English

Rethinking Beta: A Causal Take on CAPM

Theoretical Economics 2025-09-25 v3 Pricing of Securities Statistical Finance Applications

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 Rm,tRi,tR_{m,t} \to R_{i,t} conflicts with the fact that RmR_m is itself a value-weighted aggregate of its constituents, unless RmR_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 ZZ, the market RmR_m, and an asset RiR_i. The empirically plausible baseline is a \emph{fork}, Z{Rm,Ri}Z \to \{R_m, R_i\}, not RmRiR_m \to R_i. In this setting, OLS beta reflects not a causal transmission, but an attenuated proxy for how well RmR_m captures the underlying driver ZZ. Consequently, ``beta-neutral'' portfolios can remain exposed to macro or sectoral shocks, and hedging on RmR_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

Cite

@article{arxiv.2509.05760,
  title  = {Rethinking Beta: A Causal Take on CAPM},
  author = {Naftali Cohen},
  journal= {arXiv preprint arXiv:2509.05760},
  year   = {2025}
}
R2 v1 2026-07-01T05:24:30.556Z