  We provide a new characterization of second-order stochastic dominance, also
known as increasing concave order. The result has an intuitive interpretation
that adding a risk with negative expected value in adverse scenarios makes the
resulting position generally less desirable for risk-averse agents. A similar
characterization is also found for convex order and increasing convex order.
The proofs techniques for the main result are based on properties of Expected
Shortfall, a family of risk measures that is popular in financial regulation.
