Portfolio Selection with Robust Estimation (original) (raw)

An empirical comparison between robust estimation and robust optimization to mean-variance portfolio

Journal of Modern Applied Statistical Methods, 2017

Mean-variance portfolios constructed using the sample mean and covariance matrix of asset returns perform poorly out-of-sample due to estimation error. Recently, there are two approaches designed to reduce the effect of estimation error: robust statistics and robust optimization. Two different robust portfolios were examined by assessing the outof-sample performance and the stability of optimal portfolio compositions. The performance of the proposed robust portfolios was compared to classical portfolios via expected return, risk, and Sharpe Ratio. The aim is to shed light on the debate concerning the importance of the estimation error and weights stability in the portfolio allocation problem, and the potential benefits coming from robust strategies in comparison to classical portfolios.

Robust Mean-Variance Portfolio Selection

SSRN Electronic Journal, 2000

This paper investigates model risk issues in the context of mean-variance portfolio selection. We analytically and numerically show that, under model misspecification, the use of statistically robust estimates instead of the widely used classical sample mean and covariance is highly beneficial for the stability properties of the mean-variance optimal portfolios. Moreover, we perform simulations leading to the conclusion that, under classical estimation, model risk bias dominates estimation risk bias. Finally, we suggest a diagnostic tool to warn the analyst of the presence of extreme returns that have an abnormally large influence on the optimization results.

Robust optimization approaches for portfolio selection: a comparative analysis

Annals of Operations Research, 2021

Robust optimization (RO) models have attracted a lot of interest in the area of portfolio selection. RO extends the framework of traditional portfolio optimization models, incorporating uncertainty through a formal and analytical approach into the modeling process. Although several RO models have been proposed in the literature, comprehensive empirical assessments of their performance are rather lacking. The objective of this study is to fill in this gap in the literature. To this end, we consider different types of RO models based on popular risk measures and conduct an extensive comparative analysis of their performance using data from the US market during the period 2005–2020. For the analysis, two different robust versions of the mean–variance model are considered, together with robust models for conditional value-at-risk and the Omega ratio. The robust versions are compared against the nominal ones through various portfolio performance metrics, focusing on out-of-sample results.

Robust Portfolio Selection Problems

Mathematics of Operations Research, 2003

In this paper we show how to formulate and solve robust portfolio selection problems. The objective of these robust formulations is to systematically combat the sensitivity of the optimal portfolio to statistical and modeling errors in the estimates of the relevant market parameters. We introduce “uncertainty structures” for the market parameters and show that the robust portfolio selection problems corresponding to these uncertainty structures can be reformulated as secondorder cone programs and, therefore, the computational effort required to solve them is comparable to that required for solving convex quadratic programs. Moreover, we show that these uncertainty structures correspond to confidence regions associated with the statistical procedures employed to estimate the market parameters. Finally, we demonstrate a simple recipe for efficiently computing robust portfolios given raw market data and a desired level of confidence.

Robust portfolios: contributions from operations research and finance

Annals of Operations Research, 2010

In this paper we provide a survey of recent contributions to robust portfolio strategies from operations research and finance to the theory of portfolio selection. Our survey covers results derived not only in terms of the standard mean-variance objective, but also in terms of two of the most popular risk measures, mean-VaR and mean-CVaR developed recently. In addition, we review optimal estimation methods and Bayesian robust approaches.

Robust Optimization Approaches for Portfolio Selection: A Computational and Comparative Analysis

