Capm vs. Apt: an Empirical Analysis

The Capital Asset Pricing Model (CAPM), was first developed by William Sharpe (1964), and later extended and clarified by John Lintner (1965) and Fischer Black (1972). Four decades after the birth of this model, CAPM is still accepted as an appropriate technique for evaluating financial assets and retains an important place in both academic scholars and finance practitioners. It is used to estimate cost of capital for firms, evaluating the performance of managed portfolios and also to determine asset prices. Since the inception of this model there have been numerous researches and empirical testing to assess the strength and the validity of the model. Several variations of the models have been developed since then (Wei 1988, Stein, Fama & French 1993, Merton 1973). The Arbitrage Pricing Theory of Capital Asset Pricing formulated by Stephen Ross (1976) and Richard Roll (1980) offers a testable alternative to the CAPM.

Both of these asset pricing theories have gone through intense empirical and theoretical scrutiny with multiple researches supporting or refuting both the models. The purpose of this paper is to empirically investigate the two competing theories in light of the US Stock Market in relatively stable economic times. The first section will look at the logic and theoretical aspects of the competing asset pricing models. The second section analyses and discusses the existing literature and empirical analyses on both the theories. In the third section I explain the data and the testing methods employed to empirically examine the theories. The fourth section explains the results derived from the tests. The last section includes the conclusion and discusses the limits and implications of my research. SECTION I: CAPM and APT

CAPITAL ASSET PRICING MODEL (CAPM)
Sharpe’s (1964) CAPM is built upon the model of portfolio choice by Harry Markowitz (1959). According to his theory, investors choose “mean-variance-efficient” portfolio. This basically means that they choose portfolios that minimize the variance of portfolio return, given expected return, and maximize expected return, given variance. In addition to these assumptions, the CAPM makes several other key assumptions. They assume that (1) all investors are risk averse and looking to maximize wealth in a single period and can choose portfolios solely on the basis of mean and variance, (2) taxes and transaction costs do not exist, (3) all investors have homogeneous views regarding the parameters of the joint probability distribution of all security returns, and (4) all investors can borrow and lend at a riskless rate of interest (Black et al. 1972).

The CAPM is an equilibrium model that explains why each different security has its own distinct expected returns. It provides a method to quantify the risk associated with each asset. One key assumption of the CAPM is that it assumes that all the diversifiable risk can be and is eliminated in an efficient ‘market’ portfolio. An individual security’s idiosyncratic risk will be compensated for by another stock. So the risk associated with each security is its systemic risk with the market. This is measured in the CAPM by its beta (its sensitivity to the movements in the market). There is a linear relationship between the security’s beta and its expected returns. Formally the CAPM equation can be written as follows ERi= Rf+βi(ERm- Rf) (1)

Where,
ERi = Expected return on the capital asset
Rf = Risk Free Rate (Usually of 6 month Treasury bill)
βi = beta which is the sensitivity of the expected excess asset returns to the expected excess market returns. Formally, the market beta of an asset i is the covariance of its return with the market return divided by the variance of the market return. βi = Cov(Ri, Rm)σ2(Rm) (2)

Rm = Expected return of the market
A zero beta asset in the CAPM has an expected return equal to the risk free rate. The betas can be estimated using various statistical and econometric techniques. The three most commonly used techniques are the “market model” (This is the most common one. I will be using this for my testing), Scholes-Williams, and Dimson estimators. There are numerous advantages/benefits as well as some flaws in all the beta estimating techniques. Examining that fall outside the field of this paper but the limitation section looks at the problems of the different techniques very briefly. In order to compare the two models, staying consistent with the estimation techniques will be sufficient regardless of their flaws or biases. ARBITRAGE PRICING THEORY

