0 percent to 100 percent. For the underfunded plan (shown in the top two graphs of Figure 10.11), modest equity allocations can greatly decrease the probability of being underfunded. Larger equity allocations yield only modest improvement. What is also interesting is the time necessary to wait until the funding ratio is more likely to be greater than 1 than to be less than 1. This can be inferred from finding the point at which any one line intersects a horizontal line drawn at 50 percent on the vertical axis, and finding the corresponding horizon along the horizontal axis. With a 100 percent equity allocation, a plan that is 80 percent funded and makes no payouts must wait about nine years; if it pays out 7.5 percent annually, it must wait 21 years! Overfunded plans actually increase the probability of losing their surplus by allocating to more equities. This conclusion fits in with all of our results regarding overfunded plans-namely, that the risk from large equity allocations may actually outweigh the benefits. CONCLUSIONS We set out to investigate the asset allocation decision process in the presence of liabilities. We defined three important decision points in this context, the equity/bond split, the duration of the bond portfolio, and international diversification. In our initial setup, we abstracted from payouts and focused on a single-period problem in which we generalized the familiar concept of a Sharpe ratio to account for the presence of liabilities. Our new measure, the risk-adjusted change in surplus (RACS), enabled us to investigate the trade-offs faced by pension plans in addressing the three important decision points. Our main findings were: II Underfunded plans benefit more from higher equity allocations than do over-funded plans for which the RACS often decreases after a certain equity allocation is reached. II Matching the duration of the bond portfolio to that of liabilities is important for all plans, with underfunded plans benefiting the most. II Global equity diversification is an attractive opportunity for overfunded plans, which can benefit from the higher Sharpe ratio of global equity. Underfunded plans are better off investing domestically in order to benefit from the higher correlation of liabilities with domestic assets. II Fixed income diversification is not attractive for any of the plans studied. The effect of increase in Sharpe ratio of assets from moving to global fixed income is more than offset by the lower correlation of liabilities with nondomestic assets. Subsequently, we analyzed the asset allocation decision in a dynamic framework that also incorporates payouts. We calculated returns required by underfunded plans to reach fully funded status over a given horizon and found that large equity allocations are necessitated by the need to become fully funded. We also investigated the risks associated with such allocations. Just as in the single-period setup, the main finding was that underfunded plans must take more equity risk to improve their funding status.