The Low-Minus-High Portfolio and the Factor Zoo

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.