in a bond index with a different duration. The bond index we consider is the Lehman Aggregate, which had a duration of about 4.3 as of June 30, 2002. Figure 10.8 shows an efficient frontier graph like the one in Figure 10.3. In the top panel, the funding ratio is 0.8, and we see that in order to achieve the same return as in the base case, the fund must accept higher surplus risk when it chooses to invest in the Lehman Aggregate rather than the Lehman Long Government and Credit, against which liabilities are modeled. In the bottom panel the funding ratio is 1.5, and the same conclusion holds, but the loss from moving to an index with a lower duration is smaller. These results are easiest to understand if we choose a particular bond/equity split (one of the highlighted points along the lines) and consider what happens Underfunded Dollar Risk vs. Liabilities ■U.S. Equity/Lehman Long Gov't/Credit U.S. Equity/Lehman Overfunded       _^^*^* ^ r^*^*^ ♦     $25 Dollar Risk vs. Liabilities --U.S. Equity/Lehman Long Gov't/Credit U.S. Equity/Lehman Aggregate FIGURE 1 0.8 Effect of Shortening Duration of Bond Portfolio