Robust Markowitz: Comprehensively maximizing Sharpe ratio by parametric | 您所在的位置:网站首页 › sharp ratio和information ratio › Robust Markowitz: Comprehensively maximizing Sharpe ratio by parametric |
Abstract
Markowitz formulates portfolio selection and calls the optimal solutions as an efficient frontier. Sharpe initiates Sharpe ratio for frontier portfolios' reward to variability. Finance textbooks assume that there exists a line which passes through a risk-free rate and is tangent to an efficient frontier. The tangent portfolio enjoys the maximum Sharpe ratio. However, the assumption is over-simplistic because we prove that other situations exist. For example, Sharpe ratio itself may not be even well-defined. We comprehensively maximize Sharpe ratio. In such an area, this paper contributes to the literature. Specifically, we identify the other situations by parametric-quadratic programming which renders complete efficient frontiers by piecewise-hyperbola structure. Researchers traditionally view efficient frontiers by just isolated points. We accomplish handy formulae, so investors can even manually process them. The COVID-19 pandemic is unleashing crises. Unfortunately, there is quite limited research of portfolio selection for COVID. In such an area, this paper contributes to the practice. Specifically, we originate a counter-COVID measure for stocks and integrate it as a constraint into portfolio-selection models. The maximum-Sharpe-ratio portfolio outperforms stock-market indexes in sample. We launch the models for Dow Jones Industrial Average and discover outperformance out of sample. Keywords: Parametric-quadratic programming, critical-line algorithm, portfolio selection, efficient frontier, Sharpe ratio. Mathematics Subject Classification: Primary: 90C20; Secondary: 91G10.Citation: \begin{equation} \\ \end{equation} |
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