< cc = -150% -- a) o> J -200% --o -250% -- -300%         ; yfT :   -""I/------- 1-----   -------- i------ 0% 10% 20% 30% 40% 50% 60% Equity Allocation -♦-Underfunded ...... -m..... Exactly Funded 70% 80% 90% 100% Overfunded FIGURE 10.7 Effect of Global Fixed Income Diversification abilities by allocating to bonds. Thus, the correlation of equities with liabilities matters once more. It can be verified that for higher noise levels the overfunded plan actually experiences a decrease in the RACS when switching from domestic to global equity. After this discussion, it should be easy to see why the exactly funded and underfunded plans may want to stick with domestic equity. Due to a lack of funds, they cannot eliminate (in the absence of noise) or nearly eliminate (otherwise) liabilities from the asset allocation problem. For these funds, the correlation of domestic equity with liabilities is crucial. Hence these funds do not gain from diversification/ Now let us briefly turn to the issue of global fixed income diversification. The discussion centering on equity diversification provides some insights here as well. In the present context bonds are attractive because they hedge against changes in liabilities. Since we modeled liabilities with respect to a domestic bond index (as seems reasonable for most pension plans), global bonds will generally not be an attractive asset class since they correlate with liabilities to a lower extent by construction. Figure 10.7 shows that our conjecture is correct, with all funds experiencing a decrease in the RACS. Example: Choosing the Right Duration of the Bond Portfolio The last topic in the static analysis is choosing the duration of the bond portfolio. Of course, the more closely the duration of the asset portfolio matches that of the liability index the better, since it leads to better immunization against changes in liability 6Here we only considered the cases of no and full diversification. It can be shown that slightly underfunded plans may benefit from a small level of equity diversification at high equity allocations. In other words, these plans may see a small increase in the RACS by investing part of their equity outside the home country.