has unit dependence on the public equity market, then the allocation to private equity depends only on the specific return and specific volatility of the private equity portfolio, and not on total return or total volatility. Fourth, consider the special case when the expected excess return for the private equity portfolio is exactly equal to the expected excess return for the public equity portfolio-that is, when a = (l-p>E (28.8) It is clear that this case is equivalent to selecting a private equity allocation to minimize total volatility in the combined (private plus public) equity portfolio. In this situation, the optimizing allocation to private equity is 1-P f \2 (i-P)2 (28.; for any X. This reinforces our observation that an allocation due solely to diversification effects is only observed for private equity portfolios with p less than 1 with respect to the public equity market. The graphs in Figure 28.3 illustrate the fraction of the total equity portfolio that might be allocated to private equity, depending on the statistics that are assumed to be achieved for the particular private equity portfolio under consideration. As earlier in the book, in these examples we assume a risk aversion parameter of 2.857, expected excess returns to public equity of 4.1 percent, and public equity volatility of 15.9 percent. It can be seen that for p less than 1, the allocations to private equity are essentially straight lines, depending principally on the ratio between specific return and specific volatility, as discussed earlier. For p of 1.5, however, the penalty for high dependence on equilibrium public returns is clearly visible. Some of these allocations may be surprisingly large compared with recommendations seen elsewhere. However, it is clear from this analysis that the optimal allocation to private equity depends on the particular characteristics of the private equity portfolio under consideration, rather than just on the label attached to it. For those investors who can realistically expect to achieve an a of 3.0 percent or more (modest with respect to the dispersion of returns among private equity funds), with p no higher than 1.5, then an allocation to private equity of at least 10 percent of the total equity portfolio is readily justified. It should be emphasized that these results are for the two-asset case only, and without considering liquidity constraints. Somewhat different results will obtain for the multi-asset case, but the basic analysis is the same and uses the same machinery developed earlier in the book. Since private equity is highly illiquid, investors making allocations to private equity need to carefully consider their needs