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The Conditional CAPM, Cross-Section Returns and Stochastic Volatility

  • Fung, Ka Wai Terence
  • Lau, Chi Keung Marco
  • Chan, Kwok Ho

Bansal and Yaron (2004) demonstrate, by calibration, that the Consumption-Based Capital Asset Pricing Model (CCAPM) can be rescued by assuming that consumption growth rate follows a stochastic volatility model. They show that the conditional equity premium is a linear function of conditional consumption and market return volatilities, which can be estimated handily by various Generalized Autoregressive Conditonal Heterskedasticity (GARCH) and Stochastic Volatility (SV) models.We find that conditional consumption and market volatilities are capable of explaining cross-sectional return differences. The Exponential GARCH (EGARCH) volatility can explain up to 55% variation of return and the EGARCH model augmented with (cay) ̂ -a cointegrating factor of consumption, labor income and asset wealth growth- greatly enhance model performance. We proceed to test another hypothesis: if Bansal and Yaron estimator is an unbiased estimator of true conditional equity premium, then the instrumental variables for estimating conditional equity premium should no longer be significant.We demonstrate that once the theoretical conditional risk premium is added to the model, it renders all instrumental variables redundant. Also, the model prediction is consistent with observed declining equity premium.

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File URL: http://mpra.ub.uni-muenchen.de/52469/1/MPRA_paper_52469.pdf
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File URL: http://mpra.ub.uni-muenchen.de/52865/1/MPRA_paper_52865.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 52469.

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Date of creation: 2013
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Handle: RePEc:pra:mprapa:52469
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  1. Cochrane, John H, 1996. "A Cross-Sectional Test of an Investment-Based Asset Pricing Model," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 572-621, June.
  2. Martin Lettau & Sydney Ludvigson, 1999. "Resurrecting the (C)CAPM: a cross-sectional test when risk premia are time-varying," Staff Reports 93, Federal Reserve Bank of New York.
  3. Campbell, John Y, 1991. "A Variance Decomposition for Stock Returns," Economic Journal, Royal Economic Society, vol. 101(405), pages 157-79, March.
  4. Ravi Jagannathan & Zhenyu Wang, 1996. "The conditional CAPM and the cross-section of expected returns," Staff Report 208, Federal Reserve Bank of Minneapolis.
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  8. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  9. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-36, May-June.
  10. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September.
  11. Shanken, Jay, 1992. "On the Estimation of Beta-Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 5(1), pages 1-33.
  12. Riccardo Colacito & Mariano Croce, 2005. "Risks For The Long Run And The Real Exchange Rate," 2005 Meeting Papers 794, Society for Economic Dynamics.
  13. PREMINGER, Arie & HAFNER, Christian M., 2006. "Deciding between GARCH and stochastic volatility via strong decision rules," CORE Discussion Papers 2006042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Owen Lamont, 1996. "Earnings and Expected Returns," NBER Working Papers 5671, National Bureau of Economic Research, Inc.
  15. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  16. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  17. Jeff Fleming & Chris Kirby, 2003. "A Closer Look at the Relation between GARCH and Stochastic Autoregressive Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(3), pages 365-419.
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