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
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
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