The APT is the alternative model for asset pricing first developed by Ross (1976). This is a very appropriate model as it agrees perfectly with what appears to be the intuition behind the CAPM. It is based on a linear return generating process as a first principle. Also it is more sophisticated that the CAPM because it takes into account more systematic factors that might be relevant. It examines other macroeconomic variables besides the market risk, making this model more sophisticated. It captures other factors that might have been ignored by the CAPM. Formally the APT can be stated as follows. rj=Erj+bj1F1+ bj2F2+…+bjnFn+ϵj (3)

Where,
E(rj) is the jth asset’s expected return,
Fk is a systematic factor (assumed to have mean zero), bjk is the sensitivity of the jth asset to factor k, also called factor loading, and εj is the risky asset’s idiosyncratic random shock with mean zero. The APT states that if asset returns follow a factor structure then the following relation exists between expected returns and the factor sensitivities: E(rj) = rf+bj1RP1+bj2RP2+…+bjnRPn (4)

Where,
RPk is the risk premium of the factor,
rf is the risk-free rate
That is, the expected return of an asset j is a linear function of the assets sensitivities to the n factors. There are two fundamental differences between the APT and the CAPM – “Firstly, the APT allows more than just one generating factor (CAPM allows only for the market factor) and secondly, the APT demonstrates that since any market equilibrium must be consistent with no arbitrage profits, every equilibrium will be characterized by a linear relationship between each asset’s expected returns and its return’s response amplitudes of loadings on the common factor” (Roll and Ross 1980).

It is important to note that the APT is based on three key assumptions – (1) Capital markets are perfectly competitive, (2) Investors always prefer more wealth to less wealth with certainty, (3) the stochastic process generating asset returns can be represented as a k-factor model of the form specified above in equation 3 (Reinganum 1981), (4) individuals agree on both the factor coefficients (beta) and the expected returns, (5) equation 3 not only describes the ex-ante individual perceptions of the returns process but also that ex-post returns are described by the same equation (Roll & Ross 1980). There are other theoretical differences between the two models but a more thorough theoretical analysis falls outside the scope of this paper and is an area of research that has been extensively scrutinized as well. SECTION II: LITERATURE REVIEW

There has been numerous studies theoretical and empirical testing on both CAPM and the APT because of its high relevance in the finance industry. This section is divided into two sub sections – (a) Studies on CAPM, (b) Studies on APT, and (c) Comparative studies on CAPM Vs APT. The second and the third subsection intersect with each other. Because APT was developed in response to the CAPM, lots of tests on APT look at it from a comparative perspective. A. Studies on CAPM

Although, the Sharpe (1964) and Lintner (1965) version of CAPM has been a major theoretical force, it has not been an empirical. Most tests of the CAPM are based on three implications of the relationships between the expected return and the market beta of the security – (i) Betas and the expected returns are linearly related and no other variable has explanatory powers, (ii) beta premium is positive (this also implies that higher betas means higher returns) and (iii) assets uncorrelated with the market have the same expected returns as the risk free rate ( Rf) (Fama & French 2004). Although the CAPM is challenged by many studies, the influences of some earlier studies still remain and the beta is still considered to be an important variable in the pricing and evaluating of assets (especially in the context of an efficient portfolio). It is important to note here that all the studies examined below uses some sort of portfolio allocation to test for risk-return relationships.

Fama and Macbeth (1973) tests the relationship between average returns and risk for New York Stock Exchange (NYSE) common stocks (from 1935 – 1968). They employ the “two-parameter” portfolio model and models of market equilibrium derived from that model to test for three main hypotheses of the CAPM. They test for the relationship between the expected return on a security and its risk in any efficient portfolio and find a statistically significant positive linear relationship as implied by the model. They also find that no other measure of risk in addition to the portfolio risk, systematically affects the expected returns of the security (beta is the only explanatory variable). And they find via residual analysis that the risk-return regressions are consistent with an efficient capital market – a market where prices of securities fully reflect the available information.

