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Ranking Preferences by Downside Risk Aversion PowerPoint Presentation
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Ranking Preferences by Downside Risk Aversion

Ranking Preferences by Downside Risk Aversion

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Ranking Preferences by Downside Risk Aversion

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  1. Ranking Preferences by Downside Risk Aversion Donald C. Keenan Université de Cergy-Pontoise and Arthur Snow University of Georgia

  2. Greater Risk Aversion • is risk averse if • is more risk averse than u if v dislikes any increase in risk in the distribution for u • v is more risk averse than u iff

  3. Greater Downside Risk Aversion • is downside risk averse if • is more downside risk averse than u if v dislikes any increase in downside risk in the distribution for u • is more downside risk averse than u iff

  4. Greater Risk Aversion • is more risk averse than since • is not more risk averse than since • Ranking is asymmetric & transitive

  5. Greater Downside Risk Aversion • is more downside risk averse than since • is also more downside risk averse than since • Ranking is symmetric & not transitive

  6. Strongly Greater Downside Risk Aversion • is strongly more downside risk averse than u if and • Ranking is asymmetric and transitive • dislikes any TSD shift in the distribution for u iff and

  7. is strongly more downside risk averse than • is not strongly more downside risk averse than • Ranking is asymmetric and transitive

  8. Example: Saving • Saving by u increases when income risk increases if • Saving by increases if

  9. Conclusions • Identifying higher orders of risk aversion by nested order-preserving spreads in the distribution for u does not yield a strict partial ordering. • Identifying with SD shifts in the distribution for u yields a characterization and a strict partial ordering.