INTRODUCTION
One of the most important developments in modern capital theory is the Capital
Asset Pricing Model (CAPM). Simply, CAPM is a model that describes the relationship
between risk and expected return. A review of studies conducted for various
markets in the world supports the validity of CAPM. Early twentyfirst century
observed an alternative methodology for testing CAPM in the Philippine Equity
Markets in Ocampo (2003) and helped to provide the evidence
for the role of beta in explaining returns in the Philippines market. Rhaiem
et al. (2007a) investigated the estimation process of CAPM at different
time scales for French’s stock market and finally he predicted that the
CAPM are more relevant at a mediumterm horizon in a multiscale framework.
In a further research of Rhaiem et al. (2007b),
proposed a new approach based on wavelets analysis for investigating the riskreturn
relationship in the CAPM framework at different time scales for French’s
stock market. He established the predictions that CAPM are more relevant at
short and longterm horizon in a multiscale framework as compared to other
time horizons. A test in Turkey in Gursoy and Rejepova (2007)
found no meaningful relationship between beta coefficients and expost risk
premiums under the Fama and MacBeth (1973) but found
strong betarisk premium relationships with the Pettengill
et al. (1995) methodology. Recently, some researchers used different
models such as Generalized Autoregressive Conditional Hetrosecedasticity (GARCH)
model to investigate the stock market. Chigozie (2010)
investigated whether the Nigerian stock market follows a random walk by employing
GARCH model and he concluded that Nigerian stock market follows random walk
and exhibits weak form efficiency. Angabini and Wasiuzzaman
(2011) examined the change in volatility of the Malaysian stock market with
respect to the international economic crisis using both symmetric and asymmetric
GARCH models and found that there was a significant increase in volatility in
Kuala Lumpur Stock Exchange (KLSE) due to the financial crisis.
All over the world lots of researches goes on the stock markets (for example,
for Spanish stock market, (Ferruz et al., 2007)
for Istanbul stock exchange (Senol and Ozturan, 2008)
for Vietnam stock market (My and Truong, 2011) for Taiwan
stock market (Lin and Liang, 2011) and for Indian stock
market (Gunasekaran and Ramaswami, 2011) but in Bangladesh
studies related to stock market were few. Dhaka Stock Exchange (DSE), the frontline
organization for the securities market development of Bangladesh, was incorporated
on the 28th April, 1954. While many studies had been conducted on CAPM in the
Western countries, there are only a few studies in the Bangladesh context related
to CAPM. Mobarek and Mollah (2005) suggested that there
are some factors (beta, size, the ratio of pricetobook value, volume of shares
traded, earnings yield, cash flow yield, dividend yield and leverage) that influence
share returns on the DSE. Rahman et al. (2006a)
examined the riskreturn relationship within the CAPM framework and concluded
that beta is not only the factor to determine the stock return but also the
other variables such as book to market value, market capitalization and sales
are significantly important in this context DSE market. In the another study
of Rahman et al. (2006b) examined whether the
Fama and French (1992) CAPM model is applicable in Bangladesh
stock market with the consideration of four factors such as beta, book to market
value, market capitalization and sales. The results of that study strongly supported
the relationship among the variables to determine the stock return. Uddin
and Alam (2007) examined the linear relationship between share price and
interest rate on DSE through Ordinary Least Square (OLS) regression and commented
that if the interest rate is considerably controlled in Bangladesh than it will
be the great benefit of DSE.
Moreover, the applicability of the western theories to Bangladesh capital market
is suspicious owing to several differences between the developed capital markets
and the developing ones (Rahman et al., 2006a).
In order to check the applicability of the western theories to Bangladesh capital
market, the test of CAPM is important for DSE. The purpose of this study was
to examine thoroughly the validity of the CAPM in Dhaka Stock Exchange. This
study explored whether the CAPM is a suitable description of asset pricing in
Bangladesh context.
