Train a neural network on historical ETF returns and volatilities, optimizing risk budgeting via Sharpe ratio, rebalancing monthly with weights from the output layer for a 7-ETF universe.
ASSET CLASS: ETFs | REGION: Global | FREQUENCY:
Monthly | MARKET: bonds, commodities, equities | KEYWORD: Risk Budgeting, Neural Network
I. STRATEGY IN A NUTSHEL
The strategy trades ETFs (VTI, IWM, AGG, LQD, MUB, DBC, GLD) from 2011–2021. A feedforward neural network with historical returns/volatility inputs, two hidden layers (Leaky ReLU + Softmax), and a convex optimization layer allocates risk dynamically. A stochastic gate selects which assets enter the optimization. The network is retrained every 25 days with a 150-day lookback and optimized for Sharpe ratio. Portfolios are rebalanced monthly based on output weights.
II. ECONOMIC RATIONALE
The approach addresses parameter estimation and dynamic allocation using nonlinear learning, similar to a Reinforcement Learning agent. The network adapts to asset characteristics, adjusting risk budgets automatically, and filtering out unsuitable assets via stochastic gates. This mimics an experienced portfolio manager, enabling efficient, data-driven portfolio optimization without manual intervention.
III. SOURCE PAPER
End-to-End Risk Budgeting Portfolio Optimization with Neural Networks [Click to Open PDF]
Uysal, Sinem, Princeton University – Department of Operations Research & Financial Engineering (ORFE); Li, Xiaoyue, Princeton University – Department of Operations Research & Financial Engineering (ORFE); Mulvey, John M., Princeton University – Bendheim Center for Finance
<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 perfor- mance 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 port- folios 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.
IV. BACKTEST PERFORMANCE
| Annualised Return | 12.33% |
| Volatility | 8.84% |
| Beta | N/A |
| Sharpe Ratio | 1.24 |
| Sortino Ratio | N/A |
| Maximum Drawdown | -15.07% |
| Win Rate | N/A |
