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Expected stock returns and variance risk premia

  • Tim Bollerslev
  • Hao Zhou

We find that the difference between implied and realized variances, or the variance risk premium, is able to explain more than fifteen percent of the ex-post time series variation in quarterly excess returns on the market portfolio over the 1990 to 2005 sample period, with high (low) premia predicting high (low) future returns. The magnitude of the return predictability of the variance risk premium easily dominates that afforded by standard predictor variables like the P/E ratio, the dividend yield, the default spread, and the consumption-wealth ratio (CAY). Moreover, combining the variance risk premium with the P/E ratio results in an R^2 for the quarterly returns of more than twenty-five percent. The results depend crucially on the use of "model-free", as opposed to standard Black-Scholes, implied variances, and realized variances constructed from high-frequency intraday, as opposed to daily, data. Our findings suggest that temporal variation in risk and risk-aversion both play an important role in determining stock market returns.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2007-11.

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Date of creation: 2006
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Handle: RePEc:fip:fedgfe:2007-11
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  1. Amit Goyal & Ivo Welch, 1999. "Predicting the Equity Premium with Dividend Ratios," Yale School of Management Working Papers amz2437, Yale School of Management, revised 01 Nov 2002.
  2. Campbell, John & Shiller, Robert, 1988. "Stock Prices, Earnings, and Expected Dividends," Scholarly Articles 3224293, Harvard University Department of Economics.
  3. Cochrane, John H. & Campbell, John, 1999. "By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Scholarly Articles 3119444, Harvard University Department of Economics.
  4. Martin Lettau & Sydney Ludvigson & Jessica Wachter, 2005. "The declining equity premium: what role does macroeconomic risk play?," Proceedings, Board of Governors of the Federal Reserve System (U.S.).
  5. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
  6. Peter Nyberg & Anders Wilhelmsson, 2010. "Volatility Risk Premium, Risk Aversion, and the Cross-Section of Stock Returns," The Financial Review, Eastern Finance Association, vol. 45(4), pages 1079-1100, November.
  7. Jonathan Lewellen & Stefan Nagel, 2003. "The Conditional CAPM does not Explain Asset-Pricing Anamolies," NBER Working Papers 9974, National Bureau of Economic Research, Inc.
  8. Hodrick, Robert J, 1992. "Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 357-86.
  9. Keim, Donald B. & Stambaugh, Robert F., 1986. "Predicting returns in the stock and bond markets," Journal of Financial Economics, Elsevier, vol. 17(2), pages 357-390, December.
  10. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
  11. Robert F. Stambaugh, 1999. "Predictive Regressions," NBER Technical Working Papers 0240, National Bureau of Economic Research, Inc.
  12. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
  13. Neil Shephard & Ole E. Barndorff-Nielsen, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Series Working Papers 2006-W03, University of Oxford, Department of Economics.
  14. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
  15. Amit Goyal & Ivo Welch, 2004. "A Comprehensive Look at the Empirical Performance of Equity Premium Prediction," Yale School of Management Working Papers amz2412, Yale School of Management, revised 01 Jan 2006.
  16. Bollerslev, Tim & Gibson, Michael & Zhou, Hao, 2011. "Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities," Journal of Econometrics, Elsevier, vol. 160(1), pages 235-245, January.
  17. Hui Guo & Robert Whitelaw, 2005. "Uncovering the risk-return relation in the stock market," Working Papers 2001-001, Federal Reserve Bank of St. Louis.
  18. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2004. "The Cross-Section of Volatility and Expected Returns," NBER Working Papers 10852, National Bureau of Economic Research, Inc.
  19. Owen Lamont, 1996. "Earnings and Expected Returns," NBER Working Papers 5671, National Bureau of Economic Research, Inc.
  20. Ravi Bansal & Varoujan Khatachtrian & Amir Yaron, 2002. "Interpretable Asset Markets?," NBER Working Papers 9383, National Bureau of Economic Research, Inc.
  21. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  22. Ravi Bansal & Amir Yaron, 2000. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," NBER Working Papers 8059, National Bureau of Economic Research, Inc.
  23. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
  24. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, Elsevier.
  25. John Y. Campbell, 1985. "Stock Returns and the Term Structure," NBER Working Papers 1626, National Bureau of Economic Research, Inc.
  26. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  27. Campbell, John Y, 1991. "A Variance Decomposition for Stock Returns," Economic Journal, Royal Economic Society, vol. 101(405), pages 157-79, March.
  28. Robert R. Bliss & Nikolaos Panigirtzoglou, 2004. "Option-Implied Risk Aversion Estimates," Journal of Finance, American Finance Association, vol. 59(1), pages 407-446, 02.
  29. Phillippe Weil, 1997. "The Equity Premium Puzzle and the Risk-Free Rate Puzzle," Levine's Working Paper Archive 1833, David K. Levine.
  30. 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.
