce multi-index model as the replacement of CAPM. Later, Sharpe respond to the critics that the multi-index model introduced by Fama and French (1992) does not exclude beta in the model, however, the multi-index model is the expansion of the CAPM by having size factors variables into the framework. Sharpe stressed that the idea of market portfolio’s returns has no correlation with stock’s returns is inaccurate and fallacious.
2.3 Empirical Test Of CAPM In Developing and Emerging Countries
CAPM validity has also been studied in the developing and emerging countries. Findings from Brooks (2010) in empirical test of CAPM in Pakistan financial market using period sample period from 1992 to April 2006 confirms the risk return relationship is non-linear. It is contradicting from the theory of CAPM that states risk return relationship is
linear. In other words, CAPM does not hold in Pakistan financial market. Moreover, Brooks stated that the performance of the stock market backed by a high level of liquidity was outstanding. Aljinović and Džaja (2013) investigate the Capital Asset Pricing Model (CAPM) on the Central and South-East European emerging countries financial market by using monthly stock returns for nine countries for the period of January 2006 to December 2010. The result of the investigation is that CAPM does not hold on the Central and South-East European emerging countries financial market. It is supported by the fact that the higher beta is not associated with higher yield. Also, the efficient market frontier performs for each country shows that the stock market indices do not replicate the efficient frontier. The results shows that the CAPM is not adequate for assessing the capital assets on observed Central and Southeastern European emerging markets. To test the validity of beta as a measure of risk using regression analysis, it was found that higher yields do not mean a higher beta, so it is not a valid measurement of risk. The last test is conducted using the Markowitz portfolio theory to construct the efficient frontier, and the result suggests that the stock market indices are not located in the determined efficient frontier and cannot be categorized as efficient portfolio, so CAPM does not hold. In contrary, Johnson and Soenn (1996) found that in Jakarta Stock Exchange (JSX) CAPM hold. They stated that high volatility of the stock market is accompanied by high return. Also, the stock market indices are located in the efficient market frontier, as CAPM suggests.
2.4 Empirical test of CAPM in Indian Stock Market
Srinivasan (1988) finds that CAPM relationship is valid but a much larger sample is warranted to draw inferences. This study covers a time period of 1982-1985. Yalwar (1988) covers period of 1963-1982, consisting of 1922 common stocks. He finds that CAPM is a good descriptor of security return. Yalwar's study is based on rhe individual security return and not on portfolio return. Varma (1988) also finds results supportive of CAPM. Yalwar (1988) conducts an empirical test of CAPM in Indian stock Marekt by using 1992 common stock, covering period from 1963 to 1982. His study concludes that CAPM is a good indicator of security return. His argument also supported by Varma (1998) who conducted the test in the same year.
Amanullah and Kamaiah (1998) find that CAPM is not the only factor of investor’s investment decision. They argue that the investment decision making of investors are significantly influenced by price per earning’s ratio, Earning per shares, dividend and bonus. Lakshmi and Pradhan (2010) attempt to test the validity of CAPM by using the method introduced by Fama and MacBeth (1973) with a modification in the regression test. They allow the first and second moments of the security yields to fluctuate between time periods and test three variants of conditional CAPM to seize the ‘size effect’. They also use Hansen’s Generalized Method of Moments to allow the robust estimation of the parameters. The result is that the small security beta portfolio has different behavior towards the larger beta portfolio that can be seen by betas and prices of covariance risk. They found that larger stock beta is statistically significant, in contrast, smaller stock beta is insignificant. Basu and Chawla (2010) attempted the validity test of CAPM in Indian stock market by using 50 stocks consisting data between period 1th January 2003 to 1st February 2008 and categorized the
stock into 10 portfolios. Their study concludes that CAPM does not hold by three reasons. First, the intercept term is not significantly larger than zero. In addition, there is a negative relationship of beta toward excess yields that shows the capital market is not efficient. Furthermore, the regressions have an insufficient explanatory power. To sum up, the previous findings of the empirical results on CAPM validity lead to mixed conclusion. It is stated that to increase the explanatory power of the model, additional variables are needed, for example, size factor. On the other hand, the previous findings also stated that the standard form of CAPM is able explain the cross-sectional variation in security returns. The present case is circumscribed to investigate the standard form of CAPM in Indian financial market. 3. Scope of the Study
The present study is coordinated to investigate the validity of Capital Asset Pricing Model (CAPM) in Indian financial market. The investigation uses monthly data of 72 companies that are listed in the S&P BSE 100 stock index. S&P BSE 100 market index is used as the market proxy of the investigation. The investigation covers six years monthly data, from 1st January 2008 until 31st December 2013. Black et all (1972) suggests that the
monthly price are better in order to decrease the noise of the model. However, Brown and Warner (1985) have different perspective on the utilization of the data. They argue that the daily prices are better for autocorrelation in event methodology. To be consistent with the methodology introduced by Black (1972), the monthly price data is used in the examination of the model. The risk free rate is available from Reserve Bank of India (RBI) and accessible to public. The 3-months bill rate is selected as the risk free asset values since it has a better reflection on the short-term dynamics in the financial market.
