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DISCUSSION PAPER PI-0819

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

Qing-Ping Ma

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.

Keywords : Optimal asset allocation; Defined-contribution pension plan; Threshold
strategy; Constant proportion portfolio insurance (CPPI); Power utility;
Hamilton-Jacobi-Bellman equation.