  31. Bekaert, Geert & Engstrom, Eric & Xing, Yuhang, 2009. "Risk, uncertainty, and asset prices," Journal of Financial Economics, Elsevier, vol. 91(1), pages 59-82, January.
  32. Yacine Ait-Sahalia & Andrew W. Lo, 2000. "Nonparametric Risk Management and Implied Risk Aversion," NBER Working Papers 6130, National Bureau of Economic Research, Inc.
  33. George J. Jiang & Yisong S. Tian, 2005. "The Model-Free Implied Volatility and Its Information Content," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1305-1342.
  34. David M Kreps & Evan L Porteus, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Levine's Working Paper Archive 625018000000000009, David K. Levine.
  35. Gordon S. & St-Amour P., 2004. "Asset Returns and State-Dependent Risk Preferences," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 241-252, July.
  36. Andrew Ang & Geert Bekaert, 2001. "Stock Return Predictability: Is it There?," NBER Working Papers 8207, National Bureau of Economic Research, Inc.
  37. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
  38. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
  39. Wayne E. Ferson & Sergei Sarkissian & Timothy T. Simin, 2003. "Spurious Regressions in Financial Economics?," Journal of Finance, American Finance Association, vol. 58(4), pages 1393-1414, 08.
  40. Robert J. Shiller, 1984. "Stock Prices and Social Dynamics," Cowles Foundation Discussion Papers 719R, Cowles Foundation for Research in Economics, Yale University.
  41. Graham Elliott & Allan Timmermann, 2008. "Economic Forecasting," Journal of Economic Literature, American Economic Association, vol. 46(1), pages 3-56, March.
  42. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  43. Lettau, Martin & Ludvigson, Sydney, 1999. "Consumption, Aggregate Wealth and Expected Stock Returns," CEPR Discussion Papers 2223, C.E.P.R. Discussion Papers.
  44. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
  45. Fama, Eugene F. & Schwert, G. William, 1977. "Asset returns and inflation," Journal of Financial Economics, Elsevier, vol. 5(2), pages 115-146, November.
  46. Brandt, Michael W. & Wang, Kevin Q., 2003. "Time-varying risk aversion and unexpected inflation," Journal of Monetary Economics, Elsevier, vol. 50(7), pages 1457-1498, October.
  47. Geert Bekaert & Jun Liu, 1999. "Conditioning Information and Variance Bounds on Pricing Kernels," NBER Working Papers 6880, National Bureau of Economic Research, Inc.
  48. Robert J. Shiller, 1984. "Stock Prices and Social Dynamics," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 15(2), pages 457-510.
  49. Peter Carr & Liuren Wu, 2004. "Variance Risk Premia," Finance 0409015, EconWPA.
  50. Bekaert, Geert & Engstrom, Eric & Grenadier, Steven R., 2010. "Stock and bond returns with Moody Investors," Journal of Empirical Finance, Elsevier, vol. 17(5), pages 867-894, December.
  51. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2008. "High Idiosyncratic Volatility and Low Returns: International and Further U.S. Evidence," NBER Working Papers 13739, National Bureau of Economic Research, Inc.
  52. Ang, Andrew & Liu, Jun, 2005. "Risk, Return and Dividends," University of California at Los Angeles, Anderson Graduate School of Management qt1s25177n, Anderson Graduate School of Management, UCLA.
  53. Fama, Eugene F. & French, Kenneth R., 1989. "Business conditions and expected returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 25(1), pages 23-49, November.
  54. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-86, April.
  55. John H. Cochrane, 2006. "The Dog That Did Not Bark: A Defense of Return Predictability," NBER Working Papers 12026, National Bureau of Economic Research, Inc.
  56. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-51.
  57. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-73, April.
  58. Jonathan Lewellen & Stefan Nagel & Jay Shanken, 2006. "A Skeptical Appraisal of Asset-Pricing Tests," NBER Working Papers 12360, National Bureau of Economic Research, Inc.
  59. Tobias Adrian & Joshua Rosenberg, 2006. "Stock returns and volatility: pricing the short-run and long-run components of market risk," Staff Reports 254, Federal Reserve Bank of New York.
  60. Fama, Eugene F & French, Kenneth R, 1992. " The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-65, June.
  61. Mixon, Scott, 2007. "The implied volatility term structure of stock index options," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 333-354, June.
  62. John Y. Campbell & Motohiro Yogo, 2002. "Efficient Tests of Stock Return Predictability," Harvard Institute of Economic Research Working Papers 1972, Harvard - Institute of Economic Research.
  63. Itamar Drechsler & Amir Yaron, 2008. "What's Vol Got to Do With It," 2008 Meeting Papers 282, Society for Economic Dynamics.
  64. Mark Britten-Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, 04.
  65. John H. Cochrane & Monika Piazzesi, 2005. "Bond Risk Premia," American Economic Review, American Economic Association, vol. 95(1), pages 138-160, March.
  66. Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-77, December.
  67. Wu, Liuren, 2011. "Variance dynamics: Joint evidence from options and high-frequency returns," Journal of Econometrics, Elsevier, vol. 160(1), pages 280-287, January.
  68. 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.
  69. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
  70. Shanken, Jay, 1992. "On the Estimation of Beta-Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 5(1), pages 1-33.
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