Development of interpretable machine learning algorithms for multi-objective optimization of financial portfolios based on market anomalies

In this work, we apply symbolic regression, an evolutionary algorithm, to factor investing to produce a ranking score for market assets based on a universe of anomalies. The idea is to exploit the explainability of symbolic regression, which evolves a population of equations, to produce a ranking function that can be directly interpreted by a human expert to evaluate the benefits and risks of such a metric. We deployed a Bayesian Optimization process to optimize the numerical variables of the equations obtained by the symbolic regression to achieve better returns and stability. Stationary bootstrap was applied to the fitness function of the model to control the overfitting of the individuals. Additionally, the final population was evaluated using a Superior Predictive Ability Test (SPA test), comparing each individual to all the orders, producing a rank to help evaluate the final solutions. The results show how symbolic regression was able to generalize over market anomalies to produce multiple reliable ranking scores and how Bayesian Optimization was capable of optimizing a ranking score for a multi-objective optimization problem. Results also suggest that it's possible to reduce the complexity of the equation while preserving the quality of the solutions, leaving space to further research.