Factor Dimensionality and the Bias-Variance Tradeoff in Diffusion Portfolio Models

TL;DR

This paper explores how the number of factors in a diffusion model affects asset return prediction and portfolio performance, revealing an optimal factor count that balances bias and variance for better out-of-sample results.

Contribution

It introduces a conditional diffusion model for asset returns and systematically analyzes the impact of factor dimensionality on model bias, variance, and portfolio performance.

Findings

Optimal factor number improves out-of-sample performance.

Too few factors lead to underfitting and diversification.

Too many factors cause overfitting and instability.

Abstract

In this paper, we implement and evaluate a conditional diffusion model for asset return prediction and portfolio construction on large-scale equity data. Our method models the full distribution of future returns conditioned on firm characteristics (i.e.\ factors), using the resulting conditional moments to construct portfolios. We observe a clear bias--variance tradeoff: models conditioned on too few factors underfit and produce overly diversified portfolios, while models conditioned on too many factors overfit, resulting in unstable and highly concentrated allocations with poor out-of-sample performance. Through an ablation over factor dimensionality, we reveal an intermediate number of factors that achieves the best generalization and outperforms baseline portfolio strategies.