**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.