The Effect of Objective Functions on Investment and Contribution Decisions for Defined Benefit Pension Schemes

Abstract

This paper examines the effect of objective function structures on the optimal management decisions (in particular, asset allocation and surplus/deficit spread period) for a model defined benefit superannuation scheme. The objectives of employer-sponsors, members and trustees are identified, with three risks being quantified and incorporated into different objective functions as used in previous studies. These are contribution rate risk, excess contribution rate risk and funding level risk. Simulation of a model scheme which is closed to new entrants is carried out to generate numerical values for the risks and consequently a single value from the range of different objective functions observed in the literature. Investigation of whether consistency exists between various objective functions in terms of optimal strategies is undertaken. It is found that there are considerable variations in the optimal decisions derived from each objective function, based on the same set of simulated outcomes. These variations are up to 87% in equity allocation and 14 years of surplus/deficit spread period. Such variations can be explained by either the risks that are considered or the way that the risks are measured. Further analysis is then undertaken of the impact of weighting parameter values on the optimal decisions with this analysis discovering that some of the objective functions tested are not appropriate for the investigation being undertaken. An overall outcome of the paper is the confirmation that it is vital to choose the most appropriate objective function based on the function’s characteristics and on the particular circumstances of the defined benefit scheme, in order to ensure that the optimal decisions are made for the scheme.