OPTIMAL FUTURES HEADING:
QUADRATIC VERSUS
EXPONENTIAL UTILITY
FUNCTIONS
DONALD LIEN
Although quadratic and exponential utility functions both lead to mean-variance
expected utility analysis, this study demonstrates that the two approaches produce
different optimal futures hedging decisions. Specifically, the deviation between the
optimal production level and the optimal futures position is always smaller under
the exponential utility framework. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:
208–211, 2008
It is well known that, when the utility function is quadratic or exponential with
normal random variables, the expected utility depends upon only the mean and
variance. However, these two approaches should not be treated as equivalents
as they often lead to different optimal decisions. In this note, the difference
within the optimal futures hedging framework is illustrated.
The author wishes to acknowledge an anonymous referee and James Groff for helpful comments and sug-
gestions.
For correspondence, International Business Program, College of Business, University of Texas–San Antonio,
One UTSA Circle, San Antonio, TX 78249; e-mail: don.lien@utsa.edu
Received November 2006; Accepted February 2007
■ Donald Lien is the Richard S. Liu Distinguished Chair in Business in the College of Business
at the University of Texas at San Antonio in San Antonio, TX.
The Journal of Futures Markets, Vol. 28, No. 2, 208–211 (2007)
© 2008 Wiley Periodicals, Inc.
Published online in Wiley InterScience (www.interscience.wiley.com).
DOI: 10:1002/fut.20274