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Univariate and multivariate measures of risk aversion and risk premiums

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Abstract

This paper develops univariate and multivariate measures of risk aversion for correlated risks. We derive Rubinstein's measures of risk aversion from the risk premiums with correlated random initial wealth and risk. It is shown that these measures are not only consistent with those for uncorrelated or independent risks, but also have the corresponding local properties of the Arrow-Pratt measures of risk aversion. Thus Rubinstein's measures of risk aversion are the appropriate extension of the Arrow-Pratt measures of risk aversion in the univariate case. We also derive a risk aversion matrix from the risk premiums with correlated initial wealth and risk vectors. This matrix measure is the multivariate version of Rubinstein's measures and is also the generalization of Duncan's results for non-random initial wealth. The univariate and multivariate measures of risk aversion developed in this paper are applied to portfolio theory in Li and Ziemba [15].

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Authors and Affiliations

  1. Department of Finance, School of Business Administration and Economics, California State University at Fullerton, 92634, Fullerton, CA, USA

    Yuming Li & William T. Ziemba

  2. Faculty of Commerce, University of British Columbia, V6T 1Y8, Vancouver, BC, Canada

    Yuming Li & William T. Ziemba

Authors
  1. Yuming Li
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  2. William T. Ziemba
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This research was partially supported by the National Research Council of Canada.

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Li, Y., Ziemba, W.T. Univariate and multivariate measures of risk aversion and risk premiums. Ann Oper Res 45, 265–296 (1993). https://doi.org/10.1007/BF02282053

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