End-to-End Risk Budgeting Portfolio Optimization with Neural Networks

TL;DR

This paper introduces an end-to-end neural network framework for portfolio optimization that directly learns asset allocations, improving robustness and performance over traditional two-step methods, especially with embedded asset selection mechanisms.

Contribution

It proposes a novel end-to-end neural network approach combining prediction and optimization for portfolio management, including a model-based method and an asset selection mechanism with stochastic gates.

Findings

Model-based end-to-end approach achieves a Sharpe ratio of 1.16.

Gated end-to-end framework boosts Sharpe ratio to 1.24.

Outperforms traditional risk parity and equal-weight strategies.

Abstract

Portfolio optimization has been a central problem in finance, often approached with two steps: calibrating the parameters and then solving an optimization problem. Yet, the two-step procedure sometimes encounter the "error maximization" problem where inaccuracy in parameter estimation translates to unwise allocation decisions. In this paper, we combine the prediction and optimization tasks in a single feed-forward neural network and implement an end-to-end approach, where we learn the portfolio allocation directly from the input features. Two end-to-end portfolio constructions are included: a model-free network and a model-based network. The model-free approach is seen as a black-box, whereas in the model-based approach, we learn the optimal risk contribution on the assets and solve the allocation with an implicit optimization layer embedded in the neural network. The model-based end-to-end framework provides robust performance in the out-of-sample (2017-2021) tests when maximizing Sharpe ratio is used as the training objective function, achieving a Sharpe ratio of 1.16 when nominal risk parity yields 0.79 and equal-weight fix-mix yields 0.83. Noticing that risk-based portfolios can be sensitive to the underlying asset universe, we develop an asset selection mechanism embedded in the neural network with stochastic gates, in order to prevent the portfolio being hurt by the low-volatility assets with low returns. The gated end-to-end with filter outperforms the nominal risk-parity benchmarks with naive filtering mechanism, boosting the Sharpe ratio of the out-of-sample period (2017-2021) to 1.24 in the market data.