3.1. Objectives of the study
The main objective of the study is to apply the methodology introduced by Black et al (1972) to test the validity of CAPM in Indian stock market. The present study aims to describe four main objectives, which are:
To test the CAPM validity in Indian financial market by applying the methodology introduced by Black et al (1972), using the latest available data. In other words, updating the previous study with the current time and data framework.
To check empirically the relationship between risk and rate of return in Indian financial market.
To investigate the relation between the stock and market return. To analyze the linearity of expected return towards systematic risk. 3.2 Source and period of data
The present case is realized by utilizing data from Bombay Stock Exchange (BSE). The study uses monthly adjusting close price of 72 stock companies from the S&P BSE100 index listed from the period of 1st January 2008 – 31st December 2013. For the market proxy,
the monthly closing values of the S&P BSE 100 are used. For the risk free rate values, the study utilizes the interest rate on 91-days treasury bills of Indian government. All the
historical prices of stocks data of the historical prices are obtained by the Bombay Stock Exchange (BSE) website and the risk free assets historical prices are obtained from the Reserve Bank of India.
4. Methodology
To test CAPM, we take data from India stock market, 6-years period data are selected in order to consistent with methods introduced by Black et. al (1972) and Fema-MacBeth (1973). Also, according to black et al., using the monthly price fluctuations is preferred compare to daily price changing of the stocks market.
First step, to get the monthly returns of each stock price is needed. By performing calculation of the monthly returns of each individual stock price using formula below:
Rt =( Pt – Pt-1 ) / Pt-1 ,
Where Rt = returns at time t, Pt = Stock price at time t, Pt-1 = Stock price at time t-1
Next step, by using the time series analysis, we run the regression on excess return of the individual stock respective to excess market return. The entire period which to be investigated are between January, 1st 2008- December, 31st 2013. Also, consistent to the
method introduced by Black (1972), the sub period test is needed. Therefore, there are there sub-periods to be investigated:
January, 1st 2008- December, 31st2010
January, 1st 2009-December, 31st 2011
January, 1st 2010-December, 31st 2012
These three sub periods represent the beta estimation period. In general, the estimation of the betas is conducted by using the following time series regression formula (It is applied to the whole period beta estimation and also to all sub-periods beta estimation):
Rit – Rft = ai + βi(Rmt – Rft) + eit
Where: Rit = rate of return on stock i, Rft = risk free rate at time t, βi = estimate of beta for
stock i, Rmt = rate of return on the market index at time t ,eit = error
Rewriting the formula, it equivalent to:
rit = ai +(βi x rmt )+eit
Where, rit = Rit – Rft = excess return of stock i, rmt = Rmt – Rft = average risk premium, ai = the
intercept, eit = error
The purpose on this first regression is to get the beta of each stock. Beta represents the correlation between the individual stock and the market proxy, S&P BSE 100. The higher the beta, the more sensitive is the stock to the movement of the market proxy.
Furthermore, the equally weighted average portfolios are constructed based on high-low values of beta in order to improve the quality of beta on each portfolio. Moreover, after betas of each stock on each period are obtained, the sequence step is to form the portfolio based on the values of betas. The stocks with high value of beta are grouped within the high value beta, also stock with the lower value beta are grouped with lower value beta. From 72 companies stocks, we obtained 10 portfolios, with each portfolio consists 7 to 8 stocks with identical beta. The second regression we run is crossed-sectional regression. The purpose of this regression analysis is to determine the high and low portfolio betas. Following Fama, crossed-sectional regression is performed in order to get the values of the portfolios beta. The formula as follows:
rpt = ap + (βp.rmt)+ ept
Where, rp = average excess portfolio return, βp = portfolio beta, t=at time t
The value of ap is the difference between the expected return suggested by CAPM and the estimated expected return by time series regression analysis. If CAPM is valid, there must be no difference between the prediction of CAPM and the estimation of the expected return by time series analysis, therefore the value of ap must be statistically indifference from zero.
