Nonlinear Risk

Posted: 30 May 2001

See all articles by Marcelle Chauvet

Marcelle Chauvet

University of California Riverside

Simon Potter

Federal Reserve Bank of New York

Multiple version iconThere are 2 versions of this paper


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.

JEL Classification: C32, E32, E44, G12

Suggested Citation

Chauvet, Marcelle and Potter, Simon, Nonlinear Risk. Macroeconomic Dynamics, Vol. 5, No. 4, September 2001 . Available at SSRN:

Marcelle Chauvet

University of California Riverside ( email )

900 University Avenue
4136 Sproul Hall
Riverside, CA 92521
United States
(951) 827-1587 (Phone)

HOME PAGE: http://

Simon Potter (Contact Author)

Federal Reserve Bank of New York ( email )

33 Liberty Street
New York, NY 10045
United States
212-720-6309 (Phone)
212-720-1844 (Fax)

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