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Katherine Wyatt
Ken McAloon
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Logic Based Systems Lab
Brooklyn College, CUNY
Brooklyn, NY 11210
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wyatt@sci.brooklyn.cuny.edu
mcaloon@sci.brooklyn.cuny.edu
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ABSTRACT:

Structural requirements for optimal fixed-income portfolios can be
modeled with * disjunctive constraints; e.g.,* a minimum
trade requirement is "either the holding in asset *j* equals zero
or the holding in asset *j* is at least the minimum." The
complexity of quadratic programs makes adding disjunctions to a
traditional mean-variance model computationally prohibitive. However, if
absolute deviation is used to measure dispersion of returns instead of
variance, then structural requirements can be added to a portfolio
selection model with linear constraints and a linear objective
function. Absolute deviation models produce *step-shaped* programs
that can be decomposed into smaller
linear programs that share a set of constraints. When logical
(disjunctive) constraints are added to an absolute deviation model,
the resulting programs are disjunctive linear programs that
inherit the step shape of the model. We show that these programs can be
solved by combining decomposition and branch-and-bound search;
the decomposition technique provides a test for local, and in some
cases global, optimality. We consider here a model that selects the
portfolio that maximizes the trade-off between expected total
(horizon) return and expected absolute deviation from a benchmark
on scenarios of interest rate movements.

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