Modelling Alpha in a CAPM with Heterogenous Beliefs*

The alpha is one of the most used terms in finance. Yet, the alpha is mystical since it has no theory. It is, for example, in contradiction to the standard CAPM with homogenous beliefs. The purpose of this paper is to show that the alpha naturally arises in a financial market equilibrium when the CAPM is extended to heterogenous beliefs. We show that the hunt for alpha-opportunities is a zero-sum game and that alpha-opportunities erode with the assets under management. Moreover, it is shown that a positive alpha is not necessarily a good criterion for the choice between active and passive investment. Finally, we argue that the standard CAPM with homogenous beliefs can be seen as the long run outcome of our model when investors’ expectations are linked to the trading success. DOI: https://doi.org/10.12735/jfe.v5n2p01 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-147883 Veröffentlichte Version Originally published at: Hens, Thorsten; Gerber, Anke (2017). Modelling alpha in a CAPM with heterogenous beliefs. Journal of Finance Economics, 5(2):1-21. DOI: https://doi.org/10.12735/jfe.v5n2p01 Journal of Finance and Economics Volume 5, No. 2 (2017), 1-21 ISSN 2291-4951 E-ISSN 2291-496X Published by Science and Education Centre of North America ~ 1 ~ Modelling Alpha in a CAPM with Heterogenous Beliefs* Anke Gerber & Thorsten Hens 1 Department of Economics, University of Hamburg, Von-Melle-Park 5, 20146 Hamburg, Germany; E-mail: [email protected] 2 Swiss Finance Institute professor at the Swiss Banking Institute, University of Zurich, Plattenstrasse 32, CH-8032 Zurich, Switzerland, and Norwegian School of Economics and Business Administration, Helleveien 30, N-5045, Bergen, Norway; e-mail:[email protected] *Financial support by the University Research Priority Programme “Finance and Financial Markets” of the University of Zurich and the national center of competence in research “Financial Valuation and Risk Management” is gratefully acknowledged. The national centers in research are managed by the Swiss National Science Foundation on behalf of the federal authorities. Received: July 14, 2016 Accepted: January 30, 2017 Online Published: August 7, 2017 DOI: 10.12735/jfe.v5n2p01 URL: http://dx.doi.org/10.12735/jfe.v5n2p01 Copyright © A. Gerber & T. Hens Abstract The alpha is one of the most used terms in finance. Yet, the alpha is mystical since it has no theory. It is, for example, in contradiction to the standard CAPM with homogenous beliefs. The purpose of this paper is to show that the alpha naturally arises in a financial market equilibrium when the CAPM is extended to heterogenous beliefs. We show that the hunt for alpha-opportunities is a zero-sum game and that alpha-opportunities erode with the assets under management. Moreover, it is shown that a positive alpha is not necessarily a good criterion for the choice between active and passive investment. Finally, we argue that the standard CAPM with homogenous beliefs can be seen as the long run outcome of our model when investors' expectations are linked to the trading success. JEL Classifications : G11, G12, G14