## 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)

### Keywords:

downside risk; prudence; portfolio choice; labor supply
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