The Low-Minus-High Portfolio and the Factor Zoo

47 Pages Posted: 7 May 2019 Last revised: 19 Nov 2019

See all articles by Daniel Andrei

Daniel Andrei

McGill University

Julien Cujean

Ecole Polytechnique Fédérale de Lausanne

Mathieu Fournier

HEC Montreal

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Date Written: March 31, 2019


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.

Keywords: CAPM, factor zoo, anomalies

JEL Classification: G12

Suggested Citation

Andrei, Daniel and Cujean, Julien and Fournier, Mathieu, The Low-Minus-High Portfolio and the Factor Zoo (March 31, 2019). Proceedings of Paris December 2019 Finance Meeting EUROFIDAI - ESSEC, Available at SSRN: or

Daniel Andrei (Contact Author)

McGill University ( email )

1001 Sherbrooke St. W
Montreal, Quebec H3A 1G5

Julien Cujean

Ecole Polytechnique Fédérale de Lausanne ( email )

c/o University of Geneve
40, Bd du Pont-d'Arve
1211 Geneva, CH-6900

Mathieu Fournier

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H2X 2L3 H3T 2A7

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