to drive the optimization process. Let us now illustrate some of the difficulties in using standard portfolio optimizers to create optimal portfolios. One Wall Street prognosticator recently provided us with a nice set of inputs for our example by publishing a set of long-term expected returns for major asset classes. The forecasts and our estimated volatilities are shown in Table 7.1. We suspect our colleague used what he felt was informed judgment to create this outlook, but that he did not try to run the expected returns through an optimizer. We proceeded to do exactly that, not to criticize our colleague (whose anonymity we shall respect), but rather to illustrate first how an optimizer looks for small inconsistencies in a set of forecasts and forms portfolios based on those inconsistencies, and second how difficult it is to specify a portfolio optimization problem in a way that leads to what might seem to be a reasonable solution. We formed a covariance matrix using historical returns for these various assets classes (and where necessary, as for private equity, used our best proxy). We then created two optimal portfolios, one completely unconstrained except that the weights were normalized to sum to 100 percent, and the other with the addition of no shorting constraints. These optimal portfolios are shown in Table 7.2. What we see in the completely unconstrained portfolio is that indeed the optimizer found some rather interesting opportunities-to create a hugely levered exposure to the global fixed income index while shorting offsetting weights in most of its components. Similarly, the unconstrained optimal portfolio forms a large overweight to the EAFE equity index, while shorting offsetting weights in several of its components. The constrained portfolio cannot take advantage of these long/short opportunities, so it simply chooses to hold large weights in hedge funds and high yield, and a smaller weight in real estate. Notice that the constrained portfolio has a much lower return per unit of volatility. Both portfolios seem quite unreasonable, despite the fact that TABLE 7.1 A Sample Long-Term Outlook in Early 2002   Asset Class Return Volatility Japanese government bonds 4.7% 4.2% European government bonds 5.1 3.6 U.S. government bonds 5.2 4.6 U.S. equities 5.4 15.5 Global fixed income 6.0 3.6 European equities 6.1 16.6 U.S. high-grade corporate bonds 6.3 5.4 EAFE 8.0 15.3 Hedge fund portfolio 8.0 5.2 U.S. high yield 8.9 7.3 Private equity 9.0 28.9 Emerging debt 9.0 17.6 REITs 9.0 13.0 Japanese equities 9.5 19.6 Emerging market equities 11.8 23.4