Behavioural heterogeneity in the capital asset pricing model with an application to the low-beta anomaly

ABSTRACT

This study extends the capital asset pricing model (CAPM) to situations where a subset of investors is not the mean-variance optimizers. The security market line (SML) relationship of the CAPM is shown to hold when beta is suitably adjusted in the presence of such investors. The adjusted CAPM is then used to show which of the non-mean-variance behaviour is needed to explain the so-called CAPM anomalies. For instance, the adjusted CAPM explains the low-beta anomaly if the non-mean-variance investors overweight (underweight) the high-beta (low-beta) assets. Interestingly, the empirical analysis showed that two-thirds of the investors are needed to deviate from the mean-variance analysis in order to explain the low-beta anomaly.

KEYWORDS:

• CAPM
• behavioural heterogeneity
• low-beta anomaly
• security market line

JEL CLASSIFICATION:

• D53
• G1
• G4.

Acknowledgments

We are grateful to an anonymous referee and Alex Ziegler for very valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Shefrin and Statman (1994) extend the intertemporal consumption-based CAPM with heterogeneous information towards noise trading to derive a Behavioural CAPM. Our approach is much more modest since we introduce behavioural heterogeneity in the standard static CAPM with symmetric information.

² For a comprehensive survey of reasons leading to the low-beta anomaly, see Blitz, Falkenstein, and van Vliet (2013).

³ From now on ${\lambda }^i$ denotes the K-vector of risky assets and 1 denotes a K-dimensional vector of ones. $\mu$ Is the K-dimensional vector of risky assets` expected returns and COV is the KxK matrix of covariances.

⁴ For each asset, the market identity is the equality of demand and supply written in terms of asset allocations and relative wealth.

⁵ The variables are $0\le {\lambda }_k^I\le 1$, k = 1, …, K and $0\le r^I\le 1$.