Optimization Models for Equity Portfolio Management
Sebastián Ceria

Over 50 years have elapsed since Markowitz first introduced his Nobel Prize winning work on mean-variance portfolio optimization that led to the field now known as Modern Portfolio Theory (MPT). Throughout this time, MPT has withstood challenges from skeptics at both academic and financial institutions. Today, MPT is still widely accepted as a theoretical framework, but its employment by investment professionals as the main tool for portfolio construction is not as ubiquitous as we might expect. There are several reasons for the lack of acceptance of MPT among practitioners, but perhaps the most significant is the argument that “optimal” portfolios generated through the MPT process are unintuitive, inexplicable and hard to “implement”.

 First, practitioners argue that “optimal'' portfolios are very sensitive to small changes in input data, in fact, mean-variance optimizers are sometimes referred to as "error maximizers". Even slight changes to the expected returns or risk estimates can produce vastly different mean-variance optimized portfolios. The high sensitivity to input data creates a problem for the portfolio manager because of the effect that these errors might have on the optimal trade-offs between expected returns (which are uncertain) and implementation costs (which are real), such as trading costs and tax liabilities. Second, practitioners complain about the fact that MPT does not take into account many issues that are relevant when building and trading realistic portfolios. These include limits on the number of positions, minimum thresholds, transaction costs and market impact, multiple portfolio tracking, etc.

In this talk, we will describe how modern optimization techniques can help overcome all of the issues that "traditional" mean-variance optimizers face in practical portfolio management. In particular, we will discuss Robust optimization, an optimization framework that considers estimation and model error in the input parameters directly and explicitly in the optimization problem itself. We will demonstrate how Robust Mean Variance Optimization(TM) can be used to significantly reduce the error-maximization property found in classical mean-variance optimizers.