The next regression is to test the third category, whether there exists linearity between the stock beta and the expected return. In order to perform the test, the construction of the ex-post Security Market Line (SML) is needed. The SML can be constructed by conducting regression of the portfolio returns respective to portfolio betas.
rp = γ0 + γ1βp+ ep
Where: rp = average excess portfolio return, βp = estimate of beta portfolio p, γ0 = risk free
rate, γ1 = market price of risk and, ep = error.
If CAPM is valid, the values of γ0 must be equal to the risk free rate and market price of risk
must be equivalent to the average risk premium.
Test for the non-linearity is also important to be conducted between each of portfolio to justify there is none of linearity effect plays into the picture, simply by squaring the betas:
rp= γ0 + γ1βp+ γ2β2p
If CAPM is valid, the value of γ2 must be statistically equal to zero and γ0 must be equal
average risk free rate. The value of γ1 must be statistically not equal to zero.
The last test is to determine whether the expected excess returns are constructed from the systematic risk alone. Because CAPM argues that investors are requiring risk premium only on systematic risk, the firm specific risk can be eliminated through portfolio diversification. To test the expected return solely determined by the market risk, we run the regression based on following equation:
Where all the variables mentioned are the same with the previous equation, and σ²(ep) is the
residual of variance of the portfolio return. If CAPM is valid, the value of γ0, γ2 and γ3 must
be equal to zero. 5. Results
5.1 Sub Period 1 (2008-2010)
The first sub period analysis conducted by using the data of 72 companies traded in the S&P BSE 100. The length of the period is 3 years (1st January 2008 - 31st December
2010). Note that the opening price of the S&P BSE 100 in 1st January 2008 was 11,006.64
and the adjusted close price in 31st December 2010 was 10,675.02, the market value of the
market proxy is decreasing over 3 years. The market proxy loss during this sub period was (331.62) or 3.10 %.
5.1.1 Testing CAPM through Portfolios
The regression function stated in the previous section is run to determine of the beta of each stock. Afterwards, based on the beta of each stock, the portfolios consist 7-8 stock are formed. Portfolio 1 contains the highest beta stocks and portfolio 10 contains the lowest beta stocks. It is obvious in the table below, from the overall performance of the portfolios, portfolio 1 - portfolio 4 suffer higher lost compare to the other portfolios. It is consistent to what CAPM suggests, since the value of the market proxy is decreasing, the higher positive beta portfolios that provide more sensitivity to the market proxy movement are also moving in the same direction. However, portfolio 1 is violated the CAPM since the loss in portfolio 1 less than the loss in portfolio 2, 3, and 4 which inconsistent with what CAPM suggests. The beta of each portfolio is consistent with CAPM. The value of the p-value are statistically non-zero. The exception comes from the last portfolio, portfolio 10, which the p-value is larger than 0.05 (the value of maximum error tolerance). The value of R2 represents the variation of
the dependent variable explained by the explanatory variable. The R2 valueson portfolio 1 –
portfolio 9 is higher than 65 percent that means the variation of the portfolio returns can be explained from the relationship with the market index. Furthermore, the constant values of all portfolios are statistically indifference with zero, consistent with CAPM suggestion. From this result, we can conclude that the portfolio betas are useful for analyzing the relationship between risk and return in sub period 1.
Table 5.1 Sub Period 1 Portfoli osXPort folio Portfoli o Return constan
t (ap) β Std error R2 F-value P-value of β σ²(ep) P1 -0.028 -0.015 1.72 8 0.1684 0.913 105.26 0 0.011377 P2 -0.036 4E-04 1.16 8 0.079 0.96 5 277.58 0 0.00250 1 P3 -0.037 4E-04 1.16 0.164 0.83 50.71 0 0.01079
8 1 5 7 P4 -0.032 -0.005 0.99 4 0.174 0.76 6 32.67 0 0.01214 2 P5 -0.023 0.002 0.88 3 0.097 6 0.89 1 81.95 0 0.00382 2 P6 -0.015 0.01 0.91 6 0.135 3 0.82 1 45.86 0 0.00733 9 P7 -0.02 0.003 0.81 8 0.174 9 0.68 7 21.9 0 0.01226 9 P8 -0.009 0.011 0.72 7 0.1017 0.837 51.15 0 0.004148 P9 -0.023 -0.003 0.70 4 0.1607 0.658 19.21 0 0.010356 P10 -0.003 0.001 0.16 7 0.157 2 0.10 1 1.12 0.315 0.00991 8 X
5.1.2 Estimation of Security Market Line (Sub Period 1)
Table 5.2 summarizes the construction of security market line results. It is shown that the p-value of the γ1 coefficient is less than 0.05 (significant level use in the present study).
