Rethinking Beta: A Causal Take on CAPM

Paper: arXiv 2509.05760

Authors: Naftali Cohen

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 $R_{“m,t”} \to R_{“i,t”}$ 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”}, $Z \to {“R_m, R_i"}$, not $R_m \to R_i$. 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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper is mathematically dense, using advanced concepts from structural causal models (SCMs) and directed acyclic graphs (DAGs) to formalize the CAPM, demonstrating high math complexity. Empirically, it employs stylized models and large-cap U.S. equity data for validation, but it’s primarily a theoretical critique with limited backtesting or implementation-heavy analysis, so empirical rigor is strong but not extreme.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Rethink CAPM Beta as Causal?"] --> B["Methodology:<br>Structural Causal Models SCM"]
  B --> C["Data:<br>Large-cap U.S. Equity"]
  C --> D["Computation:<br>Test Fork Graph vs. Causal Chains"]
  D --> E{"Key Finding:<br>Contemporaneous Beta = Proxy<br>Not Causal Transmission"}
  E --> F["Outcome:<br>CAPM is Associational"]
  F --> G["Implication:<br>Shift to Explicit Causal Paths"]

Cited References (42)

1. Causality: Models, Reasoning, and Inference (2009)
2. Causal Inference in Statistics: A Primer (2016)
3. The conditional CAPM does not explain asset-pricing anomalies (2006)
4. Dynamic conditional beta (2016)
5. Event studies in economics and finance (1997)
6. The effect: An introduction to research design and causality (2021)
7. Asset pricing: A tale of two days (2014)
8. An intertemporal capital asset pricing model (1973)

0 of 42 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.