meet any unfunded commitments to private equity partnerships. EFFECT OF SUBOPTIMAL ALLOCATION At this point a fundamental difficulty is observed. We can derive the optimal allocation to private equity as a consequence of estimated statistics, but we have also observed that the estimated statistics are not very reliable. Furthermore, the range of illustrated results (allocation of 10 percent to 50 percent of the equity portfolio to private equity) is rather broad to be useful. One way to address this difficulty is to calculate the impact on the statistics of the overall equity portfolio if it should turn out that the private equity portfolio has different statistics from those that were assumed in developing the allocation. If reality differs from assumptions, the situation is said to be suboptimal. Then the investor can decide whether the potential gains (if the estimates turn out to be accurate) are worth the additional risks (if the estimates turn out to be inaccurate). For example, suppose that an investor decides, on the basis of some set of parameters, to select a weight w to private equity. (Note that there will be a variety of sets of parameters that may result in any given weight.) As we have shown, this allocation will generally be based (at least in part) on the expectation that the specific return a to the private equity portfolio will be positive. However, suppose that the a that is actually obtained turns out to be zero. Then the optimal thing to have done (had the true value of a been known at the time of allocation) would have been to allocate a smaller amount to private equity, and possibly none. In this case the investor will have paid a price in terms of increased total equity volatility, without receiving the expected benefit in terms of increased return. What is the impact on total equity volatility of some positive weight w} The combined volatility for the total equity portfolio that results from a selected weight iv, here called oT, is given by f \2 = (\-wf +2$w(w-l)+w1 f \2 (28.10) This function is given in Figure 28.4 for the same ranges of parameters discussed earlier. It can be seen that for low weights on private equity (for example, w = 10%), over the range of parameters discussed here, the volatility of the combined equity portfolio increases by no more than a factor of 1.06. (For example, if 0E were about 16 percent, then oT would be about 17 percent for any beta be-tweeen 1.0 and 1.5.) Many investors have weights on private equity that are up to 10 percent of their total equity portfolios, or even higher, possibly reflecting this observation. For intermediate weights on private equity the price to be paid, in terms of increased volatility, is steeper. For w = 25% and |i up to 1.0, total volatility is in the same range-an increase of up to a factor of 1.07. However, if |3 turns out to be 1.5, the increase in total volatility is a factor of 1.19. Thus, it probably makes sense to have a weight on private equity as high as 25 percent only if the investor