On the mean-standard deviation frontier

Abstract

This paper presents a characterization of the mean standard 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 CAPM (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.