Robust optimization of the investment portfolio under uncertainty conditions

Abstract

© 2019, Dorma Journals. All rights reserved. Of the goal of this study is to investigate the assessment of expected return parameters µ and return covariance matrices Σ in modern portfolio investment tasks. These parameters are used in almost all modern portfolio investment models, including the classic mean-variance Markowitz model, Black-Litterman model, “smart ”models. In practice, they are difficult to evaluate correctly, since the parameter values change every day. However, the quality of investment portfolio depends precisely on these parameters. The quality of investment portfolio is understood as a combination of risk and profitability parameters. Number of methodologies are used in this article to reduce the uncertainty of these parameters. The main idea of these methods is to reduce the sensitivity of resulting optimal portfolios to uncertain input parameters. In other words, if the parameter values µ and Σ change slightly, the final portfolio shall not radically change its structure. According the results gained in this article, one asset will not be able to dominate the final portfolio. Chopra offers using the James-Stein estimate for the expected averages, while Black and Litterman use the Bayesian estimate µ and Σ (taking into account the expert opinions). There are also selection methods and scenarios that are described in detail, for example, in. Of all these methods, the Black-Litterman model is most often used in practice.