General Theory of Portfolio Efficiency

The mean-variance analysis produces optimal portfolio choices for individual investors taking asset prices and payoff distributions as given and forms the foundation for the Capital Asset Pricing Model (CAPM). However, the strong assumptions under which it holds reduce its validity to some particular cases. In this work, we illustrate an alternative approach, called distributional analysis, to determinate and evaluate portfolio efficiency that holds in general because it considers the entire cumulative probability distribution function of returns. It is based on the price characterization of efficiency that arises from embedding the portfolio problem into the standard concave programming one. In addition, it generates the Payoff Distribution Pricing Model (PDPM) that allows to analyze the market equilibrium without suffering from the limitations that affect the CAPM. We give also an empirical application of this theory.