Hyperparameter Optimization for Portfolio Selection

Abstract

Portfolio selection involves a trade-off 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, the authors propose a systematic approach to hyperparameter optimization by leveraging recent advances in automated machine learning and multiobjective optimization. They optimize hyperparameters on a train set to yield the best result subject to market-determined realized costs. In applications to single- and multiperiod portfolio selection, they show that sequential hyperparameter optimization finds solutions with better risk–return trade-offs 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.

TOPICS: Portfolio theory, portfolio construction, big data/machine learning

Key Findings

• • The growing number of applications of machine-learning approaches to portfolio selection means that hyperparameter optimization becomes increasingly important. We propose a systematic approach to hyperparameter optimization by leveraging recent advances in automated machine learning and multiobjective optimization.

• • We establish a connection between forecast uncertainty and holding- and trading-cost parameters in portfolio selection. We argue that they should be considered regularization parameters that can be adjusted in training to achieve optimal performance when tested subject to realized costs.

• • We show that multiobjective optimization can find solutions with better risk–return trade-offs than manual, grid, and random search over hyperparameters for portfolio selection. At the same time, the solutions are more stable across in-sample training and out-of-sample testing.