Notice that aside from the risk tolerance parameter, only the mean and variance enter into the formula, since the normal distribution is symmetric.
Gamma CE-criterion:
Notice that since the gamma distrubution has a finite minimum, the CE formula includes mean, variance and downside.
Results for Tolerance = 6
R.E. Davis, "An Empirical Back Test of the Portfolio Gamma Model for Optimal Asset Allocation", Vol 4, Advances in Mathematical Programming and Financial Planning, JAI Press, 1995.