##
Rebalancing an Investment Portfolio in the Presence of Transaction
Costs

**Note:**
This paper has been superseded by our paper on
"Rebalancing an Investment Portfolio
in the Presence of Convex Transaction Costs".

**Download the paper**:

### Authors:

**John E. Mitchell**

Department of Mathematical Sciences

Rensselaer Polytechnic Institute

Troy, NY 12180 USA

mitchj@rpi.edu
**Stephen Braun**

Warren & Selbert, Inc.

Santa Barbara, CA 93101

brauns2@alum.rpi.edu

### November 28, 2002. Revised December 16, 2003.

### Abstract:

The inclusion of transaction costs is an essential element of any realistic portfolio optimization. In this paper, we consider an
extension of the standard portfolio problem in which linear transaction costs are incurred to rebalance an investment portfolio. The Markowitz
framework of mean-variance efficiency is used with costs modelled as a percentage of the value transacted. Each security in the
portfolio is represented by a pair of continuous decision variables corresponding to the amounts bought and sold.
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 quadratic programming problem.
We show that this fractional quadratic programming problem has a structure
that allows it to be reformulated as an equivalent
quadratic programming problem of size comparable to the model without transaction costs.
Theoretically, one way to reduce the measure of risk is to buy and sell the same security, which is not
an attractive practical strategy.
We show that an optimal solution to the quadratic programming reformulation
can always be found that does not simultaneously buy and sell a single security.
The results of the paper extend the classical Markowitz model to the case of proportional
transaction costs in a natural manner with limited computational cost.
Computational results for two empirical datasets are discussed.
Keywords:
Portfolio optimization, transaction costs, rebalancing, quadratic programming.

**Download the paper**:

**Optimization Online listing**

**Note:**
This paper has been superseded by our paper on
"Rebalancing an Investment Portfolio
in the Presence of Convex Transaction Costs".

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