One of the most daunting challenges facing financial advisors, a virtual high-wire act, is knowing when and how to rebalance clients' portfolios. There are no accepted rules. The rules most advisors use are ad hoc, that is, intuitive or practical but not very justifiable. Yet rebalancing challenges pervade every phase of our relationships with clients, from the times they initially ask us to review their portfolios to the times we make strategic and tactical adjustments to them.

When reviewing prospective clients' portfolios, a financial advisor's role is to recommend revisions based on their investment objectives. The first step is to determine whether the portfolio needs revision. A portfolio that is basically indistinguishable from one the advisor believes is efficient needs none. Recognizing that revision is not necessary eliminates the cost of rebalancing and enhances a portfolio's value.

Advisors who cannot recognize that one efficient portfolio is essentially equivalent to another efficient portfolio are likely to recommend rebalancing, thereby incurring unnecessary trading costs and doing a disservice to their clients. Over the relationship, the cumulative costs can be significant, not only to the client, but also to the advisor, if he or she is fee-based and derives income from assets under management.

Suppose an advisor could save a client just 1% of assets annually by eliminating needless rebalancing costs on an initial $100,000 portfolio. During a 10-year period, the difference in the portfolio's value, assuming it had a 10% annual return with rebalancing, would be $24,567.85. Assuming the advisor's fee is 1.5%, those additional fees accruing from the difference in assets is $368.52. While that may not seem like a great deal of money, consider the benefit of having retained a client pleased enough to provide referrals. Also, consider that the incremental difference could be multiplied by every $100,000 the advisor is managing. With total managed assets of $10 million, the additional incremental annual fees would amount to $36,852.

More important, advisors with a rational, disciplined approach to rebalancing are saving more than unnecessary fees for their clients; they also are saving the time and effort necessary to identify accounts that should be rebalanced and to find the right new portfolio. In the typical situation, an advisor is responsible for a number of accounts; let's assume 100. Let us also suppose he or she is sophisticated enough to use a standard mean-variance portfolio optimizer to derive a new optimal portfolio for each client. This alone is a daunting task because of the need to review the results of each stage of the optimization process and then to constrain his or her solutions until they yield a logically plausible one. Therein lies the frustration of torturing the optimization until it confesses.

The advisor would then be required to spend, on average, at most 1% of his or her time analyzing each portfolio to determine whether it needed rebalancing. In almost every instance, the client's current portfolio will not match the targeted optimal portfolio because, according to standard mean-variance optimization theory, there can be one, and only one, efficient portfolio having the greatest expected return at a specific risk level. The continuum of all such portfolios in mean-variance space is the efficient frontier. Since re-optimized portfolios rarely contain the same asset exposures from one rebalancing period to the next, they almost always require rebalancing.

Practitioners and academics have, therefore, contrived several general solutions, or hat tricks, to avoid the problem of having to rebalance a portfolio every time they optimize it. The simplest of these contrivances is to ignore the problem by assuming that once clients' strategic allocations are correct and their investment objectives are unchanged, no further action needs to be taken. This is sometimes referred to as the "set it and forget it" approach. Very cost effective in terms of trading costs, but naÔve with respect to opportunity costs.

A second and somewhat more popular contrivance is to review portfolios at fixed calendar intervals. This approach has some legitimacy since, over time, fundamental changes take place in financial markets; interest rates fluctuate, earnings estimates change, as do monetary and fiscal policies. Also, there are precedents related to reporting periods, such as monthly statements, quarter ends, mandated board meetings and so on. The flaw in this approach is that it ignores any tactical adjustments that become necessary between regular rebalancing periods.

A third hat trick, designed to overcome the shortcomings of the second, is to rebalance at fixed trigger points to ensure that the portfolio's allocations do not drift too far from their desired levels. The problem with this approach is that periods of market volatility, such as we have been experiencing over the past few years, may require frequent rebalancing to bring the portfolios' allocations to their exact strategic levels, thereby incurring the large trading costs this approach seeks to avoid.

A fourth, and perhaps most-often-used hat trick, is to rebalance to an allowed range within a set limit to reduce the number of necessary rebalancings and the degree to which the portfolio must be adjusted. This approach, however, seems to carry with it an implicit assumption that disruptions from a targeted asset exposure will revert to their origin. But that's not an optimal assumption to use in the strong bull market that lasted through March 2000 and throughout the bear market that may have ended in April.

If an advisor had a simple computerized rebalancing test, he or she could scan all 100 portfolios and easily identify those that required further attention, making the effort seem like a day at the beach in comparison to the other approaches. Assuming that only 10 of the 100 portfolios needed to be rebalanced, the advisor then has the luxury of spending an average of 10% of his or her time on each. In other words, the advisor is able to direct his or her attention to those portfolios that need it and avoid those that don't. Such a system would enable the advisor to provide equivalent oversight to all client portfolios with less effort. Perhaps the greatest economy provided by the rebalancing test therefore would accrue to the advisor.

