Plan member’s heterogeneity, economic regime effect and their implication on the management and sustainability of retirement funds

Abstract

This research studies the importance of plan members’ heterogeneity to the management of defined benefit (DB) pension fund. We propose a new multi-member model of DB pension fund that allows for heterogeneity in plan members’ retirement ages, salary growths, and other characteristics. We first solve analytically for optimal management strategy and show that the sponsor’s supplementary contribution and the fund’s allocation in risky assets are determined by the cross-product between the fund’s expected retirement liabilities and some heterogeneity-adjusted discount factors. We then demonstrate that the presence of heterogeneity can have a significant influence on the optimal management strategy and that a management decision made while ignoring heterogeneity will be suboptimal. However, solving for the true optimality decision under multi-member setting requires high computational resources, which is exponentially increasing with the number of members. We suggest a way to reduce dimensionality by approximating the multi-member problem with a series of single-member (adaptive representative agent or ARA) problems. Our ARA is the weighted average of all the remaining plan members. Higher weight is given to plan member with higher heterogeneity-adjusted expected benefit liability. Compared to the simple average approach, our novel approach is shown to be better especially under unfavorable market conditions. Lastly, we looked at the effect of heterogeneity on a country-level scale and try to understand its effects on the sustainability of a country’s social security system. In our model, we argue that population heterogeneity is the key in unifying competing theories on strategic reforms and their effects on sustainability. Different aspects of heterogeneity have characteristically different effects to the system’s aggregate taxation credit and investment return and thus the system’s lifetime estimate.