Portfolio optimization: Risk metric with increased objective space - Mendes, Marcos Huber (2021)
Markowitz's efficient EV portfolio model, given a minimum required return, minimizes the portfolio variance, a central trend risk metric calculated by the statistical method of data concentration, and thus uses a literal formula allowing the optimization solution by a quadratic algorithm, requiring little computational consumption. The evolution of the Markowitz model for asymmetric risk metrics, minimizes and/or maximizes risk, below and/or above a target t, such as downside risk, mean-separated target deviations, value at risk and conditional value at risk, however, do not allow the use of a literal formula for the optimization solution, transformed into a non-smooth algorithm, with a complex solution and greater computational consumption. The relevant aspect of the Markowitz model was to show that the most important is not the risk of the asset, but the contribution that each asset provides to the risk of the portfolio, which depends on the interrelationships between the assets, the covariance of the portfolio. Extending the reasoning as an original and relevant contribution, the article presents a new asymmetric risk metric, with greater detail of the interrelationships between assets, increasing the objective space of the optimization, with a greater number of optimized parameters, enabling the search for better results and using a literal expression allowing solution by a non-linear algorithm, less complex than the non-smooth algorithm. The bibliometric analysis carried out demonstrates the originality of the evolution of the Markowitz model for asymmetric risk metrics, presenting a literal formula for solution and with increased objective space.