Z-score vs minimum variance preselection methods for constructing small portfolios


By Francesco Cesarone, Fabiomassimo Mango, Gabriele Sabato

Abstract

Several contributions in the literature argue that a significant in-sample risk reduction can be obtained by investing in a relatively small number of assets in an investment universe. Furthermore, selecting small portfolios seems to yield good out-of-sample performances in practice. This analysis provides further evidence that an appropriate preselection of the assets in a market can lead to an improvement in the portfolio performance. For preselection this paper investigates the effectiveness of a minimum variance approach and that of an innovative index (the new Altman Z-score) based on the creditworthiness of the companies. Different classes of portfolio models are examined on real-world data by applying both the minimum variance and the Z-score preselection methods. Preliminary results indicate that the new Altman Z-score preselection provides encouraging out-of-sample performances with respect to those obtained with the minimum variance approach.

Introduction

The issue of constructing small portfolios is a well-known problem in the financial industry, particularly in the case of small investors, who should stem costs due to complexity of management. However, also big investors could take advantage from this practice if small portfolios can achieve better performance than large portfolios. This analysis provides further evidence that an appropriate preselection of the assets in a market can lead to an important improvement in the portfolio performance. More precisely, this paper investigates the effectiveness of the Z-Score index for preselecting assets of an investment universe compared with that achieved by the minimum variance approach. The Z-score is a predictive index of creditworthiness expressed as a numerical score, which essentially measures the default probability of a company. It is used here to classify the quality of a company and its out-of-sample performance in terms of market price. Different classes of portfolio models are examined on real-world data by applying both the minimum variance and the Z-score preselection methods. Preliminary results show that the new Altman Z-score method produces encouraging out-of-sample performances with respect to those obtained with the minimum variance approach.