TABLE OF CONTENTS Robert Almgren and Neil Chriss
Abstract
Modern portfolio theory produces an optimal portfolio from estimates of expected returns and a covariance matrix. We present a method for portfolio optimization based on replacing expected returns with sorting criteria that is, with information about the order of the expected returns but not their values. We give a simple and economically rational definition of optimal portfolios that extends Markowitz definition in a natural way; in particular, our construction allows full use of covariance information. We give efficient numerical algorithms for constructing optimal portfolios. This formulation is very general and is easily extended to more general cases, where assets are divided into multiple sectors or there are multiple sorting criteria available, and may be combined with transaction cost restrictions. Using both real and simulated data, we demonstrate dramatic improvement over simpler strategies.
This chapter presents a framework for portfolio selection when an investor possesses information about the order of expected returns in the cross-section of stocks, but not the values of the expected returns. Even in the simplest case of a complete ordering, there has previously been no rational way to form an optimal portfolio that makes full use of covariance information; for the first time we give a complete solution to this important problem.
In general, ordering information may be any set of inequality beliefs about the expected returns, such as the order of expected returns across all stocks, sorts within sectors or other subdivisions, decile rankings, sorts with...