Black, Jensen, and Scholes (1972) provide some additional testing of the model in the same time period (1926 – 1966) for NYSE listed common stocks as well. It corrects some of the previous testing problems by using more powerful time-series testing as opposed to just cross-sectional tests and eventually comes up with a two factor model using both cross sectional and time-series testing. They also modify the original CAPM model by relaxing the assumption of riskless borrowing and lending opportunities and hence strengthening the model. The conclusions and results of their test confirm the positive linear relationship of the beta and the expected returns of the stock but differ with Fama and Macbeth’s conclusion regarding the intercept of the CAPM linear regression. Both these studies provide empirical evidence supporting the CAPM.

Since the earlier studies, more empirical research has shown how the CAPM does not fairly represent the risk return relationship it implies. Basu (1977) evaluates the investment performance of common stocks in relation their price-earnings ratio. He uses the CAPM model, holding beta constant to see if the P/E ratios of the security contribute towards the expected return. He finds that there is a higher return for assets with lower P/E when beta is held constant. An implication of his result poses a serious challenge to the validity of the Capital Asset Pricing Model. Because CAPM says that there is no other risk present in the stock when it is put in the portfolio (since all diversifiable risks are eliminated), no other factor besides the market risk should be present. Basu (1977) finds that P/E ratios also influence the price, not just the market risk. The model fails to completely characterize the equilibrium risk-return relationship during the period he studied (NYSE firms from 1956 – 1971). It also implies that the CAPM might be mis-specified because of the omission of other relevant factors. Cheng and Grauer (1980) provide an alternative test to the CAPM.

They address the ambiguity in previous tests of CAPM (Roll 1977) which primarily examined the security market line to look at the risk-return relationships by employing the Invariance Law test. Although this is not as intuitively pleasing as the standard SML tests, it addresses the ambiguity problems with them. Their results strongly reject the CAPM on many grounds. They find statistically significant trends in estimated values of the intercept as regressors are added (CAPM implies a static intercept – the risk-free rate). They fail to reject the null hypothesis that the beta is statistically different from zero in 25% of the cases. Their new frame work of testing further challenges the empirical validity of the CAPM. Reinganum (1981) further investigates whether securities with different estimated betas systematically experience different average rates of returns.

In his study, he uses all the three beta estimation techniques to construct his beta ranked portfolios (market model, Sholes-Williams, and the Dimson estimator). The limitations of the beta estimation methods are discussed in the limitations section below. The data he looks at is the NYSE common stocks daily and monthly returns from 1935 to 1979. His results also show that there is no positive relationship between the firms or the portfolios’ beta and the mean returns on a statistically significant level. This result holds true regardless of the beta estimation technique used and for both daily as well as monthly returns. This research provides further evidence against the empirical validity of the CAPM. B. Studies on APT

There have been a number of studies testing the empirical validity of the APT since its inception. One of the first studies that tests the APT empirically was by Roll and Ross (1982). They look at individual securities from 1962 to 1972 listed in the NYSE or American Exchanges. They perform the maximum likelihood factor analysis to determine the no. of factors and the corresponding factor analysis. And then, they perform a cross-sectional analysis using general least squared regressions. The cross sectional part of this testing and portfolio allocations is very similar to most of the tests on CAPM. Their research finds four important systemic factors influences the return of a particular security – (1) Unanticipated Inflation, (2) changes in levels of industrial production (3) shifts in risk premiums, and (4) movement in the shape of the term structure of interest rates. They find that betas are statistically significant and have explanatory effects on excess returns. This also empirically proves the linear relationship between the returns and the systemic factors. This study however recognizes that its test is still a weak one and further testing is needed.

Tϋrsoy, Gϋnsel and Rjoub provide some further empirical tests of the Arbitrage Pricing Theory. They examine 13 macroeconomic variables (factors) on 11 different industry portfolios of the Istanbul Stock Exchange (2000 – 2005) to observe the effects of those variables on stock’s returns. They employed the ordinary least square (OLS) technique to do this. Although they do not find strong R2 for any of the portfolios (R2 ranges from .19 to .36), they do find a lot of variables to be statistically significant in different portfolios. For example they find unemployment rates to be significant in the portfolios of manufacturing of basic metal industry, wood production and furniture, fabric metal products, transportation and communication. Because of the large no. of variables employed and the inconsistencies in statistical significance of the different betas in different portfolios, this does not tell us much about the strength of the APT.

