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

ArXiv ID: 2507.23138 “View on arXiv”

Authors: Alejandro Rodriguez Dominguez

Abstract

A recent line of research has argued that causal factor models are necessary for portfolio optimization, claiming that structurally misspecified models inevitably produce inverted signals and nonviable frontiers. This paper challenges that view. We show, through theoretical analysis, simulation counterexamples, and empirical validation, that predictive models can remain operationally valid even when structurally incorrect. Our contributions are fourfold. First, we distinguish between directional agreement, ranking, and calibration, proving that sign alignment alone does not ensure efficiency when signals are mis-scaled. Second, we establish that structurally misspecified signals can still yield convex and viable efficient frontiers provided they maintain directional alignment with true returns. Third, we derive and empirically confirm a quantitative scaling law that shows how Sharpe ratios contract smoothly with declining alignment, thereby clarifying the role of calibration within the efficient set. Fourth, we validate these results on real financial data, demonstrating that predictive signals, despite structural imperfections, can support coherent frontiers. These findings refine the debate on causality in portfolio modeling. While causal inference remains valuable for interpretability and risk attribution, it is not a prerequisite for optimization efficiency. Ultimately, what matters is the directional fidelity and calibration of predictive signals in relation to their intended use in robust portfolio construction.

Keywords: Causal Factor Models, Portfolio Optimization, Efficient Frontier, Signal Calibration, Sharpe Ratio, Portfolio Management

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper presents advanced mathematical derivations, including theoretical analysis of misspecified models and a quantitative scaling law linking Sharpe ratios to signal alignment. It also validates these findings on real financial data (S&P 500) and synthetic data, demonstrating a strong empirical component.

  flowchart TD
    A["Research Goal<br>Is causality necessary<br>for efficient portfolios?"]
    
    B["Methodology<br>Theoretical Analysis & Counterexamples"]
    C["Data/Input<br>Simulated & Real Financial Data"]
    
    D["Computational Process<br>Testing Structural Misspecification<br>vs Predictive Validity"]
    
    E["Outcome 1<br>Distinguish Alignment, Ranking, Calibration"]
    F["Outcome 2<br>Misspecified signals can still<br>yield convex efficient frontiers"]
    G["Outcome 3<br>Quantitative scaling law:<br>Sharpe ratios contract smoothly"]
    H["Outcome 4<br>Predictive signals support<br>coherent frontiers despite imperfections"]

    A --> B
    A --> C
    B --> D
    C --> D
    D --> E
    D --> F
    D --> G
    D --> H