Sub-optimality of Threshold and Constant Proportion Portfolio Insurance Strategies in Defined Contribution Pension Plans

The threshold and constant proportion portfolio insurance (CPPI) strategies are considered for their application in managing defined-contribution (DC) pension plans. The pension plans invest in two types of asset, riskless asset and stocks, or bonds and stocks. When the objective of pension plan is to maximize expected terminal utility that is a function of terminal pension wealth with final wages as numeraire, both threshold and CPPI strategies are suboptimal to the portfolio from inter-temporal optimization. When the objective of pension plan is to minimize expected terminal disutility defined as squared difference between actual wealth and target wealth, the threshold and CPPI strategies are inferior to a corresponding static-to-riskless hybrid strategy. When the objective of pension plans is to maximize expected terminal utility that is a function of terminal wealth over a guaranteed minimum, the threshold and CPPI strategies are inferior to a minimum terminal wealth insurance (MTWI) strategy. Since the threshold strategy is not optimal in minimizing expected terminal disutility and the CPPI strategy not optimal in maximizing utility over a guaranteed minimum, for which they appear to be designed respectively, they are generally suboptimal in managing DC pension plans.