arXiv, 2020

The field of portfolio selection is an active research topic, which combines elements and methodologies from various fields, such as optimization, decision analysis, risk management, data science, forecasting, etc. The modeling and treatment of deep uncertainties for the future asset returns is a major issue for the success of analytical portfolio selection models. Recently, robust optimization (RO) models have attracted a lot of interest in this area. RO provides a computationally tractable framework for portfolio optimization based on relatively general assumptions on the probability distributions of the uncertain risk parameters. Thus, RO extends the framework of traditional linear and non-linear models (e.g., the well-known mean-variance model), incorporating uncertainty through a formal and analytical approach into the modeling process. Robust counterparts of existing models can be considered as worst-case re-formulations as far as deviations of the uncertain parameters from their nominal values are concerned. Although several RO models have been proposed in the literature focusing on various risk measures and different types of uncertainty sets about asset returns, analytical empirical assessments of their performance have not been performed in a comprehensive manner. The objective of this study is to fill in this gap in the literature. More specifically, we consider different types of RO models based on popular risk measures and conduct an extensive comparative analysis of their performance using data from the US market during the period 2005-2016. For the analysis, three different robust versions of the mean-variance model are considered, together with two other robust models for conditional value-at-risk and the omega ratio. The robust versions are compared against standard (non-robust) models through various portfolio performance metrics, focusing on out-of-sample results. The analysis is based on a rolling window approach.

Robust portfolio selection problems: a comprehensive review

Operational Research

In this paper, we provide a comprehensive review of recent advances in robust portfolio selection problems and their extensions, from both operational research and financial perspectives. A multi-dimensional classification of the models and methods proposed in the literature is presented, based on the types of financial problems, uncertainty sets, robust optimization approaches, and mathematical formulations. Several open questions and potential future research directions are identified.

On the Robustness and Sparsity Trade-Off in Mean-Variance Portfolio Selection

SSRN Electronic Journal, 2016

A well-managed portfolio is crucial to an investor's success. Robustness against parameter uncertainty and low trading costs are two desired properties when constructing a portfolio. Robust optimization techniques have been applied to improve the stability of a portfolio under parameter uncertainty. However, portfolios generated from robust procedures often suffer from being over-diversified. Hence, an investor has to hold a multitude of assets and pay a large amount of transaction costs. In this paper, we extend the classical mean-variance framework by incorporating an ellipsoidal uncertainty set and fixed transaction costs which penalize an over-diversified portfolio and promote sparsity. We explore several properties of the optimal portfolio under this model. In particular, we show that it can be approximated by a linear combination of three benchmark portfolios, including the mean-variance portfolio, the minimum-variance portfolio, and a fixed transaction cost induced portfolio. Moreover, we explicitly characterize how the number of traded assets changes by a sensitivity analysis. Our analytical results could help investors to maintain an appropriate trade-off between robustness and sparsity and thus lead to a quantitative interpretation of the so-called diversification paradox.

Robust Portfolio Optimization Using a Simple Factor Model

In this paper we examine the performance of a traditional mean-variance optimized portfolio, where the objective function is the Sharpe ratio. We show results of constructing such portfolios using global index data, and provide a test for robustness of input parameters. We continue by formulating a robust counterpart based on a linear factor model presented here. Using a dynamic universe of stocks, the results for this robust portfolio are contrasted with a naive, evenly weighted portfolio as well as with two traditional Sharpe optimized portfolios. We nd compelling evidence that the robust formulation provides signicant risk protection as well as the ability to provide risk adjusted returns superior to the traditional method. We also nd that the naive portfolio we present outperforms the traditional Sharpe portfolios in terms of many summary metrics.

Robust portfolio optimization with Value-at-Risk-adjusted Sharpe ratios

Journal of Asset Management, 2013

We propose a robust portfolio optimization approach based on Value-at-Risk (VaR) adjusted Sharpe ratios. Traditional Sharpe ratio estimates using a limited series of historical returns are subject to estimation errors. Portfolio optimization based on traditional Sharpe ratios ignores this uncertainty and, as a result, is not robust. In this paper, we propose a robust portfolio optimization model that selects the portfolio with the largest worse-case-scenario Sharpe ratio within a given confidence interval. We show that this framework is equivalent to maximizing the Sharpe ratio reduced by a quantity proportional to the standard deviation in the Sharpe ratio estimator. We highlight the relationship between the VaR-adjusted Sharpe ratios and other modified Sharpe ratios proposed in the literature. In addition, we present both numerical and empirical results comparing optimal portfolios generated by the approach advocated here with those generated by both the traditional and the alternative optimization approaches.