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DeePM: Regime-Robust Deep Learning for Systematic Macro Portfolio Management

Kieran Wood, Stephen J. Roberts, Stefan Zohren

TL;DR

DeePM (Deep Portfolio Manager), a structured deep-learning macro portfolio manager trained end-to-end to maximize a robust, risk-adjusted utility, demonstrates structural resilience across the 2010s"CTA (Commodity Trading Advisor) Winter" and the post-2020 volatility regime shift.

Abstract

We propose DeePM (Deep Portfolio Manager), a structured deep-learning macro portfolio manager trained end-to-end to maximize a robust, risk-adjusted utility. DeePM addresses three fundamental challenges in financial learning: (1) it resolves the asynchronous "ragged filtration" problem via a Directed Delay (Causal Sieve) mechanism that prioritizes causal impulse-response learning over information freshness; (2) it combats low signal-to-noise ratios via a Macroeconomic Graph Prior, regularizing cross-asset dependence according to economic first principles; and (3) it optimizes a distributionally robust objective where a smooth worst-window penalty serves as a differentiable proxy for Entropic Value-at-Risk (EVaR) - a window-robust utility encouraging strong performance in the most adverse historical subperiods. In large-scale backtests from 2010-2025 on 50 diversified futures with highly realistic transaction costs, DeePM attains net risk-adjusted returns that are roughly twice those of classical trend-following strategies and passive benchmarks, solely using daily closing prices. Furthermore, DeePM improves upon the state-of-the-art Momentum Transformer architecture by roughly fifty percent. The model demonstrates structural resilience across the 2010s "CTA (Commodity Trading Advisor) Winter" and the post-2020 volatility regime shift, maintaining consistent performance through the pandemic, inflation shocks, and the subsequent higher-for-longer environment. Ablation studies confirm that strictly lagged cross-sectional attention, graph prior, principled treatment of transaction costs, and robust minimax optimization are the primary drivers of this generalization capability.

DeePM: Regime-Robust Deep Learning for Systematic Macro Portfolio Management

TL;DR

DeePM (Deep Portfolio Manager), a structured deep-learning macro portfolio manager trained end-to-end to maximize a robust, risk-adjusted utility, demonstrates structural resilience across the 2010s"CTA (Commodity Trading Advisor) Winter" and the post-2020 volatility regime shift.

Abstract

We propose DeePM (Deep Portfolio Manager), a structured deep-learning macro portfolio manager trained end-to-end to maximize a robust, risk-adjusted utility. DeePM addresses three fundamental challenges in financial learning: (1) it resolves the asynchronous "ragged filtration" problem via a Directed Delay (Causal Sieve) mechanism that prioritizes causal impulse-response learning over information freshness; (2) it combats low signal-to-noise ratios via a Macroeconomic Graph Prior, regularizing cross-asset dependence according to economic first principles; and (3) it optimizes a distributionally robust objective where a smooth worst-window penalty serves as a differentiable proxy for Entropic Value-at-Risk (EVaR) - a window-robust utility encouraging strong performance in the most adverse historical subperiods. In large-scale backtests from 2010-2025 on 50 diversified futures with highly realistic transaction costs, DeePM attains net risk-adjusted returns that are roughly twice those of classical trend-following strategies and passive benchmarks, solely using daily closing prices. Furthermore, DeePM improves upon the state-of-the-art Momentum Transformer architecture by roughly fifty percent. The model demonstrates structural resilience across the 2010s "CTA (Commodity Trading Advisor) Winter" and the post-2020 volatility regime shift, maintaining consistent performance through the pandemic, inflation shocks, and the subsequent higher-for-longer environment. Ablation studies confirm that strictly lagged cross-sectional attention, graph prior, principled treatment of transaction costs, and robust minimax optimization are the primary drivers of this generalization capability.
Paper Structure (94 sections, 5 theorems, 63 equations, 6 figures, 4 tables, 1 algorithm)

