The Capital Asset Pricing Model (CAPM) has been invented by Sharpe (1964), and Lintner (1965)’ after the work of Markowitz’s in 1959. Since then the model has known tremendous success, its simplicity has lured many professionals and academics as well. Despite many criticisms, the CAPM is still used in modern finance and is widely present in finance textbooks. On the other hand we have the Arbitrage Pricing Theory (APT), a less restricted model when compared to the CAPM, but with its own limitations as well. The APT, invented by Ross in 1976, tries to capture the non-market influences that are responsible in making assets to move in tandem. Both models are definitely different in some aspects, and therefore their effectiveness differs. In the literature we find many studies around the two models where some even tried to compare between the two, this chapter aims at reviewing those studies that have described and tested the models as well as introducing the Stock Exchange of Mauritius. The motivation behind this study is to find out which of the models is the most appropriate to predict return in relation to the risks. Moreover little study has been done about them and no research has been carried out yet to find out which of the two is more effective. The financial environment prevailing in Mauritius is juvenile, despite rapid growth in the industry it is still small yet well regulated when compared to other countries’ financial markets. There is a gap in the literature as no comparison between the two models has been made for Mauritius! introduction to the Stock Exchange of Mauritius: The Stock Exchange of Mauritius (SEM) was established in the year 1989 under the Stock Exchange Act 1988. There are two markets under the SEM namely “Official List” (for listed companies) and “Over-the-Counter” market (for unlisted companies). There are three market indices namely SEMDEX, SEMTRI, and SEM-7. The size of the SEM is rather small compared to others worldwide and the market capitalization to date is USD 1.4 billion [1]

The CAPM, underpinning theory in finance among academics and practitioners in the industry, has had a history full of supportive research and contradictive findings. The theory itself was developed by, Sharpe (1964), and Lintner (1965), following the work of Markowitz on portfolio theory in 1959. Basically CAPM states “an investor has the choice of exposing himself to a considerable amount of risk through a combination of lending-borrowing and a correctly composed portfolio of risky securities ” (Petros, 2012, p2). Moreover it is said that higher risk, which is known as the beta (AŽA²), is associated with higher level of returns. In more technical terms we can say that the expected return on an asset above the risk-free rate is linearly related to the non-diversifiable risk (market risk) as measured by the asset’s beta. Despite many criticisms surrounding this theory, the CAPM is still a widely used theory because of its simplicity and is one of the most important chapters in portfolio theory. Moreover, “it is still the centrepiece of many investment and financial market courses” (Choudhary and Choudhary, 2006, p2). The CAPM is an intuitive model and that is why managers still use it in justifying investments despite 30 years of critics over its assumptions and usefulness. Equation of the CAPM: a = rf + AŽA²a (m – rf ) Where: rf is the risk free rate, AŽA²a is the beta of the security, m is the expected market return. According to the CAPM, if the market is efficient, the risk premium and the expected return on an asset will vary in direct proportion to the beta value. The beta factor or beta value designates the marginal contribution of the share to the risk of the whole market portfolio or risky securities. The assumptions underlying the CAPM:

There are many investors who are all price takers. All investors plan to invest over the same horizon. There are no taxes or transaction costs. Investors can borrow and lend at the same risk-free rate over the planned investment horizon. Investors only care about expected return and variance. All investors have the same information and beliefs about the distribution of returns. 7. The market portfolio consists of all publicly traded assets. Though the CAPM is popular, it has had many critics in the literature, indeed the very attractive feature of the model, namely its simplicity, sometimes poses problem. As such CAPM has proved to be unreliable in some cases, indeed in Greece CAPM proved to be a weak model to predict return as the findings show that higher beta is not necessarily associated with higher level of return. Nevertheless it does explain excess return and therefore it has its usefulness. (Michailidis et al, 2006). It is stated that there is a need for a more complicated model and the assumptions on which the theory is based are often unrealistic (Fama and French, 2004). This is because it is not conceivable to think that investors care only about the mean-variance of one-period portfolio returns, other dimensions of risks need to be considered, for example labour income and future investment opportunities that the variance miss out. Adding to this Roll (1977) mentioned that having the market portfolio at the heart of the model is “theoretically and empirically elusive” and the data required are sometimes difficult to obtain, thus encouraging the use of proxies and not the true market portfolios and therefore weakens the theory in a sense. Yu (2003) mentioned that from the research he has carried out, he found that the relationship between risk and return is non linear, also he found that asset return can be predicted using other factors as well. Moreover, research in the late 1970’s has revealed that there are other factors which are also important. Indeed we have variables like size, various price