Stable Portfolio Selection Strategy for Mean-Variance-CVaR Model under High-Dimensional Scenarios

Yu Shi,Fengwei Jiang,Xia Zhao,Yipin Zhu

doi:10.1155/2020/2767231

Abstract

This paper aims to study stable portfolios with mean-variance-CVaR criteria for high-dimensional data. Combining different estimators of covariance matrix, computational methods of CVaR, and regularization methods, we construct five progressive optimization problems with short selling allowed. The impacts of different methods on out-of-sample performance of portfolios are compared. Results show that the optimization model with well-conditioned and sparse covariance estimator, quantile regression computational method for CVaR, and reweighted L1 norm performs best, which serves for stabilizing the out-of-sample performance of the solution and also encourages a sparse portfolio.

Highlights

Mean-risk models are widely used and play an important role in financial risk management. e classical and revolutionary work is mean-variance (MV) optimization model proposed by Markowitz [1], in which variance is used to measure risk
We focus on smoothly clipped absolute deviation (SCAD) penalty proposed by Fan et al [36] and reweighted L1 norm penalty proposed by Emmanuel et al [37], since they have oracle properties
We will calculate simulation results based on the five optimization problems, respectively, and give the comparisons from the point view of the out-of-sample performance

Summary

Introduction

Mean-risk models are widely used and play an important role in financial risk management. e classical and revolutionary work is mean-variance (MV) optimization model proposed by Markowitz [1], in which variance is used to measure risk. Mean-risk models are widely used and play an important role in financial risk management. E classical and revolutionary work is mean-variance (MV) optimization model proposed by Markowitz [1], in which variance is used to measure risk. Kolm et al [2] review the development, challenges, and trends of MV optimization problems in recent six decades. Considering different risk measures focus on different characteristics of risk, some risk measures other than variance are incorporated into the mean-risk framework. Konno and Yamazaki [3] and Ogryczak and Ruszczynski [4] use absolute deviation and semideviation to measure risk, respectively, and construct mean-risk model for portfolio selection. Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) have been employed as the risk measure to conduct asset allocation (see Consigli [5], Alexander and Baptista [6], Xu et al [7], and Quaranta and Zaffaroni [8] for more details)

Methods

Results

Discussion

Conclusion