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Greater downside risk aversion. (English) Zbl 1005.91080

Summary: Although investors are concerned foremost with mean and variance, they are also sensitive to downside risk. We introduce an index of downside risk aversion to distinguish risk aversion from higher-order aspects of risk preference, including prudence. We show that the index of downside risk aversion \(S\) increases with monotonic downside risk averse transformations of utility, thereby directly linking \(S\) to the definition of downside risk aversion introduced by C. F. Menezes et al. [Am. Econ. Rev. 70, 921-932 (1980)]. Although the index \(S\) applies equally to risk averse and risk loving decision makers, for a given positive degree of risk aversion, \(S\) is greater when the index of prudence is greater and vice versa.

MSC:

91B82 Statistical methods; economic indices and measures
91B30 Risk theory, insurance (MSC2010)
91B28 Finance etc. (MSC2000)
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