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NONLINEAR RISK

  • Marcelle Chauvet (a1) and Simon Potter (a2)
    • Published online: 25 September 2001
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.

Copyright
Corresponding author
The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of New York or the Federal Reserve System. We thank participants in the 1998 Meetings of the Society of Economic Dynamics, 1999 North American Summer Meetings, and the Latin American Meetings of the Econometric Society, Conference on Nonlinear Modeling of Multivariate Macroeconomic Relations (Rotterdam), and seminar at the State University of Maringa (Brazil), and two anonymous referees for helpful comments. Address correspondence to: Marcelle Chauvet, Department of Economics, University of California, Riverside, CA 92521-0247, USA; e-mail: chauvet@mail.ucr.edu.
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Macroeconomic Dynamics
  • ISSN: 1365-1005
  • EISSN: 1469-8056
  • URL: /core/journals/macroeconomic-dynamics
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