Optimal Collective Investment: How Costly are Guarantees?

Abstract

The present paper answers the question of how the well-being of individual investors (e.g. pension beneficiaries) is affected by having their capital invested in a collective fund. To achieve this, we lay out and solve an optimal collective investment problem under a portfolio insurance constraint, whereby heterogeneous risk preferences of individual plan members are considered. We further distinguish between two types of investors, with different willingness to pay management fees, and study the impact of guarantee design, sharing rules and management fees on the individual investors' benefits. To achieve fairness among various investors, careful considerations shall be given to the management fees and the design of the sharing rule. If unfair sharing rules are applied, the unfairness in the pool increases in the long term. A flexible guarantee which consists of both a deterministic and a state-dependent component proves to have a considerable positive impact on the fairness of the collective in comparison to a purely deterministic guarantee.