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

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Ranking preferences by downside risk aversion
Ranking Preferences by Downside Risk Aversion

Donald C. Keenan

Université de Cergy-Pontoise

and

Arthur Snow

University of Georgia


Greater risk aversion
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
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 aversion1
Greater Risk Aversion

  • is more risk averse than

    since

  • is not more risk averse than

    since

  • Ranking is asymmetric & transitive


Greater downside risk aversion1
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
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


Ranking preferences by downside risk aversion


Example saving
Example: Saving

  • Saving by u increases when income risk

    increases if

  • Saving by increases if


Conclusions
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.