This paper contains 94 sections, 5 theorems, 63 equations, 6 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Decision Problem and Implementation Constraints
  3. Our Approach: Structured Deep Portfolio Management
  4. Contributions.
  5. Paper roadmap
  6. Related Literature
  7. Deep Learning for Systematic Trend
  8. Machine Learning for Portfolio Construction under Frictions
  9. Cross-Sectional Modeling with Attention and Representation Learning
  10. Graph Priors and Economic Structure
  11. Robust Objectives and Risk Measures
  12. Problem Setup and Data
  13. Universe and Decision Protocol
  14. Portfolio Returns and Frictions
  15. Features and Preprocessing
  16. ...and 79 more sections

Key Result

Proposition B.1

Let $\bm{p}_{0:L}$ be a sequence of portfolio position vectors with $\bm{p}_t\in\mathbb{R}^N$. Assume the scaling vectors satisfy $\bm{v}_t \in \mathbb{R}^N_{+}$ and are exogenous (i.e., do not depend on $\bm{p}$). Define Then $\mathcal{C}(\bm{p})$ is convex in $\bm{p}_{0:L}$.

Figures (6)

  • Figure 1: The DeePM pipeline. (1) Temporal: Per-asset history is processed via a hybrid backbone. (2) Cross-Sectional: Assets attend to the global state using a causal Directed Delay. (3) Structural/Topological: Latent embeddings are refined via a Macro-Graph GNN. (4) Objective: The network minimizes a robust loss combining pooled Net Sharpe and a worst-window SoftMin penalty.
  • Figure 2: Visualizing the Distributionally Robust Objective. This figure illustrates the mechanics of the SoftMin penalty using a synthetic mixture model (85% Normal regime $\mathcal{N}(1.0, 0.9^2)$, 15% Crisis regime $\mathcal{N}(-2.0, 1.4^2)$). Panel A demonstrates the implicit distribution shift: while the empirical history $P$ (grey) has a positive mean ($+0.55$), the adversarial reweighting $Q$ (red) shifts probability mass to the left tail, resulting in a significantly lower robust utility ($-4.37$). This effective "hallucination" of a harsher environment forces the optimizer to prioritize survival in worst-case regimes. Panel B displays the corresponding gradient weight function $q_b \propto \exp(-\mathrm{SR}_b/\tau)$. The exponential decay ensures that "easy" high-Sharpe windows contribute near-zero gradient signal (Complacency), while "hard" negative-Sharpe windows dominate the parameter updates (Panic), effectively implementing a differentiable minimax curriculum.
  • Figure 3: The Macro-Structural Prior Graph used to regularize cross-sectional attention. Edges encode deterministic economic linkages rather than data-driven correlations.
  • Figure 4: The Ragged Filtration Problem. The timeline illustrates the asynchrony of global closes relative to the portfolio decision time $t$ (Europe Close). A Cascading Filtration (red dashed arrow) utilizes the most recent data (in our case we only use close data, but an open could be used), maximizing freshness. DeePM's Directed Delay (blue solid arrow) strictly lags cross-sectional attention to $t-1$, enforcing a robust causal gap to isolate predictive impulse-responses.
  • Figure 5: Cumulative net-of-cost wealth growth for DeePM variants versus standard systematic baselines (2010--2025). The y-axis utilizes a logarithmic scale to properly visualize long-term compounding differences.
  • ...and 1 more figures

Theorems & Definitions (10)

  • Proposition B.1: Convexity of Turnover Cost
  • proof
  • Corollary B.2: Ensembling Reduces Cost (Executed Mean Policy)
  • proof
  • Proposition B.3: Optimal Penalty Decreases with Ensemble Size
  • Lemma B.4: Sufficient condition for an interior optimizer on $(0,1)$
  • proof
  • proof : Proof of Proposition
  • Proposition D.1: Gibbs / Donsker--Varadhan variational principle (discrete)
  • proof