ratios and momentum that add to the explanation of average returns provided by beta. Such problems are enough to invalidate the CAPM. (Fama and French, 2004). Therefore on this note we can already conclude that there are factors which have better prediction power, this was mentioned by Fama and French (1996) whereby it is said that accounting ratios and size of the firm can even do better than the CAPM (Petros, 2012, p2). Critics do not stop here, indeed Roll (1977) said that the market in the theory of CAPM is not about a single equity market, but rather an index of all wealth. Thus bonds, property, foreign assets, human capital and any tangibles or intangibles that increase the wealth of people should be inclusive of the market. (Petros, 2012, p7) Therefore it is found that CAPM might be very popular and surprisingly still in use, a need for a different and less restrictive model was needed in order to provide a more realistic prediction. This fact has created a need for a “better” model, or at least a model that can get over the limitations of CAPM, and there was invented the Arbitrage Pricing Theory (APT), a model that has more factor loadings and which has no restriction on the variables to be taken into account. The APT was developed by Ross in the year 1976 and as a multi factor model it has had quite some success. It is known to be a one-period model for which there is prevention of arbitrage over static portfolios of the assets being taken into consideration thus leading to a linear relationship between the expected return and its covariance with the factors. It can be said that the theory provides arbitrage-free pricing to existing assets. (Huberman and Wang, 2005) The APT has the feature of capturing the non-market influences which are responsible for making assets to move in tandem. Thus idiosyncratic factors that affect returns can be diversified away. Therefore under APT the investors are supposed to be rewarded only for the systematic risks they are undertaking, that is risks that cannot be diversified away. Being a multifactor model, the APT has the power to include several factors that influence return, and hence it is considered to be a more precise model for evaluating expected return over given risks. The factors used under the APT are diverse, though no guidance is given in the literature to which factors to be used, statistical techniques are available to pick the right factor and plug into the model. The equation of the APT is not restricted in terms of variables all the factors that have an impact on return can be included in the model. Here is the equation for the APT: Expected Return = rf + AŽA²1 (factor 1) + AŽA²2 (factor 2) + … + AŽA²n (factor n) Where: rf = the risk free interest rate, which is the interest rate the investor would expect to receive from a risk-free investment.A AŽA² = the sensitivity of the stock or security to each factor. factor = the risk premium associated with each factor. The problem with APT is that it lacks theoretical support for the factor loadings to be used. The freedom of choosing the factors to be included in the model does provide flexibility and improve accuracy. However there is the danger of picking the wrong factors or missing the right ones, therefore proper statistical methods need to be applied in order to include only all those factors that have an impact on returns. Azeez and Yonoezawa (2003) reiterated this fact by pointing out that no theoretical guidance is provided for the right economic influences that need to be plugged into the model. (Paavola, 2006, p9) Usually the statistical methods used are Principle Component Analysis and Factor Analysis, these two seems to provide the most accurate way of picking the right factors. Before comparing the two models in any country, it is important to know the differences first. Indeed there is a growing literature that tends to favour APT over CAPM because of the restrictive nature of the latter. As such, the APT being a multiple factor model allows multiple sources of systematic risks to be taken into account, performs better than the CAPM. (Paavola, 2006) However CAPM has not been “retired” from the financial world and is still in use, along with its other variants (example: ICAPM). The differences between the CAPM and the APT are as follows: The CAPM is more about how investors construct efficient portfolios and is derived from the mean variance analysis, whereas, as mentioned by Brealey et al. (2008), the APT assumes that equity’s return depend on macroeconomic factors and partly on noise (Paavola, 2006, p3). Unlike the CAPM, the APT is less restrictive in its assumption and therefore allows for an explanatory model of asset return. For the CAPM we have only the market index whereas for APT we assume that the investor will be holding a unique portfolio with its own set of betas. With APT it is possible to make predictions using a proxy for the market, whereas with CAPM this is not possible. Nevertheless, despite the differences between the two theories, APT can still be a substitute to CAPM. As a matter of fact, both agree that there is a linear relationship between the expected return of the assets and their covariance, which is a measure of risks that investors cannot avoid, with other variables. Still the two models have a few differences, but it is the potency of the model that is most important and so far the literature has been more lenient to APT than CAPM. There is definitely a conflict between simplicity and accuracy, the use of either model will depend on the context and the availability of information. But the methodology that is typical to the two also matters, some information (such as factor loadings) need to be extracted or estimated, and the methods of estimation might sometime raise doubts over the precision of the model.

