On High-Dimensional Markowitz Mean-Variance Optimized Portfolio

• Activity Number: 337
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Saswata Sahoo*+ and Soumendra Lahiri
• Companies: North Carolina State University and North Carolina State University
• Keywords: Markowitz portfolio problem ; tapered covariance estimator ; Risk ; sparsity ; high dimension

Abstract

We consider the limit distributions associated to the optimized risk of Markowitz mean variance optimized high dimensional portfolio. We plug the minimax optimal tapered covariance estimator proposed by Cai, Zhang and Zhou(2010) in the solution of the optimal portfolio problem. Under growing number of assets in the portfolio, sparse characterization of the asset cross-covariance matrix and under suitable temporal dependence of asset returns we derive the limit distribution of the appropriately scaled and centered version of the estimators of the optimal portfolio risk. Out of sample performance of the estimators and finite sample properties of the confidence interval are studied using simulated data and real data.