Simplifying and generalizing some efficient frontier and CAPM related results

Abstract

This paper simplifies, generalizes, extends, surveys and unifies results related to the efficient frontier in portfolio analysis and to asset pricing formulations of the Capital Asset Pricing Model (CAPM) type. It derives the composition and properties of many central portfolios in portfolio analysis. It also discusses and provides several CAPM type formulations involving different portfolios. In particular, the tangency portfolio properties are presented in an instructive and very simple way, focusing on similarities in going from the global minimum variance portfolio via a null index portfolio whose zero beta portfolio has a zero expected return. The Non-frontier zero beta, the Null index and the Augmented frontier CAPM versions supplement standard CAPM formulations. More importantly, the GMVP and the Benchmark versions of the CAPM do not rely on any zero beta portfolio, but require two betas.