An empirical comparison between robust estimation and robust optimization to mean-variance portfolio (original) (raw)

Portfolio Selection with Robust Estimation

Operations Research, 2009

Mean-variance portfolios constructed using the sample mean and covariance matrix of asset returns perform poorly out-of-sample due to estimation error. Moreover, it is commonly accepted that estimation error in the sample mean is much larger than in the sample covariance matrix. For this reason, practitioners and researchers have recently focused on the minimum-variance portfolio, which relies solely on estimates of the covariance matrix, and thus, usually performs better out-of-sample. But even the minimum-variance portfolios are quite sensitive to estimation error and have unstable weights that fluctuate substantially over time. In this paper, we propose a class of portfolios that have better stability properties than the traditional minimum-variance portfolios. The proposed portfolios are constructed using certain robust estimators and can be computed by solving a single nonlinear program, where robust estimation and portfolio optimization are performed in a single step. We show analytically that the resulting portfolio weights are less sensitive to changes in the asset-return distribution than those of the traditional minimum-variance portfolios. Moreover, our numerical results on simulated and empirical data confirm that the proposed portfolios are more stable than the traditional minimum-variance portfolios, while preserving (or slightly improving) their relatively good out-of-sample performance.

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 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.

Adjusted robust mean-value-at-risk model: less conservative robust portfolios

Optimization and Engineering, 2016

We examine the robust mean-VaR portfolio optimization problem when a parametric approach is used for estimating VaR. A robust optimization formulation is used to accommodate estimation risk, and we obtain an analytic solution when there is a risk-free asset and short-selling is allowed. This renders the model computationally tractable. Further, to avoid the conservatism of robust optimal portfolios, we suggest an adjusted robust optimization approach. Empirically, we evaluate the out-of-sample performance of the new approach, the robustness of obtained solutions and level of conservatism of the resulting portfolios. The empirical results highlight some benefits of our approach.

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 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.

Robust Asset Allocation with Benchmarked Objectives

Mathematical Finance, 2010

In this paper, we introduce a new approach for finding robust portfolios when there is model uncertainty. It differs from the usual worst case approach in that a (dynamic) portfolio is evaluated not only by its performance when there is an adversarial opponent ("nature"), * First version (September 2006). † This work is supported in part by an NSF CAREER Award DMI-0348746 (Lim) and the NSF Grant DMI-0500503 (Lim and Shanthikumar). Nevertheless, the opinions, findings, conclusions and recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Support from the NUS-Berkeley Risk Management Institute at the National University of Singapore and the Coleman Fung Chair in Financial Modelling (Lim) is also acknowledged.

Recent developments in robust portfolios with a worst-case approach

Robust models have a major role in portfolio optimization for resolving the sensitivity issue of the classical mean-variance model. In this paper, we survey developments of worst-case optimization while focusing on approaches for constructing robust portfolios. In addition to the robust formulations for the Markowitz model, we review work on deriving robust counterparts for valueat-risk and conditional value-at-risk problems as well as methods for combining uncertainty in factor models. Recent findings on properties of robust portfolios are introduced and we conclude by presenting our thoughts on future research directions.

Stability advances in robust portfolio optimization under parallelepiped uncertainty

Central European Journal of Operations Research, 2017

In financial markets with high uncertainties, the trade-off between maximizing expected return and minimizing the risk is one of the main challenges in modeling and decision making. Since investors mostly shape their invested amounts towards certain assets and their risk aversion level according to their returns, scientists and practitioners have done studies on that subject since the beginning of the stock markets' establishment. In this study, we model a Robust Optimization problem based on data. We found a robust optimal solution to our portfolio optimization problem. This approach includes the use of Robust Conditional Value-at-Risk under Parallelepiped Uncertainty, an evaluation and a numerical finding of the robust optimal portfolio allocation. Then, we trace back our robust linear programming model to the Standard Form of a Linear Programming model; consequently, we solve it by a well-chosen algorithm and software package. Uncertainty in parameters, based on uncertainty in the prices, and a risk-return analysis are crucial parts of this study. A numerical experiment and a comparison (back testing) application are presented, containing real-world data from stock markets as well as a simulation study. Our approach increases the stability of portfolio allocation and reduces the portfolio risk.

CVaR Robust Mean-CVaR Portfolio Optimization

ISRN Applied Mathematics, 2013

One of the most important problems faced by every investor is asset allocation. An investor during making investment decisions has to search for equilibrium between risk and returns. Risk and return are uncertain parameters in the suggested portfolio optimization models and should be estimated to solve the problem. However, the estimation might lead to large error in the final decision. One of the widely used and effective approaches for optimization with data uncertainty is robust optimization. In this paper, we present a new robust portfolio optimization technique for mean-CVaR portfolio selection problem under the estimation risk in mean return. We additionally use CVaR as risk measure, to measure the estimation risk in mean return. To solve the model efficiently, we use the smoothing technique of Alexander et al. (2006). We compare the performance of the CVaR robust mean-CVaR model with robust mean-CVaR models using interval and ellipsoidal uncertainty sets. It is observed that ...