The average risk premium between period 2008-2010 is -0.00102 or -0.102%. by using t-test, we test the value of γ1 to have value equal to the average risk premium in the null hypothesis.
The result of the test is -3.16, which larger than the critical value -1.96, therefore the null hypothesis is fail to accept. The value of γ1 is not equal to the average risk premium,
inconsistent with CAPM suggests. The value of γ0 is not significantly different from zero, as
it can be seen from the p-value. It is consistent according to CAPM that the value of γ0 has to
be equal to zero. Tabl e 5.2 Tabl e Sub Perio d 1 Secu rity Mar ket Line (SM L)X Coefficien t Std error p-value γ1 -0.0202 0.00671 0.017 γ0 -0.00384 0.00672 0.584
5.1.3. Linearity test for Sub Period 1 (2008-2010)
Table 5.3 represents the result of the non-linearity test for the sub period 1. It is shown that the value of the intercept γ0 is statistically not larger than zero since the p-value of γ0 is
larger than 0.05. The result in γ0 is consistent with CAPM. In addition, the value of γ1 is
statistically different from zero, showing that there is exist a linear relation between the beta and portfolio return. The value of γ2 is statistically not larger than zero since the p-value of
the coefficient is larger than 0.05, this result consistent with CAPM. Thus, we can conclude that linearity of betas and portfolio returns exists in sub period 1.
Table 5.3 Sub period 1 test for linearit y X Coefficien t Std. error P-value γ1 -0.05003 0.020246 0.043 γ2 0.015613 0.010092 0.166 γ0 0.008135 0.009921 0.439 5.2. Sub Period 2 (2009-2011)
The second sub period analysis conducted by using the data of 72 companies traded in the S&P BSE 100. The length of the period is 3 years (1st January 2009- 31st December
2011). Note that the opening price of the S&P BSE 100 in 1st January 2009 was 4,790.32 and
the adjusted close price in 31st December 2011 was 7,927.94, the market value of the market
proxy has been significantly fluctuating over three years. The market proxy gain during this sub period was (3,137.62) or 65.49%.
5.2.1. Testing CAPM through portfolios
Between the time-length in sub period 2, the market index return has been experiencing a dramatic change. Over three years, the market index has gained 65.49%. CAPM predicts that the higher beta results in higher returns, however, This is not the case in sub period 2. As Portfolio 1 is constructed using the higher beta stocks during period 2009-2011 compare to the stocks composition in portfolio 2 that has lower beta stock within the same period. However, as we can see in table 5.4, beta of the portfolio 1 is lower than portfolio 2’s beta. In addition, portfolio 1 that has a lower beta compare to portfolio 2 earns more return compare to portfolio 2 that contradicts CAPM. The R2 of all portfolios in sub
lowest R2 is in portfolio 8 by 0.011. The low value of R2 represents that the explanatory
variable, the excess market return cannot explain the variation of the portfolio returns. Again, this result contradicts CAPM. Furthermore, the p-value of betas in all portfolios are insignificant different from zero. From this result, we can conclude that the portfolio betas are not useful for analyzing the relationship between risk and return in sub period 2 and CAPM does not hold.
