An Efficient Factor from Basis 'Anomalies'

69 Pages Posted: 21 Sep 2016 Last revised: 8 Nov 2016

See all articles by Bingzhi Zhao

Bingzhi Zhao

Duke University, Department of Economics

Date Written: November 7, 2016


A look-ahead-bias-free, ex-ante mean-variance efficient portfolio from Size, B/M and Momentum “anomalies” has an ex-post Sharpe ratio of 2.3. It captures the non-monotonic benefits from characteristics that are ignored by multi-factors and eliminates 39 out of 42 “unique anomalies”. Based on a wide set of tests, the 1-factor model significantly out-performs and drives out the 11 factors: MKT-Rf, SMB, HML, MOM, RMW, CMA, qME, qIA, qROE, QMJ, LIQ for different combinations of 147 test assets. The efficient factor is priced at the firm-level with more than 12% per year spread that cannot be explained by the existing models.

Analytically, “anomalous” predictabilities are equivalent to 1-factor pricing, regardless of rational/behavioral cause. A projected Stochastic Discount Factor return deduced from the efficient factor is consistent with economic theory. The risk premium is empirically tied not only to consumptions but also to interest rate environment and industrial production.

Keywords: Anomaly, mean-variance efficient, multi-factors, asset-pricing

JEL Classification: G11, G12, G14

Suggested Citation

Zhao, Bingzhi, An Efficient Factor from Basis 'Anomalies' (November 7, 2016). Available at SSRN: or

Bingzhi Zhao (Contact Author)

Duke University, Department of Economics ( email )

Durham, NC
United States

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