Using Semidefinite Programming to Rebalance a Portfolio in the Presence of Transaction Costs

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Authors:

Steve Braun and John E. Mitchell
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
Troy, NY 12180 USA
brauns2@alum.rpi.edu and mitchj@rpi.edu

May 20, 2002.

Given at the 7th SIAM Conference on Optimization, Toronto, May 20-23, 2002.

Abstract:

In portfolio optimization, an acceptable balance between risk and reward is desired. Risk is represented by a quadratic objective function and reward by a linear constraint. Transaction costs can be modelled by imposing complementarity requirements on some variable pairs. We describe a semidefinite programming relaxation for the problem of rebalancing a portfolio with transaction costs and use this to develop a heuristic to find good portfolios. Computational results on real-world data sets are given.

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