Same Error, Different Function: The Optimizer as an Implicit Prior in Financial Time Series

TL;DR

This paper demonstrates that in financial time series modeling, different training procedures with similar test errors can produce models with significantly different functional behaviors, impacting decision-making and portfolio strategies.

Contribution

It reveals that optimizer choice acts as an implicit prior in underspecified neural networks, affecting model functions and decision outcomes beyond standard accuracy metrics.

Findings

Different training pipelines yield qualitatively different functions.

Predictive accuracy remains stable despite functional divergences.

Portfolio turnover varies significantly at similar Sharpe ratios.

Abstract

Neural networks applied to financial time series operate in a regime of underspecification, where model predictors achieve indistinguishable out-of-sample error. Using large-scale volatility forecasting for S$\&$P 500 stocks, we show that different model-training-pipeline pairs with identical test loss learn qualitatively different functions. Across architectures, predictive accuracy remains unchanged, yet optimizer choice reshapes non-linear response profiles and temporal dependence differently. These divergences have material consequences for decisions: volatility-ranked portfolios trace a near-vertical Sharpe-turnover frontier, with nearly $3\times$ turnover dispersion at comparable Sharpe ratios. We conclude that in underspecified settings, optimization acts as a consequential source of inductive bias, thus model evaluation should extend beyond scalar loss to encompass functional and decision-level implications.