Scaled and stable mean-variance-EVaR portfolio selection strategy with proportional transaction costs

Abstract

This paper studies a portfolio optimization problem with variance and Entropic Value-at-Risk (EVaR) as risk measures. As the variance measures the deviation around the expected return, the introduction of EVaR in the mean-variance framework helps to control the downside risk of portfolio returns. This study utilized the squared l₂-norm to alleviate estimation risk problems arising from the mean estimate of random returns. To adequately represent the variance-EVaR risk measure of the resulting portfolio, this study pursues rescaling by the capital accessible after payment of transaction costs. The results of this paper extend the classical Markowitz model to the case of proportional transaction costs and enhance the efficiency of portfolio selection by alleviating estimation risk and controlling the downside risk of portfolio returns. The model seeks to meet the requirements of regulators and fund managers as it represents a balance between short tails and variance. The practical implications of the findings of this study are that the model when applied, will increase the amount of capital for investment, lower transaction cost and minimize risk associated with the deviation around the expected return at the expense of a small additional risk in short tails.

Keywords:

• Value-at-Risk
• transaction costs
• estimation risk
• portfolio optimization
• scaled and stabilized portfolio
• downside risk

JEL Classification:

• G11
• G2
• O16
• D81

Additional information

Notes on contributors

Ebenezer Fiifi Emire Atta Mills

Ebenezer Fiifi Emire ATTA MILLS is a Researcher and holds a PhD in Financial Mathematics and Actuarial Science from Dalian University of Technology. He holds a Masters degree in Finance from Jiangsu University. His research interests are portfolio optimization, risk modeling and econometrics.

Bo Yu

Bo YU is a Professor in the School of Mathematical Sciences at Dalian University of Technology. His research interests include applied mathematics, numerical mathematics, computational mathematics and optimization.

Jie Yu

Jie YU is a Master student in the School of Mathematical Sciences at Dalian University of Technology. Her research interest includes portfolio optimization and risk management.