The ZCAPM and Previous Tests of Anomaly Portfolio Returns

James W. Kolari (), Wei Liu, Jianhua Z. Huang () and Huiling Liao ()
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James W. Kolari: Texas A&M University, Mays Business School
Wei Liu: Texas A&M University, Mays Business School
Jianhua Z. Huang: The Chinese University of Hong Kong, Shenzhen, School of Artificial Intelligence and School of Data Science
Huiling Liao: Illinois Institute of Technology, Department of Applied Mathematics

Chapter Chapter 4 in Asset Pricing Models and Market Efficiency, 2026, pp 63-90 from Springer

Abstract: Abstract Black (1972) proposed the zero-beta CAPM in an effort to reconcile empirical evidence on tests of the famed Capital Asset Pricing Model (CAPM) by Treynor (1961, 1962), Sharpe (1964), Lintner (1965), and Mossin (1966). The CAPM is a general equilibrium model that can be graphically represented by the Security Market Line (SML) defined by excess expected returns over the riskless rate of assets on the Y-axis and associated estimated betas on the X-axis. A positive linear relationship is hypothesized between expected returns and beta risk. Using U.S. stock market returns, early evidence by Black, Jensen, and Scholes (1972) showed that the SML was flatter with a higher intercept (or $$\alpha $$ α parameter) than predicted by the CAPM. More specifically, low beta stocks had higher returns than theorized by the CAPM and vice versa for high beta stocks. They inferred that, instead of using the riskless rate as in the CAPM, a higher borrowing rate should be used in line with investor practice in financial markets. Black extended this potential solution by proposing the possible existence of a zero-beta portfolio uncorrelated with the market portfolio in the CAPM. In effect, there are two factors—namely, a market factor and zero-beta factor. Unfortunately, he did not provide any guidance on how to construct a zero-beta portfolio in the real world. For this reason, no empirical model of the zero-beta CAPM is available.

Keywords: Cross-sectional market volatility factor; Machine learning (ML); Out-of-sample cross-sectional regression test; ZCAPM; Zero-beta CAPM; Zeta risk (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-031-92901-4_4

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