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What is the Shape of the Risk-Return Relation?

58 Pages Posted: 23 Mar 2009 Last revised: 9 Apr 2010

Alberto G. P. Rossi

Board of Governors of the Federal Reserve System

Allan G. Timmermann

University of California, San Diego (UCSD) - Department of Economics; Centre for Economic Policy Research (CEPR)

Date Written: March 25, 2010

Abstract

Using a flexible econometric approach that avoids imposing restrictive modeling assumptions, we find evidence of a non-monotonic relation between conditional volatility and expected stock market returns: At low-to-medium levels of conditional volatility there is a positive trade-off between risk and expected returns, but this relationship gets inverted at high levels of volatility as observed during the recent financial crisis. We propose a new measure of risk based on the conditional covariance between daily observations of a broad economic activity index and stock returns. Using this covariance measure, we find clear evidence of a monotonically increasing risk-return trade-off. Our finding of a non-monotonic mean-volatility relation helps explain the absence of a consensus in the empirical literature on the sign of the risk-return trade-off. At the same time, our finding that the expected return is a monotonically rising function of the conditional covariance measure also suggests that a positive risk-return relation can be established once a better measure of risk is used.

Keywords: risk-return trade-off, time-varying expected returns, conditional volatility, economic activity index, covariance risk, boosted regression trees.

JEL Classification: G12

Suggested Citation

Rossi, Alberto G. P. and Timmermann, Allan G., What is the Shape of the Risk-Return Relation? (March 25, 2010). AFA 2010 Atlanta Meetings Paper. Available at SSRN: https://ssrn.com/abstract=1364750 or http://dx.doi.org/10.2139/ssrn.1364750

Alberto G. P. Rossi

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

Allan G. Timmermann (Contact Author)

University of California, San Diego (UCSD) - Department of Economics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0508
United States
858-534-4860 (Phone)
858-534-7040 (Fax)

Centre for Economic Policy Research (CEPR)

77 Bastwick Street
London, EC1V 3PZ
United Kingdom

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