A financial advisor's primary objective in allocating clients' assets is to design and construct investment policies that meet their future economic needs while satisfying their risk preferences. This is accomplished by determining their total assets, helping them to formulate an objective, estimating their future financial needs and identifying their attitude toward risk.

The ultimate success of the resulting investment policy in achieving the client's objective will depend not only on the accuracy with which each of these steps is accomplished, but also, and more importantly, on the method used to determine the client's strategic asset allocation.

Most financial advisors are familiar with the "efficient frontier" first proposed by Nobel-prize winning economist Harry Markowitz in his doctoral dissertation, and later expanded upon in his 1959 book, "Portfolio Selection: Efficient Diversification of Investments." He argued that there is an "efficient frontier" that contains only those portfolios having maximum expected returns at given risk levels. Statistically, these portfolios are said to be mean-variance efficient, since the curvilinear shape of the frontier depends on the expected returns of all available investment alternatives, their variance (as a surrogate for risk) and the pair-wise covariance between them. Figure 1 contains the traditional representation of mean-variance (M-V) efficiency. The M-V Efficient Frontier is the uppermost part of the curve, bounded by the extreme left and right arrows.

Although mean-variance efficiency has been useful as a theoretical concept in promoting an understanding of market efficiency, it has not been of practical use in designing or constructing optimal portfolios. In fact, the concept has significant shortcomings, which severely limit its practical usefulness. First, M-V efficiency assumes that the relationship between return, risk and covariance is deterministic, that there is only one optimal portfolio at a specific level of return or risk. It makes no allowance for portfolios that may be statistically indistinguishable from the "one optimal M-V efficient portfolio."

Also, M-V efficiency usually employs historical average returns, standard deviations and covariances, but these observed historical values actually come from a universe of uncertain possibilities, any of which had some probability of occurring. For example, in recent months, it has been widely reported that the stock market's lackluster performance is the result of a combination of factors, such as a slowing economy, the number of high-visibility companies lowering their estimates of future sales growth and profitability, uncertainty over the future course of interest rates and doubts concerning whether the Bush administration's economic policies will be adopted by the Congress.

These factors combined resulted in levels of return and volatility that were observed and reported. Yet, absent one or more of these factors, each of which had some probability of occurring, other numbers would have been reported.

Also, historical observations frequently contain extreme values of return and volatility that are unlikely to occur in the foreseeable future. Extreme historical values do not accurately reflect the norm of the universe to which they belong. They can significantly distort the relationship between risk and return and the position of the efficient frontier over the investment horizon in which most financial advisors and their clients are interested. In fact, an efficient frontier derived from historical data is likely to overestimate returns at most risk levels.

Until recently, a financial advisor seeking to select a portfolio to optimally meet his or her client's needs was restricted to using M-V optimization procedures, usually with historical data. Depending on the client's risk preferences, the result would likely have been one of those shown in Figure 2, which contains the asset-allocation weights in six portfolios ranging in degrees of risk on a scale from 1 to 51, with 1 being the least risky and 51, the most. Annualized monthly data from January 1990 through December 1999 were used.

The results in Figure 2 are typical of those associated with M-V optimization, which ignores many asset classes that might otherwise improve a portfolio's diversification. For example, Portfolio No. 1, the least risky is, not surprisingly, composed mainly of T-bills, with only modest amounts of small-cap and international stocks. At the other extreme, Portfolio No. 51 is comprised of only large-cap stocks. Portfolios between these two extremes ignore two or more of the available asset classes. Concentrating, as it does, on few asset classes, M-V optimization results in portfolios that could be better diversified because the returns of these different asset classes do not move in unison. Hence, using a combination of all or most of the assets available is likely to reduce the overall risk of a portfolio through increased diversification.

A new approach to portfolio optimization has been developed, one that produces better-diversified portfolios than those selected by M-V methods. This new approach, "resampled efficiency optimization," recognizes the relationship between return, risk and covariance is stochastic, and there are a number of optimal portfolios at a specific risk level that are statistically equivalent.

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