Federal Reserve Bank of Atlanta
FRB Atlanta Working Paper
Risk, Return, and Volatility Feedback: A Bayesian Nonparametric Analysis
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.
Cite this item
Mark J. Jensen & John M. Maheu, Risk, Return, and Volatility Feedback: A Bayesian Nonparametric Analysis, Federal Reserve Bank of Atlanta, FRB Atlanta Working Paper 2014-6, 01 Jun 2014.
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
Keywords: Dirichlet process prior; slice sampling; dependent Bayesian nonparametrics
This item with handle RePEc:fip:fedawp:2014-06
is also listed on EconPapers
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