Fair pensions

This paper examines the allocation of market risk in a general class of collective
pension arrangements: Collective Defined Contribution (CDC) schemes. In a CDC
scheme participants collectively share funding risk through benefit level adjustments. There is a concern that, if not well designed, CDC schemes are unfair and will lead to an unintended redistribution of wealth between participants and, in particular, between generations. We define a pension scheme as fair if all participants receive an arbitrage-free return on the market risk they bear. The fact that the participants’ claim the CDC schemes’ collective assets is expressed in terms of a stochastic future, makes the arbitrage-free allocation of market risk non-trivial. It depends crucially on the specification of the discount rate process in combination with the benefit adjustment process. We show that fair CDC schemes may use a default-free market interest rate in combination with a specific horizon-dependent benefit adjustment process. Alternative discount rates are also permissible, but require additional correction terms in the benefit adjustment process.