On the mean-standard deviation frontier

Abstract

This paper presents a characterization of the meanstandard deviation frontier (MSF) in terms of pricing and averaging securities and explores the geometry of these securities relative to the geometry of the MSF. A summary of already known results is presented along with proof of new results. A measure of the distance between two mean-standard deviation frontiers is presented here. This measure is related to asset pricing models which imply that security prices can be represented by a stochastic discount factor, such as the CAP M (Capital Asset Pricing Model) and the APT (Arbitrage Pricing Theory). An application is given in which the distance between two specific frontiers can be interpreted as a measure of model misspecification.