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Consistent Estimation of the Risk-Return Tradeoff in the Presence of Measurement Error

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  • Oliver Linton

    ()

  • Anisha Ghosh

    ()

Abstract

This paper proposes an approach to estimating the relation between risk (conditional variance) and expected returns in the aggregate stock market that allows us to escape some of the limitations of existing empirical analyses. First, we focus on a nonparametric volatility measure that is void of any specific functional form assumptions about the stochastic process generating returns. Second, we offer a solution to the error-in-variables problem that arises because of the use of a proxy for the volatility in estimating the risk-return relation. Third, our estimation strategy involves the Generalized Method of Moments approach that overcomes the endogeneity problem in a least squares regression of an estimate of the conditional mean on the corresponding estimate of the conditional variance, that arises because both the above quantities are endogenously determined within a general equilibrium asset pricing model. Finally, we use our approach to assess the plausibility of the prominent Long Run Risks asset pricing models studied in the literature based on the restrictions that they imply on the time series properties of expected returns and conditional variances of market aggregates.

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Bibliographic Info

Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp605.

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Date of creation: Nov 2007
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Handle: RePEc:fmg:fmgdps:dp605

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  1. Lubos Pástor & Meenakshi Sinha & Bhaskaran Swaminathan, 2008. "Estimating the Intertemporal Risk-Return Tradeoff Using the Implied Cost of Capital," Journal of Finance, American Finance Association, vol. 63(6), pages 2859-2897, December.
  2. Hentschel, Ludger & Campbell, John, 1992. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," Scholarly Articles 3220232, Harvard University Department of Economics.
  3. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2002. "Parametric and Nonparametric Volatility Measurement," NBER Technical Working Papers 0279, National Bureau of Economic Research, Inc.
  4. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
  5. David K. Backus & Allan W. Gregory, 1992. "Theoretical Relations Between Risk Premiums and Conditional Variances," Working Papers 92-18a, New York University, Leonard N. Stern School of Business, Department of Economics.
  6. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  7. Sydney Ludvigson & Serena Ng, 2006. "The Empirical Risk-Return Relation: a factor analysis approach," 2006 Meeting Papers 236, Society for Economic Dynamics.
  8. John Y. Campbell & John H. Cochrane, 1995. "By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," NBER Working Papers 4995, National Bureau of Economic Research, Inc.
  9. 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.
  10. Benoit Perron & Oliver Linton, 2004. "The Shape of the Risk Premium: Evidence from a Semiparametric GARCH Model," FMG Discussion Papers dp514, Financial Markets Group.
  11. Corradi, Valentina & Distaso, Walter & Swanson, Norman R., 2009. "Predictive density estimators for daily volatility based on the use of realized measures," Journal of Econometrics, Elsevier, vol. 150(2), pages 119-138, June.
  12. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
  13. Whitelaw, Robert F, 1994. " Time Variations and Covariations in the Expectation and Volatility of Stock Market Returns," Journal of Finance, American Finance Association, vol. 49(2), pages 515-41, June.
  14. Andrew B. Abel, 1989. "Stock Prices Under Time-Varying Dividend Risk: An Exact Solution In An Infinite-Horizon General Equilibrium Model," NBER Working Papers 2621, National Bureau of Economic Research, Inc.
  15. Hui Guo & Robert F. Whitelaw, 2006. "Uncovering the Risk-Return Relation in the Stock Market," Journal of Finance, American Finance Association, vol. 61(3), pages 1433-1463, 06.
  16. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2001. "An Empirical Investigation of Continuous-Time Equity Return Models," NBER Working Papers 8510, National Bureau of Economic Research, Inc.
  17. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, 08.
  18. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "There is a Risk-Return Tradeoff After All," NBER Working Papers 10913, National Bureau of Economic Research, Inc.
  19. Scruggs, John T. & Glabadanidis, Paskalis, 2003. "Risk Premia and the Dynamic Covariance between Stock and Bond Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(02), pages 295-316, June.
  20. Anisha Ghosh & George Constantinides, 2008. "Asset Pricing Tests with Long Run Risks in Consumption Growth," FMG Discussion Papers dp609, Financial Markets Group.
  21. Hansen, Lars Peter & Hodrick, Robert J, 1980. "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 829-53, October.
  22. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395.
  23. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  24. Paye, Bradley S. & Timmermann, Allan, 2006. "Instability of return prediction models," Journal of Empirical Finance, Elsevier, vol. 13(3), pages 274-315, June.
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