The Low-Minus-High Portfolio and the Factor Zoo

Julien Cujean, Daniel Andrei and Mathieu Fournier

No 14153, CEPR Discussion Papers from Centre for Economic Policy Research

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 proxies for the LMH portfolio. More generally, the empiricist can uncover an infinity of proxies for the LMH portfolio, thus unleashing the factor zoo.

Date: 2019-11
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