Poon and Taylor (1991) use the same methods employed by Chen, Roll and Ross (1986) to reconsider their results and also to see if their results were applicable to the UK Stocks. They find that variables similar to those of the Roll and Ross tests do not affect share prices in the UK in the manner described. They conclude that it could be that other macroeconomic variables are at work or the methodology of the tests employed by Ross and Ross is inadequate for detecting such pricing relationships. They also note some important criticism about the methodology used by Ross and Roll. Firstly, it challenges the assumption that market prices assets in a precise, systematic, linear manner even though the exposure of the stock returns to the macroeconomic factors might not be statistically significant. Secondly, it notes that the two step regression analysis is sensitive to the number of independent variables in the regression – adding more variables results in loss of statistical significance of previous betas. Thirdly, it notes that Ross and Roll did not consider any lead/lag relationships between the asset pricing and the macroeconomic performance.

Fourthly, Roll and Ross fail to remove any seasonality associated with associated with the industrial production series. This study provides some empirical evidence that invalidates the Arbitrage Pricing Theory by showing how the factors found to be relevant and influential in Ross and Roll’s (1980) study are not statistically significant when applied to the UK Stocks – the betas associated with those macroeconomic factors are statistically insignificant. Reinganum (1980) provide some more empirical results of the Arbitrage Pricing Theory. He argues that a minimum requirement for an alternate model of capital asset pricing (CAPM) should be that it explains the empirical anomalies which arise within the sample CAPM.

One such anomaly he observes is when portfolios are formed on the basis of firm size; small firms systematically experience average rates of returns nearly 20% more per year than those of large firms. He looks at the stock data (NYSE and American Exchanges) from 1962 to 1978 to investigate whether an APT model can account for the differences in the average returns between small firms and large firms. He uses a three, four and a five factor model of APT to conduct these tests and finds that none of those models accounts for the empirical anomalies that arise within the CAPM. However, he does point out that although the results do not support the APT, the source of error can be attributed to other factors. Regardless of that, his tests show that APT is not an adequate model to determine the risk-return equilibrium in a statistically significant level. C. Comparative Studies on APT Vs CAPM

Bower, Bower & Logue (1984) look at the utility stocks in the NYSE and American Stock exchanges from 1971 to 1979. They used Ross & Roll’s four factors as its systematic influences. They performed time-series analysis and cross sectional regressions to find the betas and the risk premium sassociated with each factor to eventually come up with a multiple regression linear model reflecting the risk-return relationship. They also find the market beta and the security market line for the same securities (CAPM risk-return equation). They find two very contrasting sets of results from the two models. They found that APT to be a better model than the CAPM. The R2 for the APT was higher for all the portfolios when randomly grouped, when grouped by industry and when grouped by market beta as well. The unexplained variances were higher for CAPM in all the portfolios as well. They also perform a weak Theil’s U2 and find the APT’s U2 to be much lower than CAPM (the lower the U2, the better forecaster the model is). This paper provides strong empirical evidence in favor of APT when compared to the CAPM model. SECTION III: METHODOLOGY

DATA
The data I look are all United States data from 1980 – 1997 (monthly). I chose this time period because there were no significant long term shocks in the market or the economy during this time. The stock market crash of 19th October 1987 is an exception but the market recovered relatively fast and there were no significant long term macroeconomic changes. Also, I chose this time period because it is the most recent period experiencing relative stability in the financial markets. There was the dot com bubble 1997, recession after 9/11 in 2001 and the financial crisis at 2008. A look at the S&P graph below (figure 1) shall demonstrate that.

