Minimum funding ratios for defined-benefit pension funds

摘要

We compute minimum nominal funding ratios for defined-benefit (DB) plans based on the expected utility that can be achieved in a defined-contribution (DC) pension scheme. Using Monte Carlo simulation, expected utility is computed for three different specifications of utility:power utility, mean-shortfall, and mean-downside deviation. Depending on risk aversion and the level of sophistication assumed for the DC scheme, minimum acceptable funding ratios are between 0.87 and 1.20 in nominal terms. For relative risk aversion of 5 and a DC scheme with a fixed-contribution setup, the minimum nominal funding ratio is between 0.87 and 0.98. The attractiveness of the DB plan increases with the expected equity premium and the fraction invested in stocks. We conclude that the expected value of intergenerational solidarity, providing time-diversification to its participants, can be large. Minimum funding ratios in real (inflation-adjusted) terms lie between 0.56 and 0.79. Given a DB pension fund with a funding ratio of 1.30, a participant in a DC plan has to pay a 2.7 to 6.1 % point higher contribution on average to achieve equal expected utility.