Risk, Return, and Volatility Feedback: A Bayesian Nonparametric Analysis

Mark Jensen and John Maheu

No 2014-6, FRB Atlanta Working Paper from Federal Reserve Bank of Atlanta

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. This paper models the contemporaneous relationship between market excess returns and contemporaneous log-realized variances nonparametrically with an infinite mixture representation of their joint distribution. The conditional distribution of excess returns given log-realized variance will also have an 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 and a smooth nonlinear relationship between the conditional mean of excess returns and contemporaneous log-realized variance. 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 log-realized variance. This relationship is nonlinear. Volatility feedback impacts the whole distribution and not just the conditional mean.

Keywords: Dirichlet process prior; slice sampling; dependent Bayesian nonparametrics (search for similar items in EconPapers)
JEL-codes: C11 C14 C32 G12 (search for similar items in EconPapers)
Pages: 38 pages
Date: 2014-06-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis (2018)
Working Paper: Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis (2014)
Working Paper: Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis (2013)
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