Ranking Preferences by Downside Risk Aversion

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.