Is Causality Necessary for Efficient Portfolios? A Computational Perspective on Predictive Validity and Model Misspecification

TL;DR

This paper demonstrates that causal identification is not essential for portfolio efficiency; instead, geometric conditions like alignment, ranking, and calibration of predictive signals are key, supported by theoretical and empirical analysis.

Contribution

It challenges the notion that causality is necessary for efficient portfolios, showing geometric sufficiency conditions govern efficiency even under model misspecification.

Findings

Causal identification is not required for portfolio efficiency.

Efficiency depends on geometric conditions: alignment, ranking, calibration.

Miscalibration reduces Sharpe ratios but does not cause collapse.

Abstract

Portfolio optimization is increasingly argued to require causally identified return predictors to avoid signal inversion and optimization failure. This paper re-examines this claim by studying when predictive signals yield viable efficient frontiers, even under structural misspecification. We show that causal identification is not necessary for portfolio efficiency within static mean--variance and closely related quadratic portfolio optimization frameworks. Instead, efficiency is governed by geometric sufficiency conditions on predictive signals: directional alignment, ranking preservation, and calibration. We formally decompose portfolio efficiency into these three components and show that miscalibration alone attenuates Sharpe ratios even when alignment and ranking are preserved. Robustness is characterized as smooth degradation rather than collapse, with explicit attenuation behavior and continuity of performance under increasing misspecification. The theoretical results are supported by simulations and empirical analysis. Empirical validation combines equity-based illustrations with a large global bond universe spanning multiple currencies, countries, sectors, maturities along the term structure, seniority classes, and credit ratings, together with high-dimensional stress tests, nonlinear data-generating processes, rolling-window analyses, covariance regularization, realistic portfolio constraints, and bootstrap-based statistical validation. Across these settings, optimization geometry remains well-behaved whenever directional alignment is preserved. The results clarify the boundary between causality and portfolio optimization: causality may inform signal representation, but portfolio efficiency at the optimization stage is a geometric property conditional on a given representation.