TABLE OF CONTENTS This section studies portfolio selection from asset ordering information. We construct portfolios which, by analogy with modern portfolio theory (MPT), are efficient in the sense that they are maximally preferable to a rational investor for a fixed level of variance. The challenge in this section is to define a mathematically coherent economically sensible definition of preferable and maximally preferable. To do this requires appealing to the mathematics of convex optimization, and in particular the structure of convex cones. As a complete exposition of this subject is beyond the scope of this chapter, we refer readers to Boyd and Vandenberghe (2004) for details.
In MPT investors start with two sets of probability beliefs, concerning the first two moments of the return distributions of the stocks in their universe, and seek to find efficient portfolios that provide the maximum level of expected return for a given level of variance. In our setting these expected return beliefs are replaced by ordering beliefs whereby an investor has a set of beliefs about the order of the expected returns of a universe of assets.
We summarize the portfolio selection procedure in this section as follows. We start with a universe of stocks, a portfolio sort and a budget constraint set. A portfolio sort is information about an investor s belief as to the order of expected returns. This may be in the form of a complete or partial sort, and may possibly contain more than one sort.