Table 5.4 Sub Period 2 Portfolio sXPortfo lio Portfolio Return Constant β Std error R2 F-value P-value of β σ²(ep) P1 0.04518 0.05044 0.2786 0.36364 0.055 0.59 0.461 0.2330218 P2 0.04120 0.04733 0.3246 0.28475 0.115 1.3 0.281 0.1428891 P3 0.03272 0.03671 0.2116 0.384 0.076 0.83 0.384 0.0953140 P4 0.02204 0.02584 0.2010 0.21934 0.077 0.84 0.381 0.0847848 P5 0.02775 0.03773 0.2625 0.12922 0.292 4.13 0.07 0.0294267 P6 0.02175 0.02411 0.1248 0.17573 0.048 0.5 0.494 0.0544205 P7 0.03421 0.03425 0.0021 0.14909 0.190 0.12 0.923 0.0391717 P8 0.02128 0.02153 0.0133 0.10953 0.011 0.09 0.905 0.0211416 P9 0.04300 0.04160 -0.0742 0.03313 0.334 5.02 0.049 0.0019349 P10 0.01222 0.00996 -0.1197 0.05797 0.298 4.26 0.066 0.0059234
5.2.2. Estimation of Security market line (Sub Period 2) Table 5.5 Sub period 2 SMLX Coefficien t p-value Std. error γ1 0.030583 0.203 0.02208 γ0 0.026894 0 0.004263
Table 5.5 describes the results of the security market line test in sub period 2. CAPM states that the value of the γ1 must be equal to the average risk premium and the value of γ0
must be equal to 0. From the table above, it is shown that the p-value of γ1 is larger than 0.05,
means that the value of γ1 is not statistically different from zero. T-test also conducted to test
whether the value of γ1 is equal to the average market premium. The average market premium
during period 2009-2011 is 0.01026. By setting the null hypothesis that is the value of γ1 is
equal to the value of average risk premium, the t-test result is 4.767. The maximum tolerance level of error is 5%, so the critical value is 1.96. The t-test is larger than the critical value, so we fail to reject alternative hypothesis that is the value of γ1 is not equal to the average risk
premium. In addition the value of γ0 is statically different from zero that contradicts CAPM.
Therefore, CAPM does not hold in sub period 2. 5.2.3. Linearity test for sub period 2
Table 5.6 Sub period 2 test for linearit y X Coefficien t P-value Std. error γ1 0.000407 0.993 0.048006 γ2 0.147039 0.498 0.205884 γ0 0.025109 0.002 0.005061
Table 5.6 represents the result of the non-linearity test for the sub period 2. It is shown that the value of the intercept γ0 is statistically larger than zero since the p-value of γ0 is
smaller than 0.05. The result in γ0 is inconsistent with CAPM. In addition, the value of γ1 is
not statistically different from zero, showing that the linearity between the beta and portfolio return does not exist. The value of γ2 is statistically larger than zero since the p-value of the
coefficient is smaller than 0.05, this result is also inconsistent with CAPM. Thus, we can conclude that linearity of betas and portfolio returns do not exist in sub period 1 and CAPM does not hold.
5.3. Sub Period 3 (2010-2012)
The third sub period analysis conducted by using data of 72 companies traded in the S&P BSE 100. The length of the period is 3 years (1st January 2010- 31st December 2012).
Note that the opening price of the S&P BSE 100 in 1st January 2010 was 8,707.82 and the
adjusted close price in 31st December 2012 was 5,908.97, the market value of the market
index has been significantly fluctuating over three years. The market proxy loses during sub period 3 was 2,798.85 or 32.14%.X
5.3.1. Testing CAPM through portfolios
Table 5.7 Sub period 3 portfolio sXPortfo lio Portfolio Return Constant β Std error R2 F-value P-value of β σ²(ep) P1 -0.0134 -0.0150 2.05871 0.43183 0.694 22.73 0.001 0.040698 P2 -0.0082 -0.0096 1.80824 0.33342 0.746 29.41 0 0.024262
P3 -0.0127 -0.0142 1.84080 0.26523 0.828 48.17 0 0.0153542 P4 0.01675 0.01587 1.11394 0.16215 0.825 47.19 0 0.0057384 P5 0.06250 0.05923 4.12149 1.27402 0.511 10.47 0.009 0.3542486 P6 0.01154 0.01119 0.46434 0.1638 0.445 8.03 0.018 0.0058598 P7 0.00732 0.00649 1.04474 0.18759 0.756 31.01 0 0.0076809 P8 0.00225 0.00129 1.21398 0.26460 0.677 21.05 0.001 0.0152808 P9 0.00222 0.00155 0.84028 0.20462 0.627 16.86 0.002 0.0091386 P10 0.01311 0.01260 0.63897 0.26012 0.376 6.03 0.034 0.0147681 During sub period 3, the movement of the market index has been less volatile compare to sub period 2. The market value of market index between sub period 3 has been decreasing by 32.14% in total. Portfolio 1 is constructed with the 7 highest beta stocks and the last portfolio is constructed by the 7 lowest beta securities. Overall, the p-value of beta is less than 0.05 means that the betas values of all portfolios are different from zero. It means that the portfolio betas are useful for analyzing the relationship between risk and return in the third sub period analysis. The values of R2 are, in average, above 0.5, means that the