Figure 1: S&P 500 Index (1975-2006)
I looked at monthly prices and returns for 160 companies from the S&P 500. I use the adjusted data for this purpose. I chose adjusted closing prices and not the nominal closing prices because the adjusted closing price accounts for any corporate actions that might change the price dramatically. For example a 2:1 stock split would half the price of the stock in a day and subsequently distort my results. 16 companies were chosen randomly from each industry groups. The industry groups were Energy, IT, Industrials, Materials, Utilities, Consumer Discretionary, Consumer Staples, Financials, Telecommunication, and Healthcare. The other variables were inflation, changes in the term structure of interest rates, overall industrial production, and risk premiums for the same time period. Change in the term structure of interest rates was the difference between the 10 year Treasury Bond and the 6 month T Bill rates. The Risk Premium was the difference between monthly S&P 500 returns and the 6 month T Bill returns. The source of the data for each variable is listed in table 1.

I employ three portfolio allocations to test and examine each model. The first allocation method will test the CAPM model only. 9 portfolios are constructed according to the beta. I calculate the market beta for each company using the OLS regression method and then rank the companies according to their beta. Portfolio 1 has the lowest beta and Portfolio 9 has the highest beta. The average betas for each portfolio can be seen in Table 2.

Table 2: Portfolio Allocation I According to CAPM, securities with different betas systematically experience different average returns. Higher betas would yield higher average returns (Reinganum, 1981). This is the relationship I will be testing in the Portfolio Allocation I. I would expect to find a statistically significant positive relationship between beta levels of the portfolio and the average returns. The first allocation will not be testing the APT. In Portfolio Allocation II, I constructed ten industry portfolios. There are 16 companies in each portfolio. I perform an OLS test for each portfolio to find the market betas (for CAPM) and betas for the 4 factors of APT. The four factors I chose are inflation, risk premium, industrial production and changes in term structure of the interest rate. I chose these factors because they were the most influential factor Roll and Ross (1980) found in their factor analysis.

I looked at the statistical significance of the betas of each factor to see how valid APT was. Finding statistical significant betas for APT implies that CAPM is not adequate. This is because according to CAPM, there is no other systemic risk besides the market risk. Or in other words, no other systematic factors affect the prices and subsequently the returns of the stock. I also looked at R squares for both the models to examine which model was a better fit or which model explained the variance better. In Portfolio Allocation III, I constructed ten random portfolios. Each security was given assigned a random number and then sorted accordingly. I performed the same kinds of testing employed in Portfolio Allocation II and looked at the same variables. This method would help eliminate any systematic bias the industry that the stock belonged to would have on the stock returns. This method of portfolio allocation is used in many studies examining the two models (Reinganum (1981), Dhankar (2005), Tursoy, Gunsel, Rjoub (2008), Black, Jensen, and Scholes (1972)). SECTION IV: RESULTS

A. Portfolio Allocation I Results
Table 3: Beta Vs. Returns
The results for the Portfolio Allocation I are displayed in Table 3, 4 and figure 2.Results from the regression examining the relationship between beta and returns are shown in Table 4. Looking at the various returns for the portfolios, there is no particular relation between the beta and the returns at first look. Portfolio 1, which has the lowest beta, has a higher return than Portfolio 8 (second highest beta). This goes against the logic of CAPM.

Table 4: Beta vs Return Regression
Table 4: Beta Vs Returns Regression

The regression also goes on to show that there is not statistically significant relationship between the beta and their returns as advocated by CAPM. A look at a simple scatter plot (Figure 2)also shows how there is no real trend/relationship between the beta and the return and if there is one, it is a negative one. The first portfolio allocation test shows that CAPM’s market beta does not determine the returns that the security will experience.

Figure 2: Beta vs. Returns Scatter Plot

B. Portfolio Allocation II Results
Results for Portfolio Allocation II are as follows. Table 5 displays the regression results for APT, Table 6 displays the regression results for CAPM and Table 7 displays the R squares for both the models.

