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Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis

  • Jensen, Mark J
  • Maheu, John M

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 log-realized variances nonparametrically with an infinite mixture representation of their joint distribution. With this nonparametric representation, the conditional distribution of excess returns given log-realized 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 non-zero moments. It also allows for a smooth nonlinear relationship between the conditional mean of excess returns and log-realized 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 log-realized variance. This relationship is nonlinear. Volatility feedback impacts the whole distribution and not just the conditional mean.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 52132.

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Date of creation: Dec 2013
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Handle: RePEc:pra:mprapa:52132
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  1. Mark J Jensen & John M Maheu, 2008. "Bayesian semiparametric stochastic volatility modeling," Working Papers tecipa-314, University of Toronto, Department of Economics.
  2. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "There is a Risk-Return Tradeoff After All," CIRANO Working Papers 2004s-24, CIRANO.
  3. Delatola, E.-I. & Griffin, J.E., 2013. "A Bayesian semiparametric model for volatility with a leverage effect," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 97-110.
  4. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
  5. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(2), pages 174-196, Spring.
  6. John M. Maheu & Thomas H. McCurdy, 2009. "Do High-Frequency Measures of Volatility Improve Forecasts of Return Distributions?," Working Paper Series 19_09, The Rimini Centre for Economic Analysis, revised Jan 2009.
  7. Gallant, A.R. & Tauchen, G., 1988. "Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Papers 88-59, Chicago - Graduate School of Business.
  8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
  9. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
  10. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
  11. Chang-Jin Kim & James C. Morley & Charles Nelson, 2000. "Is There a Positive Relationship between Stock Market Volatility and the Equity Premium?," Working Papers 0023, University of Washington, Department of Economics.
  12. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
  13. John M. Maheu & Thomas H. McCurdy & Xiaofei Zhao, 2012. "Do Jumps Contribute to the Dynamics of the Equity Premium?," Working Paper Series 47_12, The Rimini Centre for Economic Analysis.
  14. Hui Guo & Robert F. Whitelaw, 2003. "Uncovering the Risk-Return Relation in the Stock Market," NBER Working Papers 9927, National Bureau of Economic Research, Inc.
  15. Jim E. Griffin & Mark F.J. Steel, 2002. "Semiparametric Bayesian Inference for Stochastic Frontier Models," Econometrics 0209001, EconWPA, revised 18 Sep 2002.
  16. Brandt, Michael W. & Kang, Qiang, 2004. "On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach," Journal of Financial Economics, Elsevier, vol. 72(2), pages 217-257, May.
  17. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  18. Ludvigson, Sydney C. & Ng, Serena, 2007. "The empirical risk-return relation: A factor analysis approach," Journal of Financial Economics, Elsevier, vol. 83(1), pages 171-222, January.
  19. Mark J. Jensen & John M. Maheu, 2012. "Bayesian Semiparametric Multivariate GARCH Modeling," Working Paper Series 48_12, The Rimini Centre for Economic Analysis.
  20. repec:cup:cbooks:9781107015319 is not listed on IDEAS
  21. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2008. "A Bayesian mixed logit-probit model for multinomial choice," Journal of Econometrics, Elsevier, vol. 147(2), pages 232-246, December.
  22. Bandi, Federico M. & Perron, Benoît, 2008. "Long-run risk-return trade-offs," Journal of Econometrics, Elsevier, vol. 143(2), pages 349-374, April.
  23. David E. Allen & Michael McAleer & Marcel Scharth, 2013. "Realized Volatility Risk," Tinbergen Institute Discussion Papers 13-092/III, Tinbergen Institute.
  24. John M. Maheu & Thomas H. McCurdy, 2007. "Components of Market Risk and Return," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(4), pages 560-590, Fall.
  25. Taddy, Matthew A. & Kottas, Athanasios, 2010. "A Bayesian Nonparametric Approach to Inference for Quantile Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 357-369.
  26. Paul Harrison & Harold H. Zhang, 1999. "An Investigation Of The Risk And Return Relation At Long Horizons," The Review of Economics and Statistics, MIT Press, vol. 81(3), pages 399-408, August.
  27. Laurent E. Calvet & Adlai J. Fisher, 2005. "Multifrequency News and Stock Returns," NBER Working Papers 11441, National Bureau of Economic Research, Inc.
  28. Veronesi, Pietro, 1999. "Stock Market Overreaction to Bad News in Good Times: A Rational Expectations Equilibrium Model," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 975-1007.
  29. John T. Scruggs, 1998. "Resolving the Puzzling Intertemporal Relation between the Market Risk Premium and Conditional Market Variance: A Two-Factor Approach," Journal of Finance, American Finance Association, vol. 53(2), pages 575-603, 04.
  30. Tim Bollerslev & Julia Litvinova & George Tauchen, 2006. "Leverage and Volatility Feedback Effects in High-Frequency Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(3), pages 353-384.
  31. Kim, Chang-Jin & Morley, James C. & Nelson, Charles R., 2005. "The Structural Break in the Equity Premium," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 181-191, April.
  32. Christopher M. Turner & Richard Startz & Charles R. Nelson, 1989. "A Markov Model of Heteroskedasticity, Risk, and Learning in the Stock Market," NBER Working Papers 2818, National Bureau of Economic Research, Inc.
  33. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
  34. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
  35. Hui Guo, 2006. "The Risk-Return Relation in International Stock Markets," The Financial Review, Eastern Finance Association, vol. 41(4), pages 565-587, November.
  36. Wu, Guojun, 2001. "The Determinants of Asymmetric Volatility," Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 837-59.
  37. Hui Guo, 2006. "On the risk-return relation in international stock markets," Working Papers 2003-012, Federal Reserve Bank of St. Louis.
  38. Harvey, Campbell R., 2001. "The specification of conditional expectations," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 573-637, December.
  39. Schwert, G William, 1990. "Indexes of U.S. Stock Prices from 1802 to 1987," The Journal of Business, University of Chicago Press, vol. 63(3), pages 399-426, July.
  40. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
  41. Conley, Timothy G. & Hansen, Christian B. & McCulloch, Robert E. & Rossi, Peter E., 2008. "A semi-parametric Bayesian approach to the instrumental variable problem," Journal of Econometrics, Elsevier, vol. 144(1), pages 276-305, May.
  42. Chib, Siddhartha & Greenberg, Edward, 2010. "Additive cubic spline regression with Dirichlet process mixture errors," Journal of Econometrics, Elsevier, vol. 156(2), pages 322-336, June.
  43. Abel Rodríguez & David B. Dunson & Alan E. Gelfand, 2009. "Bayesian nonparametric functional data analysis through density estimation," Biometrika, Biometrika Trust, vol. 96(1), pages 149-162.
  44. Lundblad, Christian, 2007. "The risk return tradeoff in the long run: 1836-2003," Journal of Financial Economics, Elsevier, vol. 85(1), pages 123-150, July.
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