The generalized value at risk admissible set: constraint consistency and portfolio outcomes

Generalized value at risk (GVaR) adds a conditional value at risk or censored mean lower bound to the standard value at risk and considers portfolio optimization problems in the presence of both constraints. For normal distributions the censored mean is synonymous with the statistical hazard function, but this is not true for fat-tailed distributions. The latter turn out to imply much tighter bounds for the admissible portfolio set and indeed for the logistic, an upper bound for the portfolio variance that yields a simple portfolio choice rule. The choice theory in GVaR is in general not consistent with classic Von Neumann-Morgenstern utility functions for money. A re-specification is suggested to make it so that gives a clearer picture of the economic role of the respective constraints. This can be used analytically to explore the choice of portfolio hedges.