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\title{Optimal Portfolios from Ordering Information}
\author{Robert Almgren \\
  University of Toronto}
\date{Computational Finance Seminar, \\
  November 1}


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\begin{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
  \emph{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.
  [Joint work with Neil Chriss, SAC Capital]
\end{abstract}


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