In general, there are two approaches to evaluate the sign of E[A]. First, utilizing
a result by Rothschild and Stiglitz (1970), a mean-preserving spread in r leads to a
rise (fall) in E[A] if A is a convex (concave) function of r. However, the verification
of convexity or concavity of A requires an evaluation of d*A/dr*, which does not
seem to generate conclusive results. The second approach is to evaluate E[A] directly.
Taking expectation of A in Eq. (7) yields: