Rethinking Beta: A Causal Take on CAPM

2025-09-06

AI Summary

This paper identifies an “aggregation paradox” in the Capital Asset Pricing Model (CAPM): treating contemporaneous market returns as a causal driver of individual stock returns is logically inconsistent, since market returns are themselves a weighted average of constituent stock returns, violating fundamental causal requirements for contemporaneous association. Method: We formalize the problem using a structural causal model (SCM) and directed acyclic graph (DAG), and empirically test causal claims on large-cap U.S. equity data via instrumental variables, leave-one-out estimation, and lagged specifications. Contribution/Results: We find that contemporaneous beta serves solely as a proxy for latent common factors and lacks direct causal effect; any genuine market influence manifests only weakly and with temporal lag. Consequently, CAPM should be reconceptualized as an associational—rather than causal—model. Explicit causal pathway modeling is critical for accurate risk attribution and robust design of beta-neutral strategies.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

The CAPM regression is typically interpreted as if the market return contemporaneously emph{causes} individual returns, motivating beta-neutral portfolios and factor attribution. For realized equity returns, however, this interpretation is inconsistent: a same-period arrow $R_{m,t} o R_{i,t}$ conflicts with the fact that $R_m$ is itself a value-weighted aggregate of its constituents, unless $R_m$ is lagged or leave-one-out -- the ``aggregator contradiction.'' We formalize CAPM as a structural causal model and analyze the admissible three-node graphs linking an external driver $Z$, the market $R_m$, and an asset $R_i$. The empirically plausible baseline is a emph{fork}, $Z o {R_m, R_i}$, not $R_m o R_i$. In this setting, OLS beta reflects not a causal transmission, but an attenuated proxy for how well $R_m$ captures the underlying driver $Z$. Consequently, ``beta-neutral'' portfolios can remain exposed to macro or sectoral shocks, and hedging on $R_m$ can import index-specific noise. Using stylized models and large-cap U.S. equity data, we show that contemporaneous betas act like proxies rather than mechanisms; any genuine market-to-stock channel, if at all, appears only at a lag and with modest economic significance. The practical message is clear: CAPM should be read as associational. Risk management and attribution should shift from fixed factor menus to explicitly declared causal paths, with ``alpha'' reserved for what remains invariant once those causal paths are explicitly blocked.

Problem

• CAPM's contemporaneous causal interpretation is inconsistent due to aggregator contradiction
• Empirical evidence supports common driver model instead of market causing returns
• Beta reflects association not causation, requiring causal paths for risk management

Innovation

• Uses structural causal model for CAPM analysis
• Proposes fork structure with external driver Z
• Recommends explicit causal paths for attribution