AStA Advances in Statistical Analysis

, Volume 98, Issue 4, pp 305–326 | Cite as

Testing monotonicity of pricing kernels

  • Yuri Golubev
  • Wolfgang K. Härdle
  • Roman TimofeevEmail author
Original Paper


The behaviour of market agents has been extensively covered in the literature. Risk averse behaviour, described by Von Neumann and Morgenstern (Theory of games and economic behavior. Princeton University Press, Princeton, 1944) via a concave utility function, is considered to be a cornerstone of classical economics. Agents prefer a fixed profit over an uncertain choice with the same expected value, however, lately there has been a lot of discussion about the empirical evidence of such risk averse behaviour. Some authors have shown that there are regions where market utility functions are locally convex. In this paper we construct a test to verify uncertainty about the concavity of agents’ utility function by testing the monotonicity of empirical pricing kernels (EPKs). A monotonically decreasing EPK corresponds to a concave utility function while a not monotonically decreasing EPK means non-averse pattern on one or more intervals of the utility function. We investigate the EPKs for German DAX data for the years 2000, 2002 and 2004 and find evidence of non-concave utility functions: the null hypothesis of a monotonically decreasing pricing kernel is rejected for the data under consideration. The test is based on approximations of spacings through exponential random variables. In a simulation we investigate its performance and calculate the critical values (surface).


Monotonicity Pricing kernel Risk aversion 

JEL Classification

C12 G12 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Yuri Golubev
    • 1
  • Wolfgang K. Härdle
    • 2
  • Roman Timofeev
    • 2
    Email author
  1. 1.CMIUniversite de ProvenceMarseille Cedex 13France
  2. 2.Center for Applied Statistics and Economics (CASE)Humboldt-Universität zu BerlinBerlinGermany

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