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Ranking Preferences by Downside Risk AversionPowerPoint Presentation

Ranking Preferences by Downside Risk Aversion

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Ranking Preferences by Downside Risk Aversion

Donald C. Keenan

Université de Cergy-Pontoise

and

Arthur Snow

University of Georgia

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

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

Greater Risk Aversion

- is more risk averse than
since

- is not more risk averse than
since

- Ranking is asymmetric & transitive

Greater Downside Risk Aversion

- is more downside risk averse
than since

- is also more downside risk averse
than since

- Ranking is symmetric & not transitive

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

- is strongly more downside
risk averse than

- is not strongly more downside
risk averse than

- Ranking is asymmetric and transitive

Example: Saving

- Saving by u increases when income risk
increases if

- Saving by increases if

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.

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