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Signature-Informed Transformer for Asset Allocation

Yoontae Hwang, Stefan Zohren

TL;DR

The paper addresses robust multi-asset allocation by replacing the traditional forecast-then-optimizer pipeline with an end-to-end approach called the Signature-Informed Transformer (SIT). SIT employs path signatures to capture rich pathwise geometry and a signature-augmented attention to encode lead–lag relationships, with training guided directly by a portfolio-focused risk objective, specifically CVaR. Empirical results on daily S&P 100 data demonstrate that SIT outperforms both traditional strategies and predictive baselines, including many deep-learning forecast models, while remaining robust to realistic transaction costs and allocation concentration. The work highlights the importance of aligning representation, interaction biases, and objective with the portfolio task, and suggests avenues for extending the framework to broader, higher-frequency, or global asset markets.

Abstract

Robust asset allocation is a key challenge in quantitative finance, where deep-learning forecasters often fail due to objective mismatch and error amplification. We introduce the Signature-Informed Transformer (SIT), a novel framework that learns end-to-end allocation policies by directly optimizing a risk-aware financial objective. SIT's core innovations include path signatures for a rich geometric representation of asset dynamics and a signature-augmented attention mechanism embedding financial inductive biases, like lead-lag effects, into the model. Evaluated on daily S\&P 100 equity data, SIT decisively outperforms traditional and deep-learning baselines, especially when compared to predict-then-optimize models. These results indicate that portfolio-aware objectives and geometry-aware inductive biases are essential for risk-aware capital allocation in machine-learning systems. The code is available at: https://github.com/Yoontae6719/Signature-Informed-Transformer-For-Asset-Allocation

Signature-Informed Transformer for Asset Allocation

TL;DR

The paper addresses robust multi-asset allocation by replacing the traditional forecast-then-optimizer pipeline with an end-to-end approach called the Signature-Informed Transformer (SIT). SIT employs path signatures to capture rich pathwise geometry and a signature-augmented attention to encode lead–lag relationships, with training guided directly by a portfolio-focused risk objective, specifically CVaR. Empirical results on daily S&P 100 data demonstrate that SIT outperforms both traditional strategies and predictive baselines, including many deep-learning forecast models, while remaining robust to realistic transaction costs and allocation concentration. The work highlights the importance of aligning representation, interaction biases, and objective with the portfolio task, and suggests avenues for extending the framework to broader, higher-frequency, or global asset markets.

Abstract

Robust asset allocation is a key challenge in quantitative finance, where deep-learning forecasters often fail due to objective mismatch and error amplification. We introduce the Signature-Informed Transformer (SIT), a novel framework that learns end-to-end allocation policies by directly optimizing a risk-aware financial objective. SIT's core innovations include path signatures for a rich geometric representation of asset dynamics and a signature-augmented attention mechanism embedding financial inductive biases, like lead-lag effects, into the model. Evaluated on daily S\&P 100 equity data, SIT decisively outperforms traditional and deep-learning baselines, especially when compared to predict-then-optimize models. These results indicate that portfolio-aware objectives and geometry-aware inductive biases are essential for risk-aware capital allocation in machine-learning systems. The code is available at: https://github.com/Yoontae6719/Signature-Informed-Transformer-For-Asset-Allocation

Paper Structure

This paper contains 28 sections, 5 theorems, 40 equations, 3 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related works
  3. Deep Learning in Asset Allocation
  4. Transformer-Based Time Series Forecasting
  5. Path Signatures in Time Series and Finance
  6. Methodology
  7. Preliminaries
  8. Notations.
  9. Problem Formulation.
  10. Signature-Informed Transformer (SIT)
  11. Signature Embeddings.
  12. Signature-Informed Self-Attention.
  13. Training Strategy
  14. Experiment
  15. Implementation details
  16. ...and 13 more sections

Key Result

Theorem 3.1

Let $\mathbf{X}_t = (X^1_t, X^2_t)$ for $t \in [0, T]$ satisfy a strict lead-lag structure of Definition def:lead-lag. Then the second-level signature cross-term is strictly positive. In particular, $\mathcal{A}(\mathbf{X}) > 0$.

Figures (3)

  • Figure 1: A depiction of flawed deep learning strategies for asset allocation.
  • Figure 2: Overview of the Signature-Informed Transformer (SIT) architecture.
  • Figure 3: Sharpe ratio sensitivity to transaction costs and allocation concentration ($\tau$). Values are mean ($\pm$ std). Left: 40 assets Right: 50 assets.

Theorems & Definitions (11)

  • Theorem 3.1: Strict Lead-Lag Implies Positive Second-Order Signature
  • proof
  • Theorem 3.2: Positive directional derivative of attention weight
  • proof
  • Definition B.1
  • Theorem B.2
  • proof
  • Theorem B.3: Positive directional derivative of attention weight
  • proof
  • Theorem D.1: HF dominates PF in CVaR
  • ...and 1 more