Explain The Limitations Of The Capital Asset Pricing Model And The Extent To Which The Multifactor Approach Has Overcome These Limitations (Essay Sample)

Explain the limitations of the Capital Asset Pricing Model and the extent to which the multifactor approach has overcome these limitations.
1 Introduction
CAPM (Current Asset Pricing Model), the widely used method to monitor the investment performance has generated a lot of debate on its usefulness. The core of the controversy is the contention by Roll (1977) that it is impossible to have a correct and unambiguous CAPM test as observing the true market value of a portfolio is impossible. Thus, the measured risk factor (Beta) for an asset not only depends on the attributes unique to the security but to the proxy used as a representative of the assets universe. Attributing to this impossibility, Roll (1977) further added that theoretically it is possible to generate polarising ranking for the winners and losers if the approximation of the market portfolio is varied. He further argued that any desired measured performance can be produced by judiciously choosing the index. The above stated argument has served as the foundation of the questions regarding the usefulness of the CAPM based methods. Rosenberg (1981) offered a contrasting view as he regarded that the criticism surrounding the market portfolio being imperfect is nothing more than an unnecessary distraction. He further contended that the likely specification errors while approximating the index are relatively unimportant. The rationale behind such opinion is that the approximation is an application of the asset pricing paradigm instead of the CAPM theory, thus the central question should be that can a reasonable estimate generate distorted results?
Due to the contrasting views, it becomes important to understand the limitations of the CAPM model which is discussed in this essay. Researchers have proposed several methods to overcome these limitations, the efficiency of one such method, the multifactor models to overcome the limitations of the CAPM will be discussed in this essay as well.
2 Review of CAPM model vs. multifactor models
2.1 Limitations of CAPM model
It is a common knowledge that the risk-free investments yield lower returns in comparison to the riskier investments. However, with the development of the CAPM model, the economists were able to precisely differentiate the returns of a risk-free investment from that of a riskier investment (Mackinlay, 1994).The CAPM model postulates a return/risk relationship for a stock which is linear (Banz, 1981). It shows that the estimated excess returns’ cross-section from the financial assets will necessarily vary with the market beta in a linear manner and will have an intercept of zero (Mackinlay, 1994).
Several studies have empirically examined the above stated implication about the risk-return relation, number of which have contradicted the CAPM and rejected the hypothesis that the excess return from the financial asset has a zero intercept with the market beta (Mackinlay, 1994) and suggested the existence of several other relevant factors which impact the price of an asset, thus an inference can be drawn that the CAPM is misspecified (Banz, 1981). The CAPM model is developed for a perfect market and if the impact of liquidity and market frictions is considered, a non-zero intercept is observed as found by Amihud & Mendleson (1986). The market portfolio being mean-variance efficient is CAPM only single testable hypothesis. The other implication like the expected return linearity with the beta, cannot be tested independently. In addition, the return’s linearity with beta depends on the mean-variance efficiency of the market portfolio. In any sample, if the beta is calculated it will satisfy the linearity relationship irrespective of the market portfolio being mean-variance efficient or not. This means that CAPM theory cannot be tested prior to the knowledge of the exact composition of the portfolio representing the market (Roll, 1977).
Brown & Brown (1987) found that the market proxy actually matters for evaluating the returns for any group of assets. The usage of proxy for market portfolios raises two difficulties- First there is a real possibility of the mean-variance efficiency of the proxy being independent of the mean-variance efficiency of the market portfolio. This can happen as all samples display efficient portfolios perfectly, thus satisfying the implications of the theory. The other difficulty is that if the selected proxy is inefficient, it will not imply anything about the market portfolio efficiency. The reasonable proxies are strongly related with one another and with the true market, irrespective of them being mean-variance efficient or not (Roll, 1977).
Brown & Brown (1987) found that despite the precision with which the market indexes are used there is no assurance of them being optimal. However, from a practical standpoint, an all-inclusive portfolio is not a necessity. A more enlightening alternative is to define the market in accordance with the relevant components. There is limited evidence on the returns being empirical sensitive to different specifications of the market portfolio as per the CAPM model. In addition, Stambaugh (1982) implied that the investor performance ranking should be robust to a wide range of estimates. However, French & Henderson (1985) have proposed that the evaluation measure cannot assess inferior or superior investment capabilities even in an ideal scenario which is free from any external difficulty in identification. The identification of the market portfolio has a severe limitation while testing the two-parameter theory that no two experts who have different opinion on the markets based composition will agree on the test results of the theory. Testing directly, the proxy’s mean-variance efficiency is computationally difficult as the individual returns have a sample covariance matrix which needs to be statistically inverted as the knowledge about the efficient set’s sampling distribution is limited. Another limitation associated with the CAPM theory is that it does not predicts the parameter value, and predicts only the linear form of the cross-sectional relation, thus the parameters cannot be accurately estimated. Another limitation is that the CAPM theory is supported by the widely-used portfolio grouping procedure even if it is wrong as the deviations of the each asset from exact linearity cancels out, while a portfolio is formed (Roll, 1977). A similar finding was observed by Miller & Scholes (1972) who found that there is a relationship between the deviations and the process asymmetry generated which otherwise are undetectable in the grouped observations.
Roll (1977) used the Jensen portfolio performance measure to criticise the return/beta linearity relation as following- The individual Jensen performance measures is zero if the used market proxy is efficient on an ex-post basis. If the market portfolio used as proxy is significantly inefficient, then only the Jensen performance measures can be significantly non-zero. However, a concern can be raised on the justification of using non-efficient proxy market portfolio for benchmarking for performance evaluation.
The risk measure, beta is criticised as well. There are two grounds for criticism- first is that irrespective of the investors’ attitude toward risk, beta always has significant positive relationship between with the individual returns which are observed on an average basis, given the market index lying on the positive slope section of the efficient frontier on an ex-post basis. Second, the beta, in particular, non-monotonically depends on the portfolio used to represent the market. Thus, it intuitively confirms that the risk can be relatively measured by the beta (Roll, 1977).
The small firms were found by Banz (1981) to have significantly higher returns (adjusted for risk) in comparison to the large firms. However, this effect of size is nonlinear and not logarithm proportionate to the market. However, there is no theoretical foundation for such an effect as it is unclear that the size is the reason or is it a proxy for reasons unknown. There are several candidates for which size can be the proxy for. One of these candidates, price-earnings ratio was eliminated by Reinganum (1980) as he found that this effect disappears when the impact of size is controlled, however when the impact of price-earnings is controlled the size effect is visible i.e. the P/E serves as the sizes’ proxy, however the reverse is not true. The book-to-market value of equity was found to have a negative relationship with the return by Stattman (1980) and was attributed as a proxy for the effect of the size. Klein & Bawa (1977) examined the impact of size of the firm on returns, and highlighted the information about the subset of securities being insufficient, as a result the investors will not be holding these securities because of their fear of the estimation risk because of the associated uncertainty with the true parameters of the returns. Subsequently, if the information availability with the investors differs, the diversification will be limited to different subsets of all market securities. The limited information availability can be attributed to the size of the firm. As a result, several investors will not find it desirable to hold the stocks of small firms Despite the availability of extensive literature not all the factors are tested so all the limitations are not known.
2.2 Alternatives to CAPM
Several alternatives for the CAPM model are suggested, which can be categorised on the basis of associated risk. The alternatives based on risk assume two conditions- investors being rational and capital markets being perfect. The models developed under this category include multifactor asset pricing models. The alternatives assuming no-risk based assume several conditions like biases in the empirical methodology...