MATERIALS AND METHODS
Data description and selected companies: The data collected from Dhaka
Stock Exchange (DSE) market consists of 80 nonfinancial companies for the period
of 1st January 2005 to 31st December 2009 by excluding the financial sector
companies and considers only the nonfinancial companies because the reporting
system of financial sector companies is quite different from nonfinancial sector
companies (Mollah, 2009). This study uses monthly data
and yearly data for all variables; because the daily data, though better for
estimating riskreturn relationship, is very noisy Basu
and Chawla (2010). The all Share Price Index (DSI) is used as a proxy for
the market portfolio. This index is a market value weighted index which is comprised
of all listed companies of the exchange and reflects general trends of the Bangladesh
stock market. Furthermore, Bangladesh government Treasurybill rate is used
as the proxy for the riskfree asset. Finally, in order to examine the riskreturn
trade off in a sample of individual companies and portfolios, the returns for
each company are taken as the dependent variable and the company’s beta,
squared beta, unique risk and interaction term of beta and unique risk are taken
as independent variables (Sources: DSE website: www.dsebd.org
and SEC website: www.secbd.org).
Details of statistical analysis: The details of statistical analysis were provided under separate heading given below: 0
Estimating the riskreturn tradeoff using the CAPM for individual companies:
According to the CAPM and followed by Basu and Chawla (2010),
returns can be explained as:
where, R_{it} is the rate of return on company i at time t, R_{ft}
is the rate of return on a risk free asset at time t, R_{mt} is the
rate of return on the market index at time t and β_{i} is the beta
of company i, to be estimated. β_{i} can also be express by Cov
(R_{i }, R_{m})/Var (R_{m}) where R_{i} is the
rate of return on company i and R_{m} is the rate of return on the market
index. The CAPM can be estimated using the two stages regression (Omran,
2007). In the first stage regression, time series data is used to estimate
systematic and unique risk. The following regression is used:
where, e_{it} is the random disturbance term in the regression equation at time t and UR refers to the unique risk (the variance of the regression residuals, e_{it}), σ_{i}^{2} refers to the variance of the returns for the company, σ_{m}^{2} refers to the variance of the returns for index, the proxy for the market portfolio.
Equation 2 can be estimated using Ordinary Least Squares (OLS). For each company in the sample, R_{it }is regressed on R_{mt} to estimate beta, β_{i}. Eq. 3 measures Unique Risk (UR) which is the difference between the total variance of the returns on the company and the company’s market risk.
By taking R_{it } R_{ft = }r_{it}, the excess return of company i and R_{mt } R_{ft = }r_{mt}, the average risk premium, the Eq. 2 can be rewritten as:
The second stage regression is cross sectional and the following regression is used:
where, r_{i} refers to the average excess returns for company i over
the whole sample, β_{i} is the estimate of the systematic risk
contained in company i and is obtained from the first stage regression in equation
(2), β_{i}^{2} is the square of β_{i},
UR refers to unique risk estimate obtained from Eq. 3, IT
is the estimate of the interaction between systematic risk and unique risk and
e_{i} is the regression residual. α_{0}, α_{1},
α_{2}, α_{3}, and α_{4} are the parameter
estimates.
Portfolios construction and estimation using the CAPM framework: The
next step is to construct portfolios. For this construction, the total number
of companies are arranged in descending order of beta and grouped into 10 portfolios
of 8 stocks each. This is done to achieve diversification and thus reduce any
errors that might occur due to the presence of unique risk as done in Amanulla
and Kamaiah (1998).
According to Michailidis et al. (2006) we define
average portfolio excess returns of companies (r_{pt}) as:
where, k is the number of companies included in each portfolio (k = 1…8), p is the number of portfolios (p = 1…10) and r_{it} is the excess return on companies. The following equation is used to estimate the portfolio betas:
where, β_{p} is the beta of portfolio p, r_{mt} is the average risk premium and e_{pt} is the random disturbance term in the regression equation,
Now, following the cross sectional regression (5):
where,
is the average excess return on portfolio p, β_{p} is an estimate
of beta of portfolio p and is obtained from the regression in equation (7),
β_{p}^{2} is the square of β_{p}, UR_{p}
refers to unique risk of portfolio returns that is UR_{p = }σ^{2}
(e_{pt}), IT_{p} is the estimate of the interaction between
systematic risk and unique risk on the portfolio and e_{p} is the random
disturbance term in the regression equation. γ_{0}, γ_{1},
γ_{2}, γ_{3} and γ_{4} are the parameter
estimates.