independent variable, in this case excess market returns, can explain the variation of the portfolio returns. Portfolio 4 has the highest beta although the portfolio is constructed with the fourth highest beta indices stock. However, when market index in overall experience loses, the highest beta portfolio has a positive return, inconsistent with what CAPM predicts. The values of R2 are overall higher than 0.5 in average, it indicates that the excess market
return variable can explain the variation of the portfolios return well. CAPM cannot be fully rejected. 5.3.2 Sub period 3 SML Table 5.8 sub period 3 SML X Coefficien t Std. deviation P value γ1 0.0112203 0.0061374 0.105 γ0 -0.008860 0.0111525 0.45
Table 5.8 provides the result of the security market line using the data from sub period 3. The value of the γ1 is insignificantly different from zero since the p-value is larger than
0.05. In addition, the value of γ0 is also statistically indifferent from zero. CAPM states that
the value of γ1 has to be equal to the average market risk premium. The average market risk
premium during sub period 3 is -0.00791 or -0.791 %. T-test is conducted to evaluate whether the value of γ1 is equal to the average market risk premium. The result of the t-test is 3.11 that
is larger than the critical value, 1.96. Based on the t-test, with 95 % confidence level the test reject the null hypothesis, so that the value of the average market premium is not equal to the value of γ1 statistically. To conclude, findings from the SML test is not consistent with
5.3.3. Sub period 3 test for linearity
CAPM predicts that the value of λ0 and λ2 will be equal to zero and the value of λ1
must be equal to the average risk premium. Table below provides the estimated values of the linearity test using the third sub period data.
Table 5.9 Sub period 3 test for linearit y X Coefficien t Std Deviation p value γ1 -0.050622 0.0103382 0.002 γ2 0.0135108 0.002187 0 γ0 0.0401924 0.0092236 0.003
From the table above, conclusion can be drawn to determine the CAPM validity. According to CAPM, the value of λ0 will be equal to zero. However, the result shows that the value of λ0
statistically non-zero since the p-value of λ0 is smaller than 0.05. In addition CAPM predicts
that the value of γ2 will be equal to zero. However, this is not the case, the value of γ1 is
statistically higher than zero. The reasoning applies in γ2 also applies in γ1, the p-value of γ2 is
greater than 0.05. Also, CAPM predicts that the value of γ1 will be statistically larger than
zero, which is the case in this period. To conclude, CAPM cannot be clearly rejected based on the observation in the linearity test during the third sub period.
5.4 All Periods (2008-2012)
The entire period analysis conducted by using data of 72 companies traded in the S&P BSE 100. The length of the period is five years (1st January 2008- 31st December 2012). Note that the opening price of the S&P BSE 100 in 1st January 2008 was 11,006.64 and the
adjusted close price in 31st December 2012 was 5,908.97, the market value of the market
index has been significantly fluctuating over five years. The market index loses during sub period 3 is 5,097.67 or 46.3%.
5.4.1. Testing CAPM through portfolios Table 5.10 Entire periods portfolios XPortfolio Portfolio return β P-value β F value R2 σ²(ep) P1 0.017627462 1.414341 0 48.43 0.4124 1.802058 P2 -0.00016767 1.063714 0 81.4 0.5412 0.606454 P3 0.009145045 0.976721 0 83.98 0.549 0.603216 P4 0.005022111 0.821701 0 62.99 0.4772 0.467692 P5 0.005965699 0.720324 0 74.04 0.5176 0.305737 P6 0.012872982 0.608048 0 61.34 0.4706 0.262984
P7 0.015523927 0.516359 0 69.53 0.5019 0.167309
P8 0.006641059 0.395582 0 34.97 0.3364 0.195214
P9 0.009797787 0.321583 0 19.92 0.224 0.226543
P10 0.019623647 0.042103 0.635 0.23 0.0033 0.34046
The movement of the market index has been dramatically fluctuating and result in significant loses in the end of 2012. However, the expected return for the high portfolio beta still positive. CAPM predicts that the value of beta will be significantly different from zero. Also, CAPM states that the higher the beta of the portfolio requires more returns. The beta values of the portfolios are all statistically different from zero, consistent with what CAPM predicts. However, the portfolio 10, which contains the lowest beta stocks, requires more return than portfolio 1, which contains the highest beta stocks, this is inconsistent with CAPM. In addition, the values of R2 are, in average, above 0.5, means that the independent
variable, in this case excess market returns, can explain the variation of the portfolio returns. But this is not the case for portfolio 10, which has R2 value only 0.003 and also the beta is
insignificant. CAPM cannot be fully accepted in the entire period case since some important elements of CAPM are violated.
