Volatility and Correlation of Returns   Evaluate the Portfolio Structure Project Expected Returns   Select a Point on the Frontier Find an Efficient Frontier FIGURE 9.1 Asset Allocation Paradigm Once the risk and return characteristics for each asset class have been defined, the investor then develops an efficient frontier, and selects a point on the efficient frontier that corresponds to his or her desired risk level. After analyzing the portfolio structure, and judging it to be inadequate, the investor imposes constraints and re-optimizes. The circle of constraints and reoptimization continues until the investor finds a portfolio that is judged to be satisfactory. Why do investors feel the need to impose constraints and reoptimize? The principal reason is because the optimal portfolio weights appear to be too extreme. Viewed differently, the investor believes that the optimal asset allocation should not make the aggressive switches between asset classes that are favored by the optimizer. The principal reason that the optimal portfolio weights may appear to be too extreme is because optimal asset allocations are quite sensitive to small changes in expected return assumptions. (This concern was crucial in the development of the Black-Litterman global asset allocation model.) A second, and related, issue is that historical average returns are quite sensitive to the choice of historical time period. Thus, we have a perplexing problem: Investors form views about expected future performance by calculating historical averages. These averages are quite sensitive to the choice of historical time period. The historical averages are then used in an optimizer, whose output (optimal portfolio weights) is quite sensitive to expected return assumptions. Little wonder, then, that practitioners are not completely satisfied with the standard methodology. A simple example may help to clarify some of these issues. Table 9.1 shows the historical average returns for three principal equity regions over two distinct time periods. The chosen equity regions are the United States, Japan, and Europe, while the time periods are the decade of the 1980s and the decade of the