Hyperparameter Optimization for Portfolio Selection

Portfolio selection involves a tradeoff between maximizing expected return and minimizing risk. In practice, useful formulations also include various costs and constraints that regularize the problem and reduce the risk due to estimation errors, resulting in solutions that depend on a number of hyperparameters. As the number of hyperparameters grows, selecting their value becomes increasingly important and difficult. In this article we propose a systematic approach to hyperparameter optimization by leveraging recent advances in automated machine learning and multi-objective optimization. We optimize hyperparameters on a train set to yield the best result subject to market-determined realized costs. In applications to singleand multi-period portfolio selection, we show that sequential hyperparameter optimization finds solutions with better return/risk tradeoffs than manual, grid, and random search over hyperparameters using fewer function evaluations. At the same time, the solutions found are more stable from in-sample training to out-of-sample testing, suggesting they are less likely to be extremities that randomly happened to yield good performance in training.