IDEAS home Printed from https://ideas.repec.org/p/fip/fednsr/61.html
   My bibliography  Save this paper

Nonlinear risk

Author

Listed:
  • Marcelle Chauvet
  • Simon M. 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.

Suggested Citation

  • Marcelle Chauvet & Simon M. Potter, 1999. "Nonlinear risk," Staff Reports 61, Federal Reserve Bank of New York.
  • Handle: RePEc:fip:fednsr:61
    as

    Download full text from publisher

    File URL: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr61.html
    Download Restriction: no

    File URL: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr61.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Harvey, Campbell R., 2001. "The specification of conditional expectations," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 573-637, December.
    2. 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.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. 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 207-232.
    5. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
    6. Fama, Eugene F. & Schwert, G. William, 1977. "Asset returns and inflation," Journal of Financial Economics, Elsevier, vol. 5(2), pages 115-146, November.
    7. 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 177-185, April.
    8. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
    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. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    11. 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.
    12. 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 357-384, March.
    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. 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 969-996, November.
    15. 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.
    16. 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.
    17. Chan, K. C. & Karolyi, G. Andrew & Stulz, ReneM., 1992. "Global financial markets and the risk premium on U.S. equity," Journal of Financial Economics, Elsevier, vol. 32(2), pages 137-167, October.
    18. 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).
    19. 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.
    20. 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.
    21. 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.
    22. Pesaran, M Hashem & Timmermann, Allan, 1995. " Predictability of Stock Returns: Robustness and Economic Significance," Journal of Finance, American Finance Association, vol. 50(4), pages 1201-1228, September.
    23. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    24. Garcia, Rene, 1998. "Asymptotic Null Distribution of the Likelihood Ratio Test in Markov Switching Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(3), pages 763-788, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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 And Accurate Model For Dynamic Asset Allocation?," Working Papers wp2004_0419, CEMFI.
    6. 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.
    7. 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.
    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. 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.

    More about this item

    Keywords

    Business cycles ; Recessions;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fip:fednsr:61. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Amy Farber). General contact details of provider: http://edirc.repec.org/data/frbnyus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.