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Decomposition of Disjunctive Linear Programs for Fixed-Income Portfolio Selection

Katherine Wyatt
Ken McAloon

Logic Based Systems Lab
Brooklyn College, CUNY
Brooklyn, NY 11210

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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