Rebalancing an Investment Portfolio in the Presence of Convex Transaction Costs including Market Impact Costs

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Authors:

John E. Mitchell
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
Troy, NY 12180 USA
mitchj at rpi dot edu

Stephen Braun
Warren & Selbert, Inc.
Santa Barbara, CA 93101
brauns2 at alum dot rpi dot edu

Optimization and Software, 28(3), 523-542, 2013.

Abstract:

The inclusion of transaction costs is an essential element of any realistic portfolio optimization. In this paper, we extend the standard portfolio problem to consider convex transaction costs that are incurred to rebalance an investment portfolio. Market impact costs measure the effect on the price of a security that result from an effort to buy or sell the security, and they can constitute a large part of the total transaction costs. The loss to a portfolio from market impact costs is typically modeled with a convex function that can usually be expressed using second order cone constraints. The Markowitz framework of mean-variance efficiency is used. In order to properly represent the variance of the resulting portfolio, we suggest rescaling by the funds available after paying the transaction costs. This results in a fractional programming problem, which can be reformulated as an equivalent convex program of size comparable to the model without transaction costs. An optimal solution to the convex program can always be found that does not discard assets. The results of the paper extend the classical Markowitz model to the case of convex transaction costs in a natural manner with limited computational cost.

Keywords: Portfolio optimization, transaction costs, market impact costs, rebalancing, conic optimization, convex optimization.

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