Table 5: CAPM Results for Industry Portfolios
The CAPM Coefficients (Betas) for all the industry are highly statistically significant (at a 99% confidence). This shows that market has a very significant influence on the returns of the stocks. These results support the CAPM and prove that CAPM passes the empirical test. However, CAPM also implies that no other variables should have a significant explanatory effect because any other systematic risk would be eliminated through diversification of the portfolio. An illustration here would be helpful to gain an intuitive understanding of how the diversifiable risk is eliminated. If a particular stock has a strong positive relationship with industrial production (for e.g. a steel company), one can find another stock that has a negative relationship with industrial production (unemployment insurance company etc). This will cancel out the systemic influence that industrial production might have on the asset of the price of a particular security when it is grouped in the single portfolio. Looking at the APT results (Table 6), we find that there is in fact other variables that statistically influences the returns of the stocks.

Table 6: APT Results for Industry Portfolios
For the IT portfolio, the betas for the risk premium and the industrial production factors are significant. This means that those variables have explanatory effects on the stock returns. For the Consumer Staples portfolio, all the factors except inflation have a statistically significant explanatory effect. A look at the results will show industrial production has a significant coefficient in all ten portfolios, risk premium in all ten portfolios as well. Changes in term structure have a statistically significant coefficient in eight out of the ten portfolios and inflation in four out of the ten portfolios. These results provide empirical evidence for the validity of APT. It shows how different macro economic factors have a statistically significant influence on the returns of the stock. An implication of this result is that CAPM is not adequate since it finds that there are other kinds of risk besides the market risk. I looked at the R squares of the two models to see which model does a better job explaining or accounting for the variances in the return. Table 7 lists the R squared for the different portfolios.

Table 7: R Squares for CAPM and APT Models, Industry Portfolios The R squares are higher with the CAPM model for most of the portfolios. This shows that market risk does capture more risks inherent in the portfolio than other macro economic variables that were tested. Looking at the R squares by itself would lead you to believe that CAPM is a better model. However since other macroeconomic variables do have a significant effect on the returns, CAPM is proven to be inadequate. Further implications of these results are discussed in Section V. C. Portfolio Allocation III Results

Results for Portfolio Allocation III are as follows. Table 8 displays the CAPM results for all ten portfolios (portfolios are randomly constructed), Table 9 looks at the APT results for the same set of portfolios and Table 10 shows the R squares using CAPM and APT for all the portfolios.

Table 8: CAPM Results for Random Portfolio Allocation
The results from the CAPM regressions for all ten portfolios are statistically significant at a very high level (99%). These results are similar to the ones found in the industry portfolios. It provides further evidence that market betas are significant even when the industry bias is removed. In other words, market risk is reflected in the returns of the portfolios. However for CAPM to hold ground based on empirical evidence, APT should be shown as statistically insignificant. There should be no other explanatory variable or no other systematic risk that affects the returns of the portfolio. The APT results are shown below.

Table 9: APT Results for Random Portfolio
Allocation The results indicate that industrial production, risk premium and changes in term structure have statistically significant betas in all the portfolios. The beta for inflation is statistically significant in four out of the ten portfolios. These results provide empirical evidence for the validity of the APT. It also implies that CAPM is not adequate as it fails to take into account some of the other macroeconomic risks. These result shows that market risk is not the only variable that influences returns as implied by the CAPM.

Table 10: R Squares for CAPM and APT Models, Random Portfolio Allocation The R squared is slightly higher when CAPM is employed as opposed to the APT. This result is again congruent with the ones found in the industrial portfolios. It shows how the market overall explains the variances better than other macroeconomic factor. Looking at the R squares might show that CAPM is a better model. However, as mentioned earlier, R squares do not capture the whole picture. Implications of these results are discussed below. SECTION V: IMPLICATIONS, LIMITATIONS, AND CONCLUSION

A. Implication
The results shown above demonstrate a couple of things about each model. The first results from portfolio allocation prove that beta does not determine the returns. It provides empirical evidence refuting the CAPM theory. Although CAPM is falsified in the first test, the other two tests (Portfolio Allocation I and II) show that market risk is significantly reflected in the asset returns. The testing for APT in these two tests shows that other macroeconomic risks are also reflected in the stock return. The two models cannot both be correct because CAPM says that only market risk is evident in the asset and no other systematic risk variable exists. Statistically significant betas for APT in both the portfolio allocation tests show that there are other macroeconomic variables that account for the returns of the security, proving CAPM inadequate.

