We provide an economic interpretation of the practice consisting in
incorporating risk measures as constraints in a classic expected return
maximization problem. For what we call the infimum of expectations class of
risk measures, we show that if the decision maker (DM) maximizes the
expectation of a random return under constraint that the risk measure is
bounded above, he then behaves as a ``generalized expected utility maximizer''
in the following sense. The DM exhibits ambiguity with respect to a family of
utility functions defined on a larger set of decisions than the original one;
he adopts pessimism and performs first a minimization of expected utility over
this family, then performs a maximization over a new decisions set. This
economic behaviour is called ``Maxmin under risk'' and studied by Maccheroni
(2002). This economic interpretation allows us to exhibit a loss aversion
factor when the risk measure is the Conditional Value-at-Risk
