The distribution of the pension plan surplus

Abstract

Private defined-benefit pension plans must, by law, pre-fun the benefits. The actual experience of the pension fund rarely matches the assumptions underlying the contributions and liabilities. If the fund is worth more than the liabilities, the plan has a surplus; otherwise, it has a deficit, called an unfunded liability.

At times, the surplus can reach such a high level that there is pressure to distribute some of it. This raises two questions. First, how much can we part with without jeopardizing the future of the pension plan? Second, to whom and in what proportion should the amount to be parted with be given? This thesis represents an attempt at answering these two questions.

We begin with the definition of a (simplified) model pension plan. A review of pension plan mathematics follows, based on the projected unit credit method. We first consider all the elements which require assumptions to value the liabilities. These assumptions, which form the valuation basis, are kept constant through time for the sake of simplicity. We then given the formulae determining the contributions and liabilities.

We continue with the definition of a criterion to determine the amount of surplus to distribute, both for the whole plan and for any subgroup. Under that criterion, the amount must be such that, with a given level of probability, there will not be an unfunded liability at the next actuarial valuation. Applying the criterion to subgroups requires an initial asset allocation. Whereas decrements are assumed to be deterministic, economic variables are simulated using the Wilkie model. These variables impact both the assets and the liabilities.

Finally, we propose a methodology that could be used to distribute the disposable surplus. This approach is based on cooperative game theory. We review this theory and discuss its applicability in the present context. We also explore bargaining theory as an alternative approach. To illustrate the approach, we apply the method to our model pension plan and discuss the properties of four sharing rules that have been proposed in the economics literature.