Benefit uncertainty and default risk in pension plans

An “overlapping generations” model for a defined-benefit pension plan is constructed on the assumptions that: (i) the benefits due to each generation of members are pre-funded and (ii) in the event of the plan being terminated, its assets would be distributed to the final generation of members. The model is used to derive formulae for the mean and variance of the benefits paid to any future generation of members, allowing for the probability of termination. It is shown that a defined-benefit plan can, under reasonable assumptions, provide a more efficient distribution of benefits than a defined contribution plan for all generations of members. Similar results are obtained for a hybrid plan in which contributions are fixed and benefits are subject to an explicit smoothing formula. The performance of these plans, however, is significantly impaired if default risk is negatively correlated with investment returns.