A simple computerized rebalancing test already exists as part of an advanced portfolio-construction process called "resampled efficient optimization." This new approach recognizes there are a number of equivalently optimal portfolios at a specific risk level. Resampled efficiency defines a region of statistical equivalence for portfolios at specified risk levels. The approach was developed by Richard O. and Robert Michaud, for which they received a U.S. patent in 1999. The process is described in a book Richard wrote, titled Efficient Asset Management, published by Harvard Business School Press in Cambridge, Mass., in 1998 and in an article I wrote published in Financial Advisor (April 2001).

To determine whether two portfolios are statistically equivalent requires control of Type 1 error: the probability of rejecting the null hypothesis (that the portfolios are indistinguishable from an efficient portfolio) when it is true. The program can then decide whether the current portfolio needs rebalancing or not. The level of Type 1 error can be adjusted to clients' trading horizons, whether they are long-term investors or more interested in reflecting current market conditions.

A notable exception to this general rule occurs when an optimal portfolio does not satisfy client risk objectives and constraints. Such a portfolio, though efficient, is not statistically equivalent to one meeting client needs and may also need rebalancing.

The results of a rebalancing test are illustrated in Figure 1. This exercise assumes that the current portfolio consists of equally weighted portions of large-cap and small-cap stocks, long-term corporate and intermediate U.S. government bonds. The resampled optimization process creates a portfolio at every risk level over the entire spectrum of risk, as indicated in the six central column headings in the portfolio weights section of the figure. The last two columns contain the historical returns and standard deviations for the assets over the 10 years ended December 31, 2000. The returns and standard deviations of each portfolio are also listed at the bottom of their respective columns.

Clients holding the current portfolio in Figure 1 but wishing to hold the conservative portfolio at the minimum risk level, 0.3%, would need their portfolios to be rebalanced. So would clients wishing to hold portfolios at risk levels up to 4.9% because those portfolios are statistically distinguishable from the current portfolio. Clients wishing to hold more aggressive portfolios from level 7.5% and higher would require no rebalancing because those portfolios are statistically indistinguishable from the current portfolio.

The relative size of equity and cash positions also may influence the rebalancing process. When rebalancing from cash, the objective to actively manage the fully invested portfolio conflicts with the need to convert the cash into securities. This situation may require a two-step rebalancing process. The first step is to find an optimal portfolio from cash, omitting active-return forecasts that consider the investors' objectives and constraints, including their desired number of securities, and trading costs estimates. The second step converts the neutral portfolio into one that considers those items.

The value of this new rebalancing process will depend, in part, on reducing turnover. A recent back-test of the process, consisting of the performance of an institutional portfolio over a five-year period, was very promising. The resampled portfolio had a higher annualized return than the actual portfolio, 0.5% vs. -0.9%; a lower standard deviation, 3.6% vs. 4.7%; and dramatically lower turnover, 11.9% vs. 54.0%.

The 140 basis-point difference in returns is great enough to have grown the resampled portfolio's assets 7.2% above the actual portfolio at the end of the five-year period. Its standard deviation, smaller by 1.1%, suggests that it did so with less volatility. The reduction in turnover of 42.1% most certainly contributed to the resampled portfolio's superior performance.

In sum, the task of rebalancing client portfolios is an expensive, time-consuming job and often is as precarious as a high-wire act. Using standard mean-variance optimizers usually complicates the process by requiring a number of iterations before an acceptable solution is found, and then making rebalancing the portfolio necessary. Advisors have, therefore, contrived several general solutions, or hat tricks, to reduce turnover. Among them are: ignoring the problem with a "set it and forget it" mentality, reviewing portfolios at fixed calendar intervals, rebalancing at fixed trigger points or rebalancing to an allowed range within a set limit. Each of these approaches has some serious limitations.

Perhaps their greatest disadvantage is that they provide an illusion that portfolio revisions are being done properly when, in fact, they divert attention from the optimal solution to the rebalancing problem. Consequently, clients are likely to suffer lower returns and greater volatility, and advisors are unable to focus their attention exclusively on those clients who need it most. The optimal solution, the simple rebalancing test, enables advisors to provide equivalent oversight to all client portfolios with less effort.

The new resampled efficient optimization process provides an automatable portfolio-rebalancing rule that eliminates the need for ad hoc approaches and simplifies the task of optimizing while dramatically reducing unproductive turnover. While it's not a day at the beach, it's the closest thing to it.

C. Michael Carty is principal and chief investment officer for New Millennium Advisors Inc., a New York City-based investment advisor. He can be reached at mcarty1@rcn.com.

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