Research hypotheses: The estimated parameters will allow testing a series
of hypotheses regarding the CAPM. For CAPM to hold0 true, the following hypotheses
should be satisfied (Elton and Gruber, 1995):
• 
γ_{0} = 0, that is γ_{0} should
not be significantly different from zero 
• 
γ_{1} > 0, that is there should be a positive
price of risk in the capital markets 
• 
γ_{2} = 0 or the Security Market Line (SML) should
represent a linear relationship 
• 
γ_{3} = 0 or the unique risk which can be diversified
should not affect return 
RESULTS AND DISCUSSION
Results of the OLS regression for individual companies:
The results from Table 1 showed the estimation of betas for
individual companies in the DSE market of Bangladesh. In the estimation of Security
Market Line (SML), the CAPM’s prediction for β_{0} was that
it should be equal to zero. But from Table 1, it was observed
that the calculated value of the intercept was 0.028 and it was significantly
different from zero. It was also noticed from Table 1 that
the estimated SML slope was 0.180. The excess return on the market portfolio
(R_{m}R_{f}) was 0.0393 (different from the estimated SML
slope), where R_{m} is the rate of return on the market index and R_{f
}is the rate of return on a risk free asset. These findings were coincided
to the findings of Omran (2007) where he examined 42
companies, over 18weeks period from 2nd March, 2001 to 26th October, 2001 in
order to analysis the CAPM in the Egyptian stock market. In his study, Omran
found that the estimated SML intercept and slope are significantly different
from zero at 5% level of significance. Hence, based on the intercept and slope
criterion the CAPM hypothesis can clearly be rejected for the individual companies
under study.
The coefficient of the square beta was 0.587 and the third hypothesis of CAPM
was accepted, that is the expected returnbeta relationship is linear. Unique
risk and the interaction term (a risk term that reflects any interaction between
the systematic risk and unique risk) did not affect the returns generating process
since the estimates of β_{3} and β_{4} are far away
from being significant. It is therefore concluded that unique risk and interaction
term had no affect on the expected return of a security. In the study of Omran
(2007) it was also found that the unique risk does not affect the returns
generating process of Egyptian stock market which was as same as this study
that unique risk did not affect the returns generating process of Bangladesh
stock market.
Stock beta coefficient estimates for individual companies:
From Table 2, it was found that the range of the estimated
stock betas was between 0.0028 and 0.5928.
Table 1: 
OLS estimates of individual companies 

*: Significant level at 1%, NS: Not significant, SE: Standard
error 
Table 2: 
Stock beta coefficient estimates of individual companies 

*, **, ***: Significant level at 1, 5 and 10%, NS: Not significant,
SE: Standard error 
Among the 80 nonfinancial companies, the highest beta attainable company was
Square Textile (β = 0.5928) and the lowest beta attainable company was
Monno Stafllers (β = 0.0028). The beta coefficients for 25 individual stocks
were found statistically significant at 1% level of significance, 6 individual
stocks were recorded statistically significant at 5% level of significance and
3 individual stocks were statistically significant at 10% level of significance.
The remaining 46 companies were statistically insignificant. These findings
were contradicted to the findings of Michailidis et al.
(2006) where he examined 100 companies listed on the Athens stock exchange
and found most of the beta coefficients for individual companies are statistically
significant at 5% level of significance and all estimated beta coefficients
are statistically significant at 10% level of significant whereas in this study,
the beta coefficients for 34 companies are statistically significant out of
80 individual companies.
One of the important hypotheses of CAPM is higher beta is associated with higher risk. The results of the study did not support the hypothesis of the CAPM theory because the result showed that higher risk is not associated with a higher level of return. The highest beta attainable company Square Textile was not the highest return observed whereas the lowest beta attainable company Monno Stafllers got higher return (Return = 0.0351) than Square Textile (Return = 0.0536). The highest return yielding company was Meghna Condensed Milk (Return = 0.0029) with β = 0.1191 and the lowest return yielding company was National Tubes (Return = 0.0557) with β = 0.1772.
Stock beta coefficient estimates for constructed portfolios: From Table
3, it was found that the range of the estimated stock portfolio betas was
recorded between 0.0274 and 0.7383. The beta coefficients for the first four
portfolios were statistically significant at 1% level of significance, the fifth
and sixth portfolios were statistically significant at 5% level of significance
and the rest four portfolios were statistically insignificant. Among the 10
portfolios, the highest beta attainable portfolio was Portfolio 1 (β =
0.7383) and the lowest beta attainable portfolio was Portfolio 10 (β =
0.0274). In this study, the coefficients of beta were found to be statistically
insignificant in 4 portfolios (Portfolio 7, 8, 9 and 10) out of 10 portfolios.
