After Lunch Webinar: Anne Balter– “Welfare effects of collective investment for heterogeneous agents”

When heterogeneous agents invest in financial markets using the same, collective investment strategy, their individual  risk preferences and risk capacities need to be aggregated to come up with a collective strategy. In this paper, we consider this problem for a social planner whose objective is to minimize the maximal certainty-equivalent regret across agents,  thus minimizing the regret from being part of the collective. For the financial investment problem, we assume leverage constraints, discrete trading and a restriction to deterministic lifecycle strategies. In order to compute the regret-minimizing investment strategy, we apply a recent technique based on evolutionary dynamics and population games. This gives an efficient algorithm for finding optimal dynamic compromises between hundreds of agents. We then explore the idea of clustering agents into groups so that instead of a single lifecycle there are, say, two or three. We find that already with relatively few groups near optimal welfare can be achieved for all agents. Moreover, in our setting with leverage constraints, CRRA utility and heterogenous wage trajectories, grouping agents only by their coefficient of risk aversion regardless of their wage trajectories leads to a near-optimal clustering.