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Nonlinear Risk

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  • Chauvet, Marcelle
  • Potter, Simon

Abstract

This paper analyzes 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 an overall negative contemporaneous relationship between the conditional expectation and variance of the monthly value-weighted excess return. However, the sign of the correlation is not stable, but instead varies according to the stage of the business cycle. In particular, around the beginning of recessions, volatility rises substantially, reflecting great uncertainty associated with these periods, while expected return falls, 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 return is 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 noncontemporaneous correlations of these two conditional moments.

Suggested Citation

  • Chauvet, Marcelle & Potter, Simon, 2001. "Nonlinear Risk," Macroeconomic Dynamics, Cambridge University Press, vol. 5(4), pages 621-646, September.
  • Handle: RePEc:cup:macdyn:v:5:y:2001:i:04:p:621-646_02
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    Cited by:

    1. Potter, Simon M., 2000. "Nonlinear impulse response functions," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1425-1446, September.
    2. 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.
    3. 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, Central European Journal of Economic Modelling and Econometrics, vol. 4(4), pages 269-288, December.
    4. Peter N. Smith & Steffen Sorensen & Michael Wickens, 2010. "The equity premium and the business cycle: the role of demand and supply shocks," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 15(2), pages 134-152.
    5. Francisco Peñaranda, 2004. "Are Vector Autoregressions an Accurate Model for Dynamic Asset Allocation?," Working Papers wp2004_0419, CEMFI.
    6. Blake LeBaron, 1994. "Chaos and Nonlinear Forecastability in Economics and Finance," Finance 9411001, University Library of Munich, Germany.
    7. Simon M. Potter, 1999. "Nonlinear time series modelling: an introduction," Staff Reports 87, Federal Reserve Bank of New 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. 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.
    10. 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.
    11. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-125, April-Jun.
    12. Franz Alberto Hamann, 1996. "Puede Explicarse el Precio Externo del Café con un Modelo Econométrico no Lineal?," Borradores de Economia 065, Banco de la Republica de Colombia.
    13. Hansen,B.E., 1999. "Testing for linearity," Working papers 7, Wisconsin Madison - Social Systems.
    14. Lokshin, Michael & Ravallion, Martin, 2000. "Short-lived shocks with long-lived impacts? - household income dynamics in a transition economy," Policy Research Working Paper Series 2459, The World Bank.
    15. 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.

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