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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. 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.

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  • Jensen, Mark J. & Maheu, John M., 2014. "Risk, Return, and Volatility Feedback: A Bayesian Nonparametric Analysis," FRB Atlanta Working Paper 2014-6, Federal Reserve Bank of Atlanta.
  • Handle: RePEc:fip:fedawp:2014-06
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    Cited by:

    1. Jin, Xin & Maheu, John M., 2016. "Bayesian semiparametric modeling of realized covariance matrices," Journal of Econometrics, Elsevier, vol. 192(1), pages 19-39.
    2. Worapree Maneesoonthorn & Catherine S. Forbes & Gael M. Martin, 2016. "Inference on Self-Exciting Jumps in Prices and Volatility using High Frequency Measures," Monash Econometrics and Business Statistics Working Papers 8/16, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    Keywords

    Dirichlet process prior; slice sampling; dependent Bayesian nonparametrics;

    JEL classification:

    • 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

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