A Hybrid Optimization and Data-Driven Approach to Understand the Role of the Risk-Aversion Profile Parameter in Portfolio Optimization Problems with Shorting Constraints

This study contributes to the optimization literature with an approach that would help investors understand how the risk-aversion profile hyper-parameter affects both excess returns, risk, and the Sharpe index curves in portfolio optimization problems with shorting constraints. These curves were characterized by examining the original optimization problem and reducing it to a one-dimensional optimization problem. The problem variable was the excess return, and the minimum level of risk is expressed as a function of it. The functional form for the minimum level of risk curve was also proposed, which allows us to determine an analytical expression for the previously mentioned curves. The study provides significant findings for the financial literature as (i) an upper and lower bound for the risk-aversion profile hyper-parameter, (ii) the optimal value for the risk-aversion profile hyper-parameter, (iii) a reduced version of the optimization problem which is easier to solve, and of course, (iv) an analytical expression for the excess return, risk and Sharpe ratio curves as functions of the previously mentioned hyper-parameter. All those findings are reported using the Mean-Squared Variance (MSV) portfolio optimization problem as the baseline model, representing the two objectives of the minimization function of the problem (excess return and risk) in the same unit