Optimización robusta de portafolios mediante Near Optimal Centering

Abstract

Portfolio optimization is the most used tool by the academy to create investment portfolios; however, the asset management industry has moved away from this tool because it su_ers mainly of two problems: the lack of robustness of portfolio weights that make up the optimal portfolio, due to that these weights are very sensitive to changes in the input parameters; and the tool tends to generate portfolios with extreme weights or poorly diversi_ed portfolios. In the literature, there are several methods that try to solve both problems; in this paper we will discuss six of these methods: resampling, shrinkage, worst case, Black Litterman, risk factors and maximum distance optimization (MDO); and we will also develop a new method called near optimal centering (NOC). The resampling method attempts to obtain more robust portfolios by generating several samples to estimate the input parameters and averaging the weights that result from the optimization process of each sample. The shrinkage method attempts to obtain more robust portfolios by making the estimation of the input parameters more robust. The worst case method attempts to obtain more robust portfolios by stressing the input parameters. The Black Litterman method attempts to obtain more robust portfolios by incorporating the analyst's views into the estimation of the input parameters. The risk factors method attempts to obtain more robust portfolios by basing the estimation of the input parameters on a factor model speci_ed by the analyst. The MDO method attempts to obtain more robust portfolios by exploring the region below the e_cient frontier and _nding near optimal portfolios that are as far apart as possible and then combine them according to the analyst's objectives. Finally, this paper presents the NOC method, which explores the region below the e_cient frontier and de_nes a permissible region as well as the MDO method, and then de_nes the analytical center of this region as the optimal portfolio. This paper seeks to demonstrate the advantages of the NOC method over other optimization methods, for this purpose 35 optimization methods were compared for 4 sample sizes over 81 months. The results of the experiments suggest that the NOC method improves the robustness and diversi_cation properties of the portfolios in a greater proportion compared to other robust optimization methods, without sacri_cing performance levels outside the sample.