A Simple Approach for Measuring Higher-Order Arrow-Pratt Coefficients of Risk Aversion

Cary Deck (), Rachel J. Huang (), Larry Y. Tzeng () and Lin Zhao ()
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Cary Deck: Department of Economics, University of Alabama, Tuscaloosa, Alabama 35487; and Economic Science Institute, Chapman University, Chapman University, Orange, California 92866
Rachel J. Huang: Department of Finance, National Central University, Taoyuan 32001, Taiwan
Larry Y. Tzeng: Department of Finance, National Taiwan University, Taipei 10617, Taiwan
Lin Zhao: School of Business Administration, Southwestern University of Finance and Economics, Chengdu 611130, China

Management Science, 2025, vol. 71, issue 8, 6979-6996

Abstract: Although the importance of the second-order Arrow-Pratt coefficients of risk aversion is well established, the importance of higher-order risk attitudes has only recently begun to be recognized. In this paper, we introduce a nonparametric approach to directly measure higher-order Arrow-Pratt coefficients of risk aversion in an expected utility framework using choices between compound lotteries and show how it can be easily implemented in behavioral studies. Specifically, we provide a theoretical basis for using risk apportionment to reveal the intensity of higher-order risk attitudes, and then draw upon our theoretical results to develop a simple, systematic, and generalizable procedure for eliciting higher-order Arrow-Pratt coefficients. We demonstrate our approach in a laboratory experiment and find that the modal second-order, third-order, and fourth-order Arrow-Pratt coefficients are positive and small. Further, we find that degrees of risk aversion are positively correlated across orders. Additionally, we discuss alternative implementations of our procedure.

Keywords: Arrow-Pratt risk aversion; risk apportionment; prudence; temperance; laboratory experiment (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:71:y:2025:i:8:p:6979-6996

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