Financial Management

CAPM is alive and well : A review and Synthesis

By : Bhaskar Tripathi,

Basic CAPM Model : Synthesis

The Capital Asset Pricing Model is a set of predictions concerning equilibrium expected returns on risky assets. Alpha is the difference between the expected return of the sector fund and the "fair return" for the fund based on its historical responsiveness to market movements. Beta is a measure of the sector funds's responsiveness to market movements.

Introduction Sources:

The CAPM is Alive and Well: A Review and Synthesis1. http://onlinelibrary.wiley.com/doi/10.1111/j.1468-036X.2009.00530.x/full

2. Sector Selection Methodology http://www.alphaprofit.com/mutual-fund-selection.html

3. Modern portfolio theory http://en.wikipedia.org/wiki/Modern_portfolio_theory

AbstractThe first article reinstitutes the investor faith in CAPM model and talks about how CAPM is very closely coupled to the actual investment practices at the ground level. The general criticism of CAPM model that it does not fit empirical asset pricing well cast doubt on the validity of model have been explained. The challenges for CAPM model are also discussed and it is concluded that M-V analysis and the CAPM are in fact, alive and doing well. The article however does not claim that the other alternate theories are wrong.

The second article talks about the sector selection methodology using CAPM basic model and the underlying assumptions.

The third paper details out the modern portfolio theory that attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets.

Summary

The Main Criticisms of M-V Analysis and the CAPM

Modern Portfolio Theory :

Modern portfolio theory (MPT) is a theory of finance which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets. Although MPT is widely used in practice in the financial industry , in recent years the basic assumptions of MPT have been widely challenged by fields such as behavioural economics. 

Criticisms of MPT and CAPM:

Despite its theoretical importance, critics of MPT question whether it is an ideal investing strategy, because its model of financial markets does not match the real world in many ways.Efforts to translate the theoretical foundation into a viable portfolio construction algorithm have been plagued by technical difficulties stemming from the instability of the original optimization problem with respect to the available data. Recent research has shown that instabilities of this type disappear when a regularizing constraint or penalty term is incorporated in the optimization procedure

Criticisms of M-V Analysis and CAPM Model

Empirical criticisms of the Mean Variance and the CAPM

The M-V criterion and the CAPM rely on the Normal distribution assumption. Numerous studies test the goodness of fit of actual rates of return distributions to the Normal distribution. In almost all cases, the null hypothesis asserting that the distribution of rates of return is Normal is strongly rejected; hence, one of the main justifications of the M-V analysis and the CAPM loses ground.

Testing the CAPM directly reveals only minimal support for the expected linear risk-return relationship; in some cases it reveals a strong rejection of the CAPM, when beta reveals almost no explanatory power of the variation in mean returns.

Deriving the M-V efficient set, it is generally found that some of the investment weights of the tangency portfolio are negative. Moreover, as the number of assets increases, it is empirically shown that the percentage of assets corresponding to the tangency portfolio with negative weights approaches 50%. These findings contradict the CAPM because, in order to guarantee equilibrium, the investment weights of the tangency portfolio must all be positive.

Overcoming the Theoretical Criticisms of the CAPMEmperical Validity of CAPM

• Shortly after the theoretical model of the CAPM was published, testing the model empirically was in fashion and was a subject researched by top researchers in finance.

• From these empirical studies, one is tempted to conclude that the CAPM is empirically, questionable, which allegedly drastically reduces its value. Unfortunately, in the empirical studies ex post parameters are employed, simply because the ex ante parameters are unknown.

• The study showed that regardless of the possible measurement errors involved in the measurement of rates of returns, the CAPM cannot be rejected on an ex ante basis

• There are differences between the ex post and the ex ante parameters, and it can be shown that with small changes in the parameters - which take into account these possible differences - the CAPM cannot be rejected.

• Finally, even with the ex post data, the CAPM empirical results are not always negative. Actually, the results depend on the sub-period selected for such testing.

For example: The paper explains that for the ten portfolios ordered by their book to market ratio (B/M), Fama and French (2004) report a negative relationship between average return and beta for the period 1963–2003. However, using the same data, Levy (2008b) reports a strong positive relationship between these two variables for the sub-period 1927-1962 and even a stronger relationship (with 84% explanation power) for the whole period 1927–2007. Thus, even with ex post data, the empirical results remain ambiguous.

Overcoming the Theoretical Criticisms of the CAPM

…Continued

Emperical Validity of CAPM

The CAPM relates to the expected rate of return of each security i and to its risk as follows

where r is the risk-free interest rate and μm is the expected rate of return on the market portfolio. If the CAPM is intact, it is expected that it will not be significantly different from the risk free interest rate and that will not be significantly different from μm− r. Virtually all empirical tests reveal that this is not the case; therefore, the CAPM is rejected

Conclusion :

Based on the above study described in the papers, if we take into account even small possible differences between ex post and ex ante parameters the CAPM cannot be rejected and still holds good for the real time market models.

The article talks about the test conducted named as Levi’s test and shows that CAPM is theoretically valid even when one accepts the BE&P framework and even when expected utility is invalid.

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