Rethinking Beta: A Causal Take on CAPM

ArXiv ID: 2509.05760 “View on arXiv”

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.

Keywords: Capital Asset Pricing Model (CAPM), Causal Inference, Structural Causal Models, Beta-Neutral Portfolios, Aggregator Contradiction, Equities

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail
  • Why: 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.
  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"]