investors in private equity partnerships must pay fees, typically reducing expected return by 2 to 3 percent. We have performed some simulations that suggest that a value of a very near zero would be consistent with the data in the Venture Economics database, once again noting the limitations of the data. Here again, different private equity investors can produce portfolios with very different values of a, depending on their choices in manager selection and portfolio construction. What of manager skill? Examination of the historical data suggests that particular managers with excess skill or information may be able to deliver a of up to 10 percent or even higher (while others, as noted, may have negative a). To the extent that these managers with unusual skill are doing unusual deals, this may also have the effect of lowering p, although in this case the non-public-market risk term o may increase. As has been observed in previous chapters, this can be a good trade- O^ represents relatively cheap risk, while the public-market component controlled by p is the relatively expensive part. OPTIMAL ALLOCATION EXAMPLES_______________ In the general, multi-asset case, the model described earlier can be used to augment the global covariance matrix and calculate optimal weights for private equity. However, some additional insight can be gained by considering a simple two-asset situation, where the investor simply wishes to substitute private equity for some fraction w of an existing public-equity portfolio. Using the results of Chapter 4 and the model defined earlier, we see that the optimal weight for private equity (as a fraction of the total equity portfolio) is given by oc + (XoJ-m.J(1-P) x[o^+(l-P)2oj] (28.6) Here X is the risk-aversion parameter described earlier in the book. This is an interesting result for several reasons. First, from the numerator it can be seen that there are essentially two reasons to allocate to private equity. The first is if the private equity portfolio has some positive source of return, a, unrelated to returns in the public market. The second is that if the private equity portfolio has p less than 1, there is also a diversification rationale for an allocation to private equity. Second, it is interesting to examine the behavior of this allocation for its dependence on the market p. The most important point is that since the multiplier Xo2 - )J. must be positive, then wo must decrease as p increases. Thus we see that the rationale for an allocation to private equity must rely in large part on its nonequilibrium innovative components, such as new or innovative businesses. Third, look at the simplifications that arise if p = 1. In this case, it can be seen that