Zero-Beta CAPM with Heterogeneous Beliefs

35 Pages Posted: 27 Aug 2007 Last revised: 20 Jun 2008

See all articles by Xuezhong He

Xuezhong He

University of Technology Sydney (UTS) - Finance Discipline Group, Business School; Financial Research Network (FIRN)

Lei Shi

Macquarie University; Financial Research Network (FIRN)

Date Written: August 16, 2007

Abstract

This paper extends the standard Black's zero-beta CAPM with homogeneous beliefs to the case with heterogeneous beliefs in terms of risk aversion coefficients, expected payoffs, and variance/covariance matrices of the payoffs of risky assets among heterogeneous agents within the mean-variance framework. Investors are bounded rational in the sense that they make their optimal decision based on their beliefs. By introducing and constructing a consensus belief of the market, we obtain equilibrium prices of risky assets and show that Black's zero-beta CAPM holds under the consensus belief. Various impacts of heterogeneity on the market equilibrium and agents' optimal portfolios are analyzed. In particular, we show that under market aggregation, the biased belief (from the market belief) of investors makes the optimal portfolio of the investor be mean-variance inefficient while the market portfolio is always on the efficient frontier. This demonstrates that, within this framework, bounded rational investors may never achieve their mean-variance efficiency under aggregation. At the same time, the efficiency of the whole market, measured by the efficiency of the market portfolio, can be achieved. The results also shed a light on the empirical finding that managed funds under-perform comparing to the market indices on average.

Keywords: asset prices, heterogeneous beliefs, portfolio analysis, zero-beta CAPM, optimality

JEL Classification: G12, D84

Suggested Citation

He, Xue-Zhong 'Tony' and Shi, Lei, Zero-Beta CAPM with Heterogeneous Beliefs (August 16, 2007). 20th Australasian Finance & Banking Conference 2007 Paper, Available at SSRN: https://ssrn.com/abstract=1009386 or http://dx.doi.org/10.2139/ssrn.1009386

Xue-Zhong 'Tony' He

University of Technology Sydney (UTS) - Finance Discipline Group, Business School ( email )

Haymarket
Sydney, NSW 2007
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Lei Shi (Contact Author)

Macquarie University ( email )

New South Wales 2109
Australia
+612 98508478 (Phone)

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

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