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Optimal Portfolios from Ordering Information

Summary: Optimal Portfolios
from Ordering Information
Robert Almgren
and Neil Chriss
December 10, 2004
Modern portfolio theory produces an optimal portfolio from esti-
mates 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 sim-
ple 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 gen-
eral 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.


Source: Almgren, Robert F. - Courant Institute of Mathematical Sciences, New York University


Collections: Mathematics