Optimal Design of the Attribution of Pension Fund Peformance to Employees

The paper analyses a defined-contribution pension fund in continuous time. According to a prespecified attribution scheme the interest rate paid on the employees' accounts is a linear function of the fund's investment performance. An attribution scheme consists of a articipation rate and an intercept. For each attribution scheme the pension fund maximises the expected utility of the funding ratio at the end of a planning horizon and the employees derive utility from their savings accounts at the time they exit the plan. Solving the optimisation problem of the pension fund leads to constant optimal investment strategies. For the pension fund and the employees, respectively, indirect utility functions can be derived on the set of attributions. It turns out that all Pareto-optimal attribution schemes are characterised by the same optimal participation rate. As a main result, we derive the total welfare gain - measured by the increase in appropriate certainty equivalents of the pension fund and the employees, respectively - that installs from replacing no participation with optimal participation. For reasonable parameter values a substantial increase in the risk-adjusted rate of return on employees' accounts can be achieved if the welfare gain is fully attributed to the employees.