TITLE:
Aversion to Risk and Downside Risk in the Large and in the Small under Non-Expected Utility: A Quantile Approach
AUTHORS:
Jean-Paul Chavas, Kwansoo Kim
KEYWORDS:
Risk, Quantile, Variance, Skewness, Downside Risk
JOURNAL NAME:
Theoretical Economics Letters,
Vol.5 No.6,
December
29,
2015
ABSTRACT: This paper proposes a decomposition of the cost of risk (as measured by a
risk premium) across intervals/quantiles of the payoff distribution. The
analysis is based on general smooth risk preferences. While this includes the
expected utility model as a special case, the investigation is done under a
broad class of non-expected utility models. We decompose the risk premium into
additive components across quantiles. Defining downside risk as the risk
associated with a lower quantile, this provides a basis to evaluate the cost of
exposure to downside risk. We derive a local measure of the cost of risk
associated with each quantile. It establishes linkages between the cost of
risk, risk preferences and the distribution of risky prospects across quantiles
(as measured by quantile variance and skewness). The analysis gives new and
useful information on how risk aversion, exposure to downside risk and
departures from the expected utility model interact as they affect the risk
premium.