The better R squares for CAPM shows that market risks and movements explain the variance in the stock returns better than all the macroeconomic factors in the APT model. Although it explains the variance better, it ignores other significant risks present in the stock returns. This can be problematic when calculating the stock price and making investment decisions. These results show that the APT might have a slight edge over the CAPM just because it is not falsified and the results for it were statistically significant. However it’s weaker R squared values (although not significantly weaker) show that it cannot explain the variances in the returns as well as the CAPM can. Financial practitioners should use both the models in junction and not choose one over the other. Although my results show APT is stronger and CAPM is inadequate, CAPM’s better R sq. and the statistical significance of its betas should not be ignored. B. Limitations

There are some limitations in this whole research one must keep in mind. Overcoming these limitations will strengthen the research but the results of the tests I have done are still valid and provide insightful empirical evidence that has serious and meaningful implications. The first big limitation of this paper is the lack of econometric sophistication. For example the use of more complicated model than the OLS regression model like the GARCH would give more accurate results. It would account for the noise present in the financial data. Also for my APT testing, I use Ross & Roll’s (1980) factors. I could perform my own factor analysis to come up with the macroeconomic variables relevant for my data which would strengthen my APT results. Again, due to lack of my sophistication in econometrics and Stata, I could not use this step. However, these macroeconomic factors (inflation, industrial production, changes in term structure, risk premiums) are used in other studies too (Poon & Taylor, 1991) and still present valid evidence for the strength of the model.

Another limitation of my paper is the beta estimation technique I use, specially for the CAPM models. I use the time series OLS regression to estimate betas (this is the market model). Using the market model estimator might be problematic for daily returns of nonsynchronous trading problems. And if nontrading is a serious problem this might lead to biases in the estimation which would affect the results (Reinganum, 1981). Other two estimation methods are However, even the Scholes Williams estimator might be biased and inconsistent if nontrading is a serious enough problem according to Dimson. Using all three estimation techniques would have led me to come to a conclusive answer; my answer is limited only to the market model.

The bias evident in the market model estimating technique is present in my results and should be eliminated by using these other estimation method. On a broader perspective, my research looks at stock market data for a very specific time period. The external validity of this research is only application to developed stock markets during times of stability. The findings of this paper would not be applicable to developing stock markets or when the stock market demonstrates extreme volatility or experiences other kinds of exogenous or endogenous shocks. In the real world, markets experience these fluctuations, hence lays my biggest limitation. There has not been enough testing of these models for times of crisis and shocks in the financial markets. This is an area where more empirical analysis and testing are warranted. C. Concluding Remarks

The results have shown that both models are not perfect. APT is better because it takes into account systematic risks other than the market risk as opposed to the CAPM which just accounts for the market risk. The empirical validity of the APT refutes the adequacy of CAPM as an asset pricing model. But the greater R squared demonstrated by the CAPM should not be forgotten as well. The risk averse and the rational investor would benefit using both models and coming to the most sound decision. Market risks should not be ignored but neither should other macroeconomic risks. Further research in more realistic market condition is needed to see which model is better for varying market conditions. The choice of the models will have serious consequences for the investor as well as for the market as a whole. Perhaps, there will be a model that incorporates the strength of both these models and eliminates the weaknesses, but until then both models should be used in conjunction for the best results. Acknowledgments

I would like to thank Professor Tymoigne for providing my some valuable sources and guiding me through the process of this research, Professor Schleef for helping me brainstorm, Dilara Zhamakayeva, Merica Shrestha and Lame Ungwang (Undergraduate Economics Students) for helping me collect and assemble the huge amounts of data.

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