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

34 Pages Posted: 22 Aug 2013 Last revised: 1 Oct 2016

Date Written: September 28, 2016

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

Suggested Citation

Elmiger, Sabine, Can the CRRA-Lognormal Framework Explain CAPM-Anomalies in the Cross-Section of Stock Returns? (September 28, 2016). Swiss Finance Institute Research Paper No. 13-43. Available at SSRN: https://ssrn.com/abstract=2312273 or http://dx.doi.org/10.2139/ssrn.2312273

Sabine Elmiger (Contact Author)

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006
Switzerland

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