Bayesian Inference in Empirical Finance

Posted: 1 May 2010 Last revised: 23 Feb 2011

See all articles by Michael Verhofen

Michael Verhofen

University of St. Gallen - Swiss Institute of Banking and Finance; Allianz Global Investors

Date Written: May 1, 2010


The purpose of this dissertation is to use Bayesian econometrics in different areas of Empirical Finance. First, I give an introduction to Bayesian Inference in Finance. Second, the effect of model and parameter uncertainty on return predictability is analyzed. Third, I use regime-switching models for time-varying risk premia. Fourth, conditional asset pricing models are estimated and tested based on Markov Chain Monte Carlo (MCMC) methods. Finally, the behavior of mutual fund managers is analyzed by using Dynamic Bayesian Networks.

In the second chapter, titled "Bayesian Inference in Finance," I give an overview of Bayesian approaches in Finance with an emphasis on empirical and theoretical asset pricing. First, the foundations of Bayesian inference with a focus on the linear model are presented. Then, I turn to numerical Bayesian methods, i.e., Markov Chain Monte Carlo methods, in financial econometrics and present empirical evidence. Finally, Bayesian asset pricing models and Bayesian approaches in portfolio theory are presented.

The third chapter of this dissertation investigates the impact of model uncertainty on tactical industry allocation. Using Bayesian Model Averaging, I analyze the sample evidence on return predictability in the presence of model uncertainty for tactical industry allocation within the U.S. stock market and address the posterior importance of various variables in predicting industry returns. The performance of the Bayesian approach is compared with traditional statistical model selection criteria and a naive iid forecast in an out-of-sample analysis. Finally, a variance decomposition into model risk, estimation (parameter) risk, and forecast error is conducted.

The fourth chapter of the dissertation investigates the effects of market regimes on style allocation. Using Markov Chain Monte Carlo methods, I estimate a multivariate regime-switching model for the Carhart (1997) four factor model. I find two clearly separable regimes with different mean returns, volatilities and correlations. Regime-switching induces investors to change their portfolio style over time depending on the investment horizon, the risk aversion and the prevailing regime.

The fifth chapter of the research project investigates the use of Markov Chain Monte Carlo methods for testing conditional asset pricing models. In contrast to traditional approaches, it is truly conditional because the assumption that time variation in betas is driven by a set of conditioning variables is not necessary. Moreover, the approach has exact finite sample properties and accounts for errors-in-variables. Using S&P 500 panel data, I analyze the empirical performance of the CAPM and the Fama and French (1993) three-factor model.

In the final chapter of this dissertation, I use Dynamic Bayesian Network to analyze the behavior of mutual fund managers. As rational agents mutual fund managers are assumed to take excessive risk after periods of poor performance due to the compensation structure. Using a large data set of US mutual funds, the impact of prior performance on the risk-taking of mutual fund managers is analyzed empirically. In contrast to previous studies, I do not solely focus on the volatility as a measure of risk, but also consider alternative definitions of risk and style. Using a Dynamic Bayesian Network, I am able to capture non-linear effects and to assign exact probabilities to the mutual fund managers' adjustment of behavior.

Suggested Citation

Verhofen, Michael, Bayesian Inference in Empirical Finance (May 1, 2010). Available at SSRN:

Michael Verhofen (Contact Author)

University of St. Gallen - Swiss Institute of Banking and Finance ( email )

Unterer Graben 21
St. Gallen, CH-9000


Allianz Global Investors ( email )


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