A probabilistic approach to portfolio selection with risk-aversion coefficients estimated via logistic regression

This work presents a probabilistic risk-aversion approach to portfolio selection that combines a logistic regression-based risk assessment framework with a mixed-integer optimization algorithm with mean semi-absolute deviation (MSAD) as the risk criterion. It allows us to incorporate uncertainty in the portfolio selection analysis as well as performance analysis by Monte Carlo simulation and compares the portfolios with different levels of risk over time instead of applying a deterministic system of selection based on historical data. The technical indicators of the LQ45 index predict the risk-aversion coefficient and can steer the model to the direction of the market. Under cardinality, quantity, and liquidity constraints, seven portfolios constructed from major Indonesian stock indices can be optimized with a Branch-and-Bound method that operates in GEKKO Python. Simulation results on 10,000 runs are taken to give the portfolios probabilistic rankings of return and risk. The probability values computed using the Monte Carlo method are plotted against the sample size to illustrate the convergence behavior of the algorithm. Eventually, to evaluate the robustness of the algorithm, variations in the probability values are examined by adding normally distributed noise into the model input parameters.