Time-Varying Beta: A Boundedly Rational Equilibrium Approach

Quantitative Finance Research Centre Research Paper No. 275

31 Pages Posted: 22 Oct 2010

See all articles by Carl Chiarella

Carl Chiarella

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

Roberto Dieci

Department of Mathematics, University of Bologna

Xuezhong He

Xi'an Jiaotong-Liverpool University (XJTLU); University of Technology Sydney (UTS) - Finance Discipline Group, Business School

Date Written: May 1, 2010

Abstract

By taking into account conditional expectations and the dependence of the systematic risk of asset returns on micro- and macro-economic factors, the conditional CAPM with time-varying betas displays superiority in explaining the cross-section of returns and anomalies in a number of empirical studies. Most of the literature on time-varying beta is motivated by econometric estimation rather than explicit modelling of the stochastic behaviour of betas through agents' behaviour. Within the mean-variance framework of repeated one-period optimisation, we set up a boundedly rational dynamic equilibrium model of a financial market with heterogeneous agents and obtain an explicit dynamic CAPM relation between the expected equilibrium returns and time-varying betas. By incorporating the three most popular types of investors, fundamentalists, chartists and noise traders, into the model, we show that, independent of the fundamentals, there is a systematic change in the market portfolio, risk-return relationships, and time varying betas when investors change their behaviour, such as the chartists acting as momentum traders. In particular, we demonstrate the stochastic nature of time-varying betas and show that the commonly used rolling window estimates of time-varying betas may not be consistent with the ex-ante betas implied by the equilibrium model. The results provide a number of insights into an understanding of time-varying beta.

Keywords: equilibrium asset prices, CAPM, time-varying betas, heterogeneous expectations

JEL Classification: G12, D84

Suggested Citation

Chiarella, Carl and Dieci, Roberto and He, Xue-Zhong 'Tony', Time-Varying Beta: A Boundedly Rational Equilibrium Approach (May 1, 2010). Quantitative Finance Research Centre Research Paper No. 275, Available at SSRN: https://ssrn.com/abstract=1695334 or http://dx.doi.org/10.2139/ssrn.1695334

Carl Chiarella (Contact Author)

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

PO Box 123
Broadway, NSW 2007
Australia
+61 2 9514 7719 (Phone)
+61 2 9514 7711 (Fax)

HOME PAGE: http://www.business.uts.edu.au/finance/

Roberto Dieci

Department of Mathematics, University of Bologna ( email )

Piazza di Porta San Donato, 5
Bologna, I-40126
Italy

HOME PAGE: http://www.unibo.it/Faculty/default.aspx?UPN=roberto.dieci%40unibo.it

Xue-Zhong 'Tony' He

Xi'an Jiaotong-Liverpool University (XJTLU) ( email )

111 Renai Road, SIP
Suzhou, JiangSu province 215123
China

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

Haymarket
Sydney, NSW 2007
Australia

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