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Macroeconomic Dynamics (2002), 6: 242-265 Cambridge University Press
Copyright © 2002 Cambridge University Press
Published online by Cambridge University Press 16 May 2002

THE SHARPE RATIO AND PREFERENCES: A PARAMETRIC APPROACH

Martin Lettau a1c1 and Harald Uhlig a2
a1 Federal Reserve Bank of New York and CEPR
a2 Center for Economic Research, Tilburg University, and CEPR

Abstract

We use a log-normal framework to examine the effect of preferences on the market price for risk, that is, the Sharpe ratio. In our framework, the Sharpe ratio can be calculated directly from the elasticity of the stochastic discount factor with respect to consumption innovations as well as the volatility of consumption innovations. This can be understood as an analytical shortcut to the calculation of the Hansen–Jagannathan volatility bounds, and therefore provides a convenient tool for theorists searching for models capable of explaining asset-pricing facts. To illustrate the usefulness of our approach, we examine several popular preference specifications, such as CRRA, various types of habit formation, and the recursive preferences of Epstein–Zin–Weil. Furthermore, we show how the models with idiosyncratic consumption shocks can be studied.


Key Words: Sharpe Ratio; Hansen–Jagannathan Bounds; Volatility Bounds; Equity Premium.

Correspondence:
c1 We thank Parantap Basu, Paul Söderlind, two anonymous referees, and seminar participants at Carnegie-Mellon, Columbia, Mannheim, Montreal, NYU (Economics), NYU (Stern), and Ohio State for useful comments and Matt Darnell for editorial assistance. The views are those of the author(s) and do not necessarily reflect those of the Federal Reserve Bank of New York or the Federal Reserve System. Any errors and omissions are the responsibility of the authors. Address correspondence to: Martin Lettau, Federal Reserve Bank of New York, Research Department—3E, 33 Liberty Street, New York, NY 10045, USA; e-mail: Martin.Lettau@ny.frb.org.

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