5.4.2. Entire Periods SML Table 5.11 Entire periods SML X Coefficien t Std. Error P-value γ1 -0.00392 0.005292 0.48 γ0 0.012903 0.004159 0.015
Table 5.11 provides the results of the security market line test conducted using the entire period data (2008-2012). CAPM states that the value of γ1 must be equal to the average
risk premium and the value of γ0 must be equal to zero. From the table above, it is shown that
the p-value of γ1 is larger than 0.05, means that the value of γ1 is not statistically different
from zero. T-test also conducted to test whether the value of γ1 is equal to the average market
premium. The average market premium during period 2008-2012 is -0.00824 or -0.824%. By setting the null hypothesis to the value of γ1 equals to the value of average risk premium, the
t-test result is 0.81. The maximum tolerance level of error is 5%, so the critical value is 1.96. The t-test is smaller than the critical value, so we fail to reject null hypothesis that is the value of γ1 is equal to the average risk premium. On the other hand, the value of γ0 is statically
different from zero that contradicts CAPM. Therefore, CAPM cannot be also fully accepted or rejected here.
5.4.3. Entire period test for linearity Table
Entire period test for linearit yX γ1 -0.03647 0.014328 0.038 γ2 0.022376 0.009416 0.049 γ0 0.021473 0.004894 0.003
Table 5.12 represents the result of the non-linearity test for the entire period. Based on CAPM, the estimated value of γ0 and γ2 are statistically equal to zero and the estimated value
of γ1 is statistically not equal to zero. In table 5.12, It is shown that the value of the intercept
γ0 is statistically larger than zero since the p-value of γ0 is smaller than 0.05. The result in γ0 is
inconsistent with CAPM. In addition, the value of γ1 is statistically different from zero,
showing that the linearity between the beta and portfolio return exists. The value of γ2 is
statistically different from zero since the p-value of the coefficient is smaller than 0.05, this result is inconsistent with CAPM. Thus, CAPM cannot be rejected fully because even though the values γ0 and γ2 not zero, the value of γ1 is larger than zero, which consistent with CAPM.
5.4 Test of Non-systematic risk for all sub periods and total periods.
The last test is conducted to test whether the non-systematic risk plays role in the construction of expected excess returns of the portfolios. As CAPM suggests, the expected excess return of the portfolios solely determined by the systematic risk. The idea is that firm-specific risk can be eliminated by portfolio diversification so there will be linear relation between the expected excess returns of the portfolios and the excess market returns. The value of γ̂0 represents the firm specific risk, which according to CAPM must be equal to zero.
The value γ̂1 represents the correlation between expected excess return of the portfolios and
market excess returns, which according to CAPM must be not equal to zero and equal to the average risk premium. The values of γ̂2 and γ̂3 represent the linearity and the firm specific risk
of portfolios that according to CAPM must be equal to zero. 5.13 Non-systemat ic risk tests result tableXV ariable Time Period
Total Period Sub-periods
1 2 3 γ̂0 0.023042 0.012857 0.023826 0.014970 s(γ̂0) 0.094196 0.013363 0.005462 0.019348 γ̂1 -0.01822 -0.05333 -0.01195 -0.00736 s(γ̂1) 0.165463 0.022089 0.05188 0.031269 γ̂2 0.007329 0.017467 0.104917 -0.00684 s(γ̂2) 0.076202 0.011114 0.218658 0.014144
γ̂3 0.065744 -0.41632 0.061676 0.545417 s(γ̂3) 0.083654 0.735421 0.079042 0.375121 γ1 = R̅m -0.00824 -0.02767 -0.0189 0.000795 t(γ̂0) 0.244616 0.96 4.36 0.77 t(γ̂1 - γ1) -0.06 -1.16 0.133 -0.26 t(γ̂2) 0.096183 1.57 0.48 -0.48 t(γ̂3) 0.785902 -0.57 0.78 1.45
5.4.1. Non-systematic risk test in sub period 1
To begin with, we look at the t-test values on variable γ̂0, γ̂1, γ̂2, γ̂3 .The t-test values on
variable γ̂0 is 0.96 which is smaller than the critical values (-1.96 and 1.96), so we fail to
reject null hypothesis, meaning that the values of γ0 is equal to zero. In addition, with 95
percent of confidence level, we can conclude that the value of γ̂1 is equal to γ1, which is
consistent with CAPM. The value of the t-test on variable γ̂3 is -0.57, that is smaller than the
critical values used in the test. Based on the t-test conducted in the variable γ̂3, there is not
enough evidence to conclude that the value of γ̂3 is significantly different from zero. To
conclude, in sub period 3, CAPM holds.