The findings in terms of beta coefficients were dissimilar to the findings of
Basu and Chawla (2010) because in his study, the beta
coefficients were found insignificant in 7 of the 10 portfolios.
The results of the constructed portfolio also did not support the CAPM hypothesis
that higher risk (beta) is associated with a higher level of return. Portfolio
1 for example, the highest beta portfolio, yielded lowest portfolio return (Return
= 0.0379). In contrast, Portfolio 10, the lowest beta portfolio produced higher
return (Return = 0.0313) than Portfolio 1. The highest return (Return = 0.0249)
yielding portfolio was Portfolio 6 whose β = 0.2580. These results were
similar to the results obtained from the stock beta coefficient estimates for
individual companies (Table 2) in this study that contradict
CAPM theory’s basic hypothesis.
Results of the OLS regression for the constructed portfolios: The results
of Table 4 indicated that the portfolio intercept, which was
the most significant numerical value, significantly different from zero at 1%
level of significance. The estimated portfolio slope was not equal to the excess
return on the market portfolio and was insignificant. These findings were supported
to the findings of Basu and Chawla (2010) where he examined
10 portfolios, covering 50 stocks, over a 5year period from 1st January 2003
to 1st February 2008 in order to check the validity CAPM in the Indian stock
market context. In his study, Basu showed that the intercept term is significantly
different from zero for all the 10 portfolios and the estimated portfolio slope
is not equal to the excess return on the market portfolio in 9 out of 10 portfolios.
According to CAPM, intercept term should be equal to zero and the slope should
be equal to the excess return on the market portfolio. Hence, based on the intercept
and slope criterion the CAPM hypothesis can clearly be rejected for the constructed
portfolio also.
The coefficients of square beta, unique risk and interaction term were insignificant which indicated that the expected returnbeta relationship was linear in portfolios and residual risk and interaction term had no affect on the expected return of the constructed 10 portfolios.
Yearwise results of the OLS regression for individual companies: Since
the analysis on the entire fiveyear period for individual companies and constructed
portfolios yield strong evidence against the CAPM, this analysis examined whether
a similar approach on yearly data for individual companies would provide any
different evidence.
Table 3: 
Stock beta coefficient estimates of constructed portfolios 

*, **: Significant level at 1 and 5, NS: Not significant,
SE: Standard error 
Table 4: 
OLS regression estimates of constructed portfolios 

*: Significant level at 1, NS: Not significant, SE: Standard
error 
Table 5: 
Yearwise OLS regression estimates of individual companies 

*, ***: Significant level at 1 and 10%, NS: Not significant,
SE: Standard error 
The CAPM was tested separately for each of the fiveyear period and the results
in Table 5 did not support the CAPM hypothesis. These findings
were supported to the findings of Michailidis et al.
(2006), where he examined the validity CAPM for the Greek stock market using
weekly stock returns from 100 companies listed on the Athens stock exchange
for the period of January, 1998 to December, 2002. In that study, the author
tested CAPM separately for each of the five year period and the results were
statistically better for some years but finally did not support the CAPM hypothesis.
The intercept term in the year 2007 and 2009 showed insignificance which was different than the other three years and the expected returnbeta relationship was not linear in the year 2008 whereas in other four years the relationship showed linearity.
CONCLUSION
The study examines the validity of the CAPM and investigates a riskreturn relationship within the CAPM framework using DSE data. The findings of the study are not supportive of the CAPM theory’s basic hypothesis in both casesindividual companies and portfolios. The results also contradict the CAPM’s another hypotheses that the intercept term should equal zero and the slope should equal the excess returns on the market portfolio. Thus, it can be concluded that CAPM is not a suitable indicator of asset prices in Bangladesh over the chosen sample period. To test the nonlinearity between return and beta, the square of the beta coefficient is introduced in the model. The findings indicate that the CAPM linear relationship is sufficient to describe the returns generating process. Additionally, the test conducts to investigate whether the CAPM adequately captures all important aspects of reality by including the unique risk and the interaction term of systematic risk and unique risk of stocks. The result shows that the investors are rewarded for market risk (systematic risk) but not for unique risk.
While this study is successful in invalidating the CAPM, further research could be attempted to test the validity of other asset pricing models in Bangladesh Stock Market. A comparative study of asset pricing models could also be attempted for a more thorough analysis. This study can be used as a source of reference and a guide for future research.