When Heterogeneity Helps: Stability in Lifetime Pension Pools

Lifetime pension pools lead to benefit variability driven by investment performance and the pool’s mortality experience, raising important questions about income stability, particularly in heterogeneous pools. This article examines how heterogeneity in member characteristics affects the stability of income payments in lifetime pension pools operating under a whole-pool-based adjustment in which benefits are adjusted uniformly across all members. We use the stable income period (SIP) as an intuitive, time-based measure of stability defined as the maximum horizon over which income remains within a prescribed band around its initial level with a given confidence. Using Monte Carlo simulations, we analyze the effects of mortality and wealth heterogeneity on income stability. We show that while a larger pool size improves stability through diversification, heterogeneity can enhance or reduce stability for some groups relative to specific homogeneous benchmarks, depending on the interaction among relative age, wealth, and group size. In particular, certain heterogeneous pools outperform selected homogeneous benchmarks from the perspective of a given reference group, while others are strictly dominated by one or more groups. Because direct calculation of the SIP can be computationally intensive, we also develop an analytical proxy and identify a control variate that significantly improves the tractability of the SIP without altering qualitative conclusions. Finally, we discuss how the SIP can serve as a practical design tool to inform rules and contribution limits, while also helping mitigate the effects of heterogeneity in real-world pools.