Robust Markowitz: Comprehensively maximizing Sharpe ratio by parametric-quadratic programming

Abstract

<p style='text-indent:20px;'>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.</p><p style='text-indent:20px;'>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.</p><p style='text-indent:20px;'>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.</p>