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Can the CRRA-Lognormal Framework Explain CAPM-Anomalies in the Cross-Section of Stock Returns?

Sabine Elmiger
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Sabine Elmiger: University of Zurich

No 13-43, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: A large number of empirical studies find systematic deviations from the CAPM. The CAPM tends to understate the returns on low-beta stocks and overstate the returns on high-beta stocks, i.e. the security market line is too steep. Other well-documented anomalies are the size premium and the value premium. The CAPM is a special case of the consumption-based CAPM. This study adresses the question whether the consumption-based CAPM with constant relative risk aversion preferences and lognormally distributed dividends can explain CAPM-anomalies. An example of an economy with power utility and lognormal dividends is examined that can be solved in closed form. The model leads to a security market line that is flatter than in the CAPM and generates a size and a value premium. The comparative statics suggest that cross-sectional anomalies and the equity premium puzzle are tightly linked.

Keywords: CAPM; CCAPM; CRRA; lognormality; multiple assets; beta premium; value premium; size premium (search for similar items in EconPapers)
Pages: 34 pages
Date: 2013-08, Revised 2016-10
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