Jensen, Mark J and Maheu, John M (2013): Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis.

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Abstract
The relationship between risk and return is one of the most studied topics in finance. The majority of the literature is based on a linear, parametric relationship between expected returns and conditional volatility. However, there is no theoretical justification for the relationship to be linear. This paper models the contemporaneous relationship between market excess returns and logrealized variances nonparametrically with an infinite mixture representation of their joint distribution. With this nonparametric representation, the conditional distribution of excess returns given logrealized variance will also have a infinite mixture representation but with probabilities and arguments depending on the value of realized variance. Our nonparametric approach allows for deviation from Gaussianity by allowing for higher order nonzero moments. It also allows for a smooth nonlinear relationship between the conditional mean of excess returns and logrealized variance. Parsimony of our nonparametric approach is guaranteed by the almost surely discrete Dirichlet process prior used for the mixture weights and arguments. We find strong robust evidence of volatility feedback in monthly data. Once volatility feedback is accounted for, there is an unambiguous positive relationship between expected excess returns and expected logrealized variance. This relationship is nonlinear. Volatility feedback impacts the whole distribution and not just the conditional mean.
Item Type:  MPRA Paper 

Original Title:  Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis 
Language:  English 
Keywords:  Dirichlet process prior, MCMC, realized variance 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C11  Bayesian Analysis: General C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models G  Financial Economics > G1  General Financial Markets G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing ; Trading Volume ; Bond Interest Rates 
Item ID:  52132 
Depositing User:  John Maheu 
Date Deposited:  11. Dec 2013 09:21 
Last Modified:  11. Dec 2013 09:46 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/52132 