Stein estimators are not only useful in modifying return estimates, but also can significantly improve estimation of the covariance matrix and enhance the stability of the optimization process in both M-V or resampled efficient portfolios. Oliver Ledoit developed a covariance estimation method in which the number of assets can be very large and the number of historic periods of useful data very small, making it eminently suitable for applications involving short-term asset allocation.
The most potentially rewarding inputs to a portfolio optimization process are those that contain accurate proprietary estimates of future events. Modern portfolio theory cautions that such clairvoyance is rare in efficient markets. Yet financial advisors who believe they can add value to the optimization process may use a Bayesian approach to forecasting returns.
A Bayesian approach uses reasonable estimates, or a set of assumptions, to impose an exogenous structure on the optimization process. It transforms the optimization by reducing dependence on pure statistically estimated data, as is done by using raw historical data or Stein estimators. A wide range of applications is available using Bayesian procedures. For example, one could forecast returns of a best-case, worst-case and maximum-likelihood case to determine the sensitivity of the resulting asset allocations to each of those scenarios. The suitability of results, of course, will depend on the quality and accuracy of the inputs.
There is a significant difference between mean-variance and resampled efficient optimization in the area of portfolio rebalancing, one which clearly favors using resampling. Since M-V efficiency assumes that there is a deterministic relationship between return, risk and covariance, there is only one optimal portfolio at any specified level of return or risk.
Portfolios that are M-V re-optimized rarely contain the same asset exposures from one rebalancing period to the next, and therefore almost always incur trading costs. To mitigate these costs, financial advisors have adopted a number of heuristic policies to avoid rebalancing clients' portfolios. Among these policies are:
1) "Set it and forget it," implying that the initial strategic allocation is correct and no further action is warranted.
2) "Rebalance at fixed calendar periods" to ensure the portfolio is reviewed regularly so that any necessary tactical adjustments may be made to the strategic allocation. This policy, however, ignores portfolio misalignment between periods.
3) "Rebalance at fixed trigger points" to ensure that the portfolio's allocations do not drift too far from their desired levels. During periods of market volatility this policy may require frequent rebalancing to bring the portfolio's allocations to their exact strategic levels, thereby incurring large trading costs.
4) "Rebalance to an allowed range within a set limit" is intended to reduce the number of necessary rebalancings, and the degree to which the portfolio must be adjusted, but still is costly.
Each of these widely practiced rebalancing policies is unable to objectively determine whether the existing portfolio is statistically equivalent to the target portfolio. Thus, any attempt at rebalancing is likely to result in costs that may, or may not, be warranted.