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Rethinking Beta: A Causal Take on CAPM

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  • 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.

Suggested Citation

  • Naftali Cohen, 2025. "Rethinking Beta: A Causal Take on CAPM," Papers 2509.05760, arXiv.org, revised Sep 2025.
  • Handle: RePEc:arx:papers:2509.05760
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    3. Lewellen, Jonathan & Nagel, Stefan, 2006. "The conditional CAPM does not explain asset-pricing anomalies," Journal of Financial Economics, Elsevier, vol. 82(2), pages 289-314, November.
    4. Shanken, Jay, 1992. "On the Estimation of Beta-Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 5(1), pages 1-33.
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