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The asset pricing implications of the mean-variance approach, the capital asset pricing theory and the arbitrage pricing theory



The asset pricing implications of the mean-variance approach, the capital asset pricing theory and the arbitrage pricing theory

Introduction

Modern asset pricing theories rest on the notion that the expected return of a particular asset depends only on that component of the total risk embodied in it that cannot be diversified away. (Chiarella, 1992) Market equilibrium, by definition, precludes a price system under which diversification earns a reward, and thus, in a world of costless arbitrage, the fundamental question for asset pricing reduces to the identification and measurement of the relevant component of risk that exercises influence on an asset's expected return. (Hommes, 2006) In the capital-asset-pricing model a particular mean-variance efficient portfolio is singled out and used as a formalization of essential risk in the market as a whole, and the expected return of an asset is related to its normalized covariance with this market portfolio—the so-called beta of the asset. (Abel, 2002) The residual component in the total risk of a particular asset, inessential risk, does not earn any reward because it can be eliminated by another portfolio with an identical cost and return but with lower level of risk. On the other hand, in the arbitrage pricing theory a given finite number of factors is used as a formalization of systematic risks in the market as a whole, and the expected return of an asset is related to its exposure to each of these factors, and now summarized by a vector of factor loadings. The reward to the residual component in the return to a particular asset, unsystematic or idiosyncratic risk, can be made arbitrarily small simply by considering portfolios with an arbitrarily large number of assets. (Chiarella, 2002)

Asset Pricing Implications Of The Mean-Variance Approach

The Sharpe-Lintner-Mossin Capital Asset Pricing Model (CAPM) plays a central role in modern finance theory. It is founded on the paradigm of homogeneous beliefs and rational representative agent. However, from the theoretical perspective this paradigm has been criticised on a number of grounds (e.g. Williams (1977), Varian (1985), Detemple and Murthy (1994), Cecchetti et al. (2000), Abel (1989, 2002), Calvet et al. (2004), Jouini and Napp (2006), in particular concerning its extreme assumptions about information of the economic environment and computational ability on the part of the rational representative economic agent. It is found from the empirical literature that (see Harvey (1989) the fundamental CAPM equation that relates expected returns on assets to their portfolio risk is not well supported. For instance the security market line does not have the predicted slope and the measure of portfolio risk, the so-called beta coefficient, is time varying in ways that are not consistent with the theory. There has been some work on extending the mean-variance model to allow for differences in beliefs across agents (see Williams (1977), Varian (1985), Detemple and Murthy (1994) Cecchetti et al. (2000), Abel (1989, 2002), Calvet et ...