Optimal Portfolios from Ordering Information

Abstract

Modern portfolio theory produces optimal portfolios from estimates of expected returns and a covariance matrix. Such optimal portfolios are efficient portfolios, that is they provide the maximum level of expected return for a given level of risk. We present a method for portfolio selection based on replacing expected returns with ordering information, that is, with information about the order of the expected returns. Such information may arise in a variety of ways including from firm characteristics or past price history. We extend Markowitz' notion of an efficient portfolio by introducing a preference relation on the set of possible portfolios and defining an efficient portfolio as one which is most preferable among those with a given level of risk. The preference relation we define is simple and economically rational. The optimal portfolios thus derived are theoretically superior all other possible portfolios and return Markowitz optimal portfolios in the case where expected returns are known. We provide efficient numerical algorithms for constructing optimal portfolios within this framework. The formulation is very general and works equally well in cases where assets are divided into multiple sectors or where there are multiple sorting criteria. Using both real and simulated data, we demonstrate that not only are the methods herein theoretically superior but in practice they produce dramatic improvement over simpler portfolio construction techniques.