The Recovery Potential for Underfunded Pension Plans

In this paper, we consider defined benefit schemes which are designed to provide participants with a specific “ambition”, which we model as a stochastic benchmark, where its market value is higher than the market value of the contributions. We consider strategies based on preferences which become more risk-averse in disadvantageous scenarios (CRRA utilities) and preferences which become less risk-averse in such scenarios (SAHARA utilities). We also examine the influence of constraints that force the replacement ratio to exceed a certain lower bound. We find that by
a suitable choice of the parameters and of SAHARA utility functions, the average replacement ratio can be improved, with only a slightly higher probability of worse replacement ratios than in the CRRA case. We also investigate the effect of downward jumps in asset prices for both types of strategies. When the extra risk due to such jumps is compensated for by a higher value of the average rate of return for those assets, outcomes actually improve a bit in the sense that the probability of ending up above the minimally guaranteed level of the funding ratio increases for both CRRA and
SAHARA-based investment portfolios. This suggests that optimization based on SAHARA preferences with lower bound constraints can be a useful tool to generate good investment strategies whenever the market value of the “ambition” is higher than the market value of the contributions.