This paper utilizes Black's (1972) zero-beta CAPM to derive an alternative form dubbed the ZCAPM. The ZCAPM posits that asset prices are a function of market risk composed of two components: average market returns and cross-sectional market volatility. Market risk associated with average market returns in the CAPM market model is known as beta risk. We refer to market risk related to cross-sectional market volatility as zeta risk. Unlike the three-moment CAPM, the latter zeta risk is hypothesized to have two-sided effects on asset prices. To test ZCAPM theory, an empirical ZCAPM is developed from expectation-maximization (EM) methods. Using U.S. stock returns from January 1965 to December 2010, out-of-sample cross-sectional asset pricing tests demonstrate that zeta risk loadings are consistently significant at a high level across a variety of different tests assets. By comparison, other factors in popular three- and four-factor models are less significant and priced in some but not all test assets. We conclude that the ZCAPM holds promise as a robust asset pricing model.

In a recent book, Kolari et al. developed a new theoretical capital asset pricing model dubbed the ZCAPM. Based on out-of-sample cross-sectional tests using U.S. stocks, the ZCAPM consistently outperformed well-known multifactor models popular in the finance literature. This paper presents further evidence that expands their sample period from 1927 to 2020. Results are provided for the subperiods 1927 to 1964 and 1965 to 2020. Our results corroborate those of KLH. In cross-sectional tests, the ZCAPM outperforms the CAPM as well as the Fama and French three-factor model and Carhart four-factor model. Outperformance is found in terms of both higher goodness of fit and the statistical significance of factor loadings. Interestingly, the earlier subperiod results highlight problems with the endogeneity of test assets in cross-sectional tests of multifactor models.

This article examines the issue of cross-sectional correlation due to partially overlapping event windows. Kolari and Pynnönen find that, in the case of event-date clustering, even relatively low cross-sectional correlation among abnormal returns seriously biases standard tests to over-reject the null hypothesis of zero average abnormal return. Unlike Kolari and Pynnönen, who assume that firms share the same event window in calendar time, we generalize the approach to a case where the windows overlap only partially in calendar time. This generalization implies a modification to their test statistics that accounts for the average percentage of overlaps in the event windows. Also, the paper proposes estimators of the average correlation and covariance-variance ratios needed for adjustment to this more general case of partial overlaps.

In this paper, we show the importance of accounting for heterogeneity among sample firms in stochastic frontier analysis. For a fairly homogenous sample of German savings and cooperative banks, we analyze how alternative theoretical assumptions regarding the nature of heterogeneity can be modeled and the extent which the respective empirical specifications affect estimated efficiency levels and rankings. We find that the level of efficiency scores is affected in the case of both cost and profitmodels. On the cost side especially, level and rank correlations show that different specifications identify different banks as being best or worst performers. Our main conclusion is that efficiency studies in general and bank efficiency studies in particular should account for heterogeneity across sample firms. Especially when efficiency measures are employed for policy purposes, a careful choice of models and transparency regarding maximization methods are essential to be able to make inferences about managerial behavior.