A large CVaR-based portfolio selection model with weight constraints

Abstract

Although the traditional CVaR-based portfolio methods are successfully used in practice, the size of a portfolio with thousands of assets makes optimizing them difficult, if not impossible to solve. In this article we introduce a large CVaR-based portfolio selection method by imposing weight constraints on the standard CVaR-based portfolio selection model, which effectively avoids extreme positions often emerging in traditional methods. We propose to solve the large CVaR-based portfolio model with weight constraints using penalized quantile regression techniques, which overcomes the difficulties of large scale optimization in traditional methods. We illustrate the method via empirical analysis of optimal portfolios on Shanghai and Shenzhen 300 (HS300) index and Shanghai Stock Exchange Composite (SSEC) index of China. The empirical results show that our method is efficient to solve a large portfolio selection and performs well in dispersing tail risk of a portfolio by only using a small amount of financial assets. AbstractAlthough the traditional CVaR-based portfolio methods are successfully used in practice, the size of a portfolio with thousands of assets makes optimizing them difficult, if not impossible to solve. In this article we introduce a large CVaR-based portfolio selection method by imposing weight constraints on the standard CVaR-based portfolio selection model, which effectively avoids extreme positions often emerging in traditional methods. We propose to solve the large CVaR-based portfolio model with weight constraints using penalized quantile regression techniques, which overcomes the difficulties of large scale optimization in traditional methods. We illustrate the method via empirical analysis of optimal portfolios on Shanghai and Shenzhen 300 (HS300) index and Shanghai Stock Exchange Composite (SSEC) index of China. The empirical results show that our method is efficient to solve a large portfolio selection and performs well in dispersing tail risk of a portfolio by only using a small amount of financial assets.

Portfolio Optimization Modelling with R for Enhancing Decision Making and Prediction in Case of Uganda Securities Exchange

“…It is the allocation of capital to the available assets so as to maximize return on the investment and minimize risk (Mayanja et al, 2013). It has been applied by various scholars (Polak et al, 2010;Li et al, 2014;Xu et al, 2016) in finance to generate an understanding how risk may be minimized while profits are maximized. Portfolio Optimization research can be traced to the work of Markowitz (1952), who developed a model to solve the problem of selecting stocks.…”

“…They, therefore, advocated for decision models to come into play. Quantitative and mathematical models have been increasingly applied to decision making and prediction, especially in aspects of business management with highly complex characteristics (Watson & Brown, 1978;Xu, Zhou, Jiang, Yu, & Niu, 2016;Li et al, 2014). Namugaya, Weke, & Charles (2014) employed different univariate Generalized Autoregressive Conditional Heteroscedastic (GARCH) models for modelling stock return volatility on the USE.…”

“…Risk measure is a key research component in portfolio optimization (Xu et al, 2016). Risk is the chance of exposure to adverse consequences of uncertain future events (ACCA, 2017).…”

“…Financial institutions use VaR model to manage risk. Xu et al (2016) used a large CVaR-based method for portfolio selection. Risk management is a subject of interest in finance and management, therefore a comprehensive understanding of portfolio optimization models by Ugandan investors will enable them to assess the performance of stocks listed on the USE and thus preventing wrong investment decisions.…”

“…Portfolio Optimization research can be traced to the work of Markowitz (1952), who developed a model to solve the problem of selecting stocks. Markowitz's mean-variance (MV) model is a quadratic program model, where the variance of each stock is adapted for measuring risk (Xu et al, 2016).…”