The Relation between Mean-Variance Efficiency and Arbitrage Pricing

The mean-standard deviation diagram has proven to be a valuable tool for understanding equilibrium asset-pricing theory. First introduced by Markowitz (1952, 1959) and Tobin (1958), the diagram helps students and researchers alike to develop intuition about the Capital Asset Pricing Model (CAPM). Its properties are useful for analyzing the conditions under which the market portfolio is mean-variance efficient and for linking the location of the market portfolio in the diagram with the validity of the CAPM. In addition, its simple geometry seems to be the critical inspiration for Roll's (1977) argument that the CAPM cannot feasibly be tested because the market portfolio is unobservable and because of "a mathematical equivalence between the individual return/'beta' linearity relation and the market portfolio's mean-variance efficiency" (p. 129). Recent research on equilibrium asset pricing, both theoretical and empirical, has tended to focus on multibeta pricing models, especially the Arbitrage Pricing Theory (APT). This paper will show that the simple intuition derived from the

[1]  R. C. Merton,et al.  An Analytic Derivation of the Efficient Portfolio Frontier , 1972, Journal of Financial and Quantitative Analysis.

[2]  Gary Chamberlain,et al.  FUNDS, FACTORS, AND DIVERSIFICATION IN ARBITRAGE PRICING MODELS , 1983 .

[3]  Bruce N. Lehmann,et al.  The empirical foundations of the arbitrage pricing theory , 1988 .

[4]  Nai-fu Chen,et al.  Some Empirical Tests of the Theory of Arbitrage Pricing , 1983 .

[5]  Phoebus J. Dhrymes,et al.  A Critical Reexamination of the Empirical Evidence on the Arbitrage Pricing Theory , 1984 .

[6]  Sheridan Titman,et al.  Approximate Factor Structures: Interpretations and Implications for Empirical Tests , 1985 .

[7]  Jonathan E. Ingersoll,et al.  Some Results in the Theory of Arbitrage Pricing , 1984 .

[8]  Stephen J. Brown,et al.  A New Approach to Testing Asset Pricing Models: The Bilinear Paradigm , 1983 .

[9]  R. C. Merton,et al.  AN INTERTEMPORAL CAPITAL ASSET PRICING MODEL , 1973 .

[10]  Richard Roll,et al.  AMBIGUITY WHEN PERFORMANCE IS MEASURED BY THE SECURITIES MARKET LINE , 1978 .

[11]  Stephen A. Ross,et al.  Mutual fund separation in financial theory—The separating distributions , 1978 .

[12]  A. E. Maxwell,et al.  Factor Analysis as a Statistical Method. , 1964 .

[13]  J. Tobin.  Liquidity Preference as Behavior towards Risk , 1958 .

[14]  F. Black.  Capital Market Equilibrium with Restricted Borrowing , 1972 .

[15]  Jay Shanken,et al.  The Arbitrage Pricing Theory: Is It Testable? , 1982 .

[16]  Richard Roll,et al.  A Critique of the Asset Pricing Theory''s Tests: Part I , 1977 .

[17]  M. Rothschild,et al.  Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets , 1982 .

[18]  Gregory Connor,et al.  A Unified Beta Pricing Theory , 1984 .

[19]  Sheridan Titman,et al.  Factor pricing in a finite economy , 1983 .

[20]  S. Ross,et al.  An Empirical Investigation of the Arbitrage Pricing Theory , 1980 .

[21]  Stephen A. Ross,et al.  Yes, The APT Is Testable , 1985 .

[22]  Philip H. Dybvig.  An explicit bound on individual assets' deviations from APT pricing in a finite economy , 1983 .

[23]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .