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Nonlinear risk

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  • Marcelle Chauvet
  • Simon Potter

Abstract

This paper proposes a flexible framework for analyzing the joint time series properties of the level and volatility of expected excess stock returns. An unobservable dynamic factor is constructed as a nonlinear proxy for the market risk premia with its first moment and conditional volatility driven by a latent Markov variable. The model allows for the possibility that the risk-return relationship may not be constant across the Markov states or over time. We find a distinct business cycle pattern in the conditional expectation and variance of the monthly value-weighted excess return. Typically, the conditional mean decreases a couple of months before or at the peak of expansions, and increases before the end of recessions. On the other hand, the conditional volatility rises considerably during economic recessions. With respect to the contemporaneous risk-return dynamics, we find an overall significantly negative relationship. However, their correlation is not stable, but instead varies according to the stage of the business cycle. In particular, around the beginning of recessions, volatility increase substantially, reflecting great uncertainty associated with these periods, while expected returns decrease, anticipating a decline in earnings. Thus, around economic peaks there is a negative relationship between conditional expectation and variance. However, toward the end of a recession, expected returns are at its highest value as an anticipation of the economic recovery, and volatility is still very high in anticipation of the end of the contraction. That is, the risk-return relation is positive around business cycle troughs. This time-varying behavior also holds for non-contemporaneous correlations of these two conditional moments.

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Bibliographic Info

Paper provided by Federal Reserve Bank of New York in its series Staff Reports with number 61.

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Date of creation: 1999
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Handle: RePEc:fip:fednsr:61

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Related research

Keywords: Business cycles ; Recessions;

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References

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  1. 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.
  2. John Y. Campbell, 1985. "Stock Returns and the Term Structure," NBER Working Papers 1626, National Bureau of Economic Research, Inc.
  3. 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.
  4. Robert J. Shiller & John Y. Campbell, 1986. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Cowles Foundation Discussion Papers 812, Cowles Foundation for Research in Economics, Yale University.
  5. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  6. Backus, David K & Gregory, Allan W, 1993. "Theoretical Relations between Risk Premiums and Conditional Variances," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 177-85, April.
  7. René Garcia, 1995. "Asymptotic Null Distribution of the Likelihood Ratio Test in Markov Switching Models," CIRANO Working Papers 95s-07, CIRANO.
  8. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  9. Kim, C-J., 1991. "Dynamic Linear Models with Markov-Switching," Papers 91-8, York (Canada) - Department of Economics.
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  11. Harvey, Campbell R., 2001. "The specification of conditional expectations," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 573-637, December.
  12. Pesaran, M Hashem & Timmermann, Allan, 1995. " Predictability of Stock Returns: Robustness and Economic Significance," Journal of Finance, American Finance Association, vol. 50(4), pages 1201-28, September.
  13. Chauvet, Marcelle & Potter, Simon, 2000. "Coincident and leading indicators of the stock market," Journal of Empirical Finance, Elsevier, vol. 7(1), pages 87-111, May.
  14. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
  15. Hansen, B.E., 1991. "The Likelihood Test Under Non-Standard Conditions: Testing the Markov Trend Model of GNP," RCER Working Papers 279, University of Rochester - Center for Economic Research (RCER).
  16. K.C. Chan & G. Andrew Karolyi & Rene M. Stulz, 1992. "Global Financial Markets and the Risk Premium on U.S. Equity," NBER Working Papers 4074, National Bureau of Economic Research, Inc.
  17. 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.
  18. Brock, W.A. & Dechert, W.D. & LeBaron, B. & Scheinkman, J.A., 1995. "A Test for Independence Based on the Correlation Dimension," Working papers 9520, Wisconsin Madison - Social Systems.
  19. 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.
  20. Chauvet, Marcelle, 1998. "An Econometric Characterization of Business Cycle Dynamics with Factor Structure and Regime Switching," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 969-96, November.
  21. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  22. Chen, Nai-Fu & Roll, Richard & Ross, Stephen A, 1986. "Economic Forces and the Stock Market," The Journal of Business, University of Chicago Press, vol. 59(3), pages 383-403, July.
  23. Kandel, Shmuel & Stambaugh, Robert F, 1990. "Expectations and Volatility of Consumption and Asset Returns," Review of Financial Studies, Society for Financial Studies, vol. 3(2), pages 207-32.
  24. 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.
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Citations

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Cited by:
  1. Piotr Płuciennik, 2012. "The Impact of the World Financial Crisis on the Polish Interbank Market: A Swap Spread Approach," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 4(4), pages 269-288, December.
  2. Chauvet, Marcelle & Potter, Simon, 2000. "Coincident and leading indicators of the stock market," Journal of Empirical Finance, Elsevier, vol. 7(1), pages 87-111, May.
  3. Han, Yufeng, 2012. "State uncertainty in stock markets: How big is the impact on the cost of equity?," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2575-2592.
  4. Franz Alonso Hamann S., 1996. "Puede Explicarse El Precio Externo Del Café Con Un Modelo Econometrico No Lineal?," BORRADORES DE ECONOMIA 003408, BANCO DE LA REPÚBLICA.
  5. Nyberg, Henri, 2010. "QR-GARCH-M Model for Risk-Return Tradeoff in U.S. Stock Returns and Business Cycles," MPRA Paper 23724, University Library of Munich, Germany.
  6. Smith, Peter N & Sorensen, Steffen & Wickens, Michael R., 2009. "The Equity Premium and the Business Cycle: the Role of Demand and Supply Shocks," CEPR Discussion Papers 7227, C.E.P.R. Discussion Papers.
  7. Peter N Smith & Steffen Sorensen & Mike Wickens, 2007. "The Asymmetric Effect of the Business Cycle on the Equity Premium (This is an extensively revised version of earlier paper No. 06/04)," Discussion Papers 07/11, Department of Economics, University of York.
  8. Vit Posta, 2012. "Time-Varying Risk Premium in the Czech Capital Market: Did the Market Experience a Structural Shock in 2008–2009?," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 62(5), pages 450-470, November.
  9. Francisco Peñaranda, 2004. "Are Vector Autoregressions And Accurate Model For Dynamic Asset Allocation?," Working Papers wp2004_0419, CEMFI.

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