The early empirical tests on the CAPM usually were based upon certain implications, indeed we note that expected returns on all assets are linearly related to their betas, and no other variable has marginal explanatory power. Moreover beta premium is positive implying that the expected return on market portfolio is higher than the expected return on assets whose returns are not correlated with the market return minus the risk free rate. All of these implications are hinting towards the fact that these tests were carried out using regressions. Either it was cross-section or time series regressions (Fama and French,2004). To test CAPM, either individual assets can be used, or these assets can be grouped as portfolios. This was done by Black, Jensen and Scholes (1972), they decided to group the stocks of the New York Stock Exchange (NYSE) into portfolios within a time frame of 34 years (1931 to 1965). From that the results were that high beta intercepts tend to be negative, unlike a low beta intercept which tend to be positive (Choudhary and Choudhary, 2006, p2). Other studies have used similar methodology, as such Choudhary and Choudhary (2006) who followed the suggested methodology of Black et al (1972) and went to fetch the closing prices of some 278 companies from the BSR 500 index and as market portfolio, the monthly closing values of the BSE Sensex Index were used to measure risk free return, the yield on 91-days treasury bills of the Government of India was taken. The study covered the period from January 1996 to December 2009, here again we have a portfolio formation process starting with the period 1996-98 that was used to estimate the beta of the individual securities and ranked them by beta and construct 1 to 20 portfolios. The beta was estimated using the monthly return, the stock monthly return was regressed against the chosen market index, and as mentioned above the 278 were grouped into portfolios of 20. This was done in order to eliminate firm-specific part of returns, thus improving the precision of the estimates of the beta and the expected rate of return of the portfolios. The conclusion was such that it voided the basic hypothesis of the theory (higher beta yield to higher returns), and the prediction that the intercept to be equal to zero and that the slope should be equal to the excess returns on the market portfolio was contradicted. However the linear structure of the CAPM as a good explanation of security returns was confirmed. Similar methodology was used by Petros (2006) and again the basic hypothesis of CAPM was inconsistent with the findings. Moreover the linear relationship between expected return and beta was again confirmed. Thus it can be found that using the CAPM to make predictions about return is not the best choice. According to Roll (1997) such time-series and cross-section regressions do not really test the CAPM, what is rather tested is whether or not a specific proxy for the market portfolio is efficient in the set of portfolios that can be constructed from it. Adding to this, there might be problem fetching data, because the data for true market portfolio of all assets are likely beyond reach (Fama and French, 2004). Critics about CAPM do not stop here, in the literature we have Basu (1977), Banz (1981), Bhandari (1988) , Statman (1980), and Rosenberg et al (1985), who used ratios, to be more precise, they used Earnings per Share, Market Capitalization, Debt-equity ratios and Book-to-Market ratios respectively. All of these different ratios proved to perform better than the CAPM, and further reiterated by Fama and French (1992) and Fama and French (1993) that ratios perform better where regression has failed to provide reliable answers (Fama and French, 2004, p12,13). The APT on the other hand, has a particular problem, and that is the choice of factor loadings in the model. This theory was tested in several economies around the world however the method of estimation of the factors to be used is rather common, that is PCA and Factor Analysis. The factors that are used in the APT should have particular characteristics, as mentioned by Berry et al (1988), three properties are required namely, at the beginning of every period the factor should not be predictable to the market. Secondly it is important that each factor has its importance in the stock market, and finally, each factor should influence expected return, therefore they must have non-zero prices. Roll and Ross (1980) and Lehmann and Modest (1988) both have put more emphasis on the first property (Gagnetti, 2006) Factor analysis was first proposed by Gehr (1978) and Roll and Ross (1980) as a technique to estimate the common factors and factor loadings of security returns at the same time. Nevertheless, Chen et al (1986) instead tried macroeconomic variables to explain asset returns (Gagnetti, 2006). Groesnewold and Fraser (1997) also worked with macroeconomic variables that affect share returns based on a general hypothesis. But Cheng (1995) did an even more interesting work by performing a factor analysis of both a sample of securities and of the most important categories of macroeconomic variable and later used canonical correlation techniques to compare the two. Testing the APT usually involves time series data to estimate factor loadings for each asset, and the regress the sample mean returns on the factor loadings using a cross-section regression. This method of finding for the required factors substitute the arbitrary and controversial method of “trial and error” and provides a more scientific way of picking the right factors that is required for the model according to the context it is being used. Gagnetti (2006) has used the same common methodology, as such PCA was used to find the factors required and the software SPSS 8.0 was used to determine the number of factors needed. The result was that 8 factors were selected and the testing concluded that APT is a more robust model than the CAPM, as it was a comparison between the two models.

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