Working Paper: CEPR ID: DP14153
Authors: Daniel Andrei; Julien Cujean; Mathieu Fournier
Abstract: Regardless of whether the CAPM is rejected for valid reasons or by mistake, a single long-short portfolio will always explain, together with the market, 100% of the cross-sectional variation in returns. Yet, this portfolio, which we coin the “Low-Minus-High (LMH) portfolio,” need not proxy for fundamental risk. We show theoretically how factors based on valuation ratios (e.g, book-to-market), or on investment rates, can be proxiesfor the LMH portfolio. More generally, the empiricist can uncover an infinity of proxies for the LMH portfolio, thus unleashing the factor zoo.
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Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| LMH portfolio (G19) | 100% of the cross-sectional variation in returns (C29) |
| observable variables (like market-to-book ratios) (C29) | LMH portfolio (G19) |
| LMH portfolio (G19) | risk premium (G19) |
| LMH portfolio (G19) | correlation with value and investment factors (G11) |
| LMH portfolio (G19) | captures risk (G22) |
| existing factors (like the Fama-French three-factor model) (G41) | explain returns of LMH portfolio (G12) |
| mismeasurement in betas (C46) | confusion in interpretation of factors (C38) |