Pension Funding in a Stochastic Environment: The Role of Objectives in Selecting an Asset Allocation Strategy

For larger defined benefit pension plans variability in funding levels and contribution rates arises primarily from variability in real investment returns relative to salary growth. Recent work by Dufresne (1988, 1989, 1990) and Haberman (1994) has shown how this uncertainty can be reduced by chosing an appropriate amortization strategy. In the present paper we first consider to what extent the effectiveness of the decision making strategy is compromized by uncertainty in the model parameters. We then extend previous work by considering, in a simple fashion, how the asset allocation strategy can also be used to control variability. The obvious approach is to make use of less volatile assets. This reduces uncertainty in funding levels while the lower expected investment returns raise the mean contribution rate. However, lower risk assets have a tendency to produce returns which are positively correlated through time. This has the effect of increasing the variability in the funding level over that which might be expected, reducing the benefits of, for example, a switch fom equities into bonds. It is argued that clearly defined, mathematical objectives must exist for a fund to settle on an appropriate asset allocation strategy. Such objectives should define what levels of uncertainty are tolerable and which events are to be avoided (for example, the event that the solvency level falls below 90%). It is described how the Inverse-Gamma distribution provides a good approximation to the stationary distribution of the fund size. Using this approximation, a simple argument shows that an objective which provides an upper bound on the probability of insolvency favours a strategy which holds a fixed amount in a low risk asset and any surplus in a higher risk asset over the rebalancing strategy which maintains a fixed proportion in each asset class independent of the current funding level.