Optimal mean-variance portfolio selection using Cauchy-Schwarz maximization

Fund managers highly prioritize selecting portfolios with a high Sharpe ratio. Traditionally, this task can be achieved by revising the objective function of the Markowitz mean-variance portfolio model and then resolving quadratic programming problems to obtain the maximum Sharpe ratio portfolio. This study presents a closed-form solution for the optimal Sharpe ratio portfolio by applying Cauchy-Schwarz maximization and the concept of Kuhn-Tucker conditions. An empirical example is used to demonstrate the efficiency and effectiveness of the proposed algorithms. Moreover, the proposed algorithms can also be used to obtain the optimal portfolio containing large numbers of securities, which is not possible, or at least is complicated via traditional quadratic programming approaches.