5.4.2. Non-systematic risk test in sub period 2
The same procedure on analyzing the data of sub period 1 applies to this period. The values of γ̂0 is larger than zero, this is not consistent with CAPM. The value of γ̂1 is equal to
the values of average risk premium, consistent with CAPM prediction. The value on γ̂2 is
equal to zero, consistent with CAPM. Furthermore, the last variable, γ̂3, that represents the
non-systematic risk is equal to zero, means that there is non-systematic risk come into the picture of the expected return construction. Although variables γ̂1, γ̂2, and γ̂3 meet CAPM
requirements, variable γ̂0 is not. Therefore, we cannot fully accept CAPM in second sub
period.
5.4.3. Non-systematic risk test in sub period 3
At table 5.13, it is clear that at sub period 3, the t-test value on variable γ̂0 is0.77,
which is smaller than the critical values so the values of γ̂0 is not statistically different from
zero. The value of γ̂2 and γ̂3 are respectively having test values -0.48 and 1.45. Both of the
t-test values are smaller than the critical values, means that both of them are not significantly different from zero, which consistent with CAPM. Furthermore, the value of γ̂1 is statistically
equal to the γ1, as what CAPM suggests. Based on the test, CAPM is valid by using data from
the third sub period.
5.4.4. Non-systematic risk test in entire period
The non-systematic risk test is also conducted using the entire period data. The t-test values of γ̂0 and γ̂2 are respectively 0.244 and 0.096. The t-test uses 95 percent confidence
level on the test and the critical values of the rejection region of the null hypothesis are either if the t-test value larger than 1.96 or smaller than -1.92. The t-test values of γ̂0 and γ̂2 are less
than 1.96, so we fail to reject the null hypothesis. Therefore, the values of γ̂0 and γ̂2 are not
significantly different from zero. The same test also applies in testing the value γ̂3. The value
of the t-test in γ̂3 also is also less than 1.96, the same conclusion can be drawn by using 95
percent of confidence level. Finally, the t-test is also performed in testing value of γ̂1 whether
it is equal to the value of the average risk premium. The null hypothesis states that the value of γ̂1 is equal to the value of γ1. By using the same critical values in the previous test, having
the t-test values -0.06, the null hypothesis cannot be rejected; the value of γ̂1 is statistically not
different from the value of γ1. The result of the test of the values on γ̂0, γ̂1, γ̂2 and γ̂3 are
consistent with what CAPM predicts, therefore, CAPM is valid in the entire period. 6. Summary and Conclusion
The present study investigates the empirical validity of Capital Asset Pricing Model (CAPM) in Indian stock market. The investigation is conducted by using the monthly return of 72 stocks listed in S&P BSE 100 index. Four sub periods are being studied to understand the behavior of the stocks towards market index by using 10 portfolios each sub period, when 1 portfolio consists 7-8 stocks. From the results section, following conclusion can be drawn from the present study.
For the first test, testing CAPM through portfolio based on the relation between percentage returns of the portfolio with market returns in most cases support CAPM, however, the results from the findings cannot be fully used as an evidence to conclusively support CAPM.
In each sub period test, the results give the impression of ambiguity on the CAPM validity. Argument of CAPM is supported in one test and rejected in sequence tests. In most cases, the constant have non-positive values, means that the determination of
expected return is solely based on the market return, supporting the validity of CAPM.
The value of R2 indicates how well is the relationship between risk and return can be
explained by market index. For sub period 1 and 3 the values of R2 are high, in
contrast, the values of R2 in sub period 2 and entire period is poor. Again,
inconclusive evidence of CAPM appears.
The result of test in Security Market Line and test non-linearity partially support CAPM, although some evidence shows the CAPM prediction does not hold.
The evidence that higher beta provides higher return appears in the results, supporting CAPM hypothesis.
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