Resampled efficiency is based on the simple notion that historical returns are merely observed elements in a probability distribution of possible outcomes, and the distribution from which they originate is most important in determining the optimality of a portfolio. In recognizing the statistical nature of the optimization process, one can infer that the M-V efficient frontier is overly restrictive and not very realistic. Instead, there is an efficient region of portfolio choices in which all portfolios are statistically indistinguishable from each other, irrespective of their asset allocation or weightings.

Figure 3 describes the configuration of the "Resampled Efficient Region." It has an upper boundary, similar in nature but not identical to an M-V efficient frontier, and a lower boundary, which defines a region in which all portfolios are statistically indistinguishable from each other at a specific risk level.

The resampled efficient region defines a new, more realistic efficient frontier, one that is bounded on both sides by possible random outcomes. By significantly reducing the distortions extreme historical observations impose on estimating return and risk, it facilitates locating a new, "true" efficient frontier, which lies within the resampled efficient region.

The results shown in Figure 4 are typical of those associated with resampled efficient optimization because they include most asset classes available to improve a portfolio's diversification. For example, in contrast to Portfolio No. 1 derived in the M-V optimization, the resampled efficient Portfolio No. 1 contains five asset classes instead of three. Its Portfolio No. 51 comprises all six asset classes, rather than only large-cap stocks, as in the case of M-V efficiency. Moreover, portfolios in between the two extremes also contain all six of the available asset classes. In sum, resampled efficient optimization results in portfolios that are better diversified than those using M-V optimization.

The M-V optimization results illustrated in Figure 2 relate to only five specific risk levels contained in a range of risk from 1 to 51. Figure 5 maps the asset allocations over the entire spectrum of risk. Each asset's weighting in a portfolio is vertically indicated by color above the horizontal axis. The combined weightings of all assets in a portfolio, at any risk level, sum to 100 percent along the vertical axis.

A common characteristic shared by all such composition maps related to M-V optimization is the sharp change in the weighting that each asset undergoes in moving from one risk level to another. For example, Treasury bills clearly dominate the lowest-risk portfolios and then drop out halfway across the risk spectrum. Large-cap stocks are omitted from the lowest-risk portfolio, but they totally dominate the high-risk aggressive portfolio.

In contrast, the resampled optimization results illustrated in Figure 6 contain some portion of all six asset classes as the portfolios incrementally increase in risk. This is a common characteristic of composition maps related to resampled efficient optimization: a gradual change in the weighting of each asset in moving from one risk level to another with many assets used in the portfolio.

A basic tenet of modern portfolio theory states that returns to underdiversified portfolios possess two elements of risk. The first, systematic risk, is related to the returns of the overall market and cannot be further reduced through diversification. The second, unsystematic risk, is unrelated to returns of the market but is related to a specific investment. Unsystematic risk, therefore, can be eliminated through further diversification. Since unsystematic risk can be eliminated, investors holding underdiversified portfolios are not generally compensated for assuming the additional risk they bear. Consequently, the more diversified portfolios resulting from resampled efficient optimization represent superior investments to M-V derived portfolios.

Estimates other than those based on historical data can result in dramatically different asset allocations. Many financial advisors do not fully understand the limitations of using raw historical data in estimating the returns necessary to create optimized portfolios. This is unfortunate, since modern estimation methods are theoretically superior and can often result in better-performing portfolios. There are essentially two methods for enhancing performance: Stein estimators, which efficiently forecast future returns using historical data, and Bayesian procedures, which use proprietary estimates of future events to forecast returns.

Charles Stein, a pioneer in modern multivariate estimation, developed a method for refining inputs for asset allocation. His method uses information about a group of return estimates as a reference point to determine whether the estimate for a given asset is normal or extreme. Using this method, a return estimate far from the global mean that is highly volatile is assumed to be likely to revert to less extreme returns, while an extreme estimate with a small variance is less likely to revert to the group's mean.