Robust regression and outlier detection
Robust regression and outlier detection
Computing efficient frontiers using estimated parameters
Annals of Operations Research
An Interior Point Algorithm for Large-Scale Nonlinear Programming
SIAM Journal on Optimization
Robust portfolio selection problems
Mathematics of Operations Research
Robust M-estimation of multivariate GARCH models
Computational Statistics & Data Analysis
Heuristic methods for the optimal statistic median problem
Computers and Operations Research
Robust estimation of efficient mean---variance frontiers
Advances in Data Analysis and Classification
Robust optimization framework for cardinality constrained portfolio problem
Applied Soft Computing
Optimal Allocation of a Futures Portfolio Utilizing Numerical Market Phase Detection
SIAM Journal on Financial Mathematics
Portfolio Selection Using Tikhonov Filtering to Estimate the Covariance Matrix
SIAM Journal on Financial Mathematics
Hybrid Adaptive Large Neighborhood Search for the Optimal Statistic Median Problem
Computers and Operations Research
Computing the Nondominated Surface in Tri-Criterion Portfolio Selection
Operations Research
Regularized robust optimization: the optimal portfolio execution case
Computational Optimization and Applications
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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, 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. However, 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 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.