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Michaud Resampled Efficiency™ Optimization

The Michaud efficient frontier is a generalization of the Markowitz mean-variance efficient frontier that includes investment uncertainty in investment information in defining portfolio optimality. 

Markowitz mean-variance optimization provides the classical definition of portfolio optimality. Markowitz efficient portfolios have maximum return for a given level of risk or, equivalently, minimum risk for a given level of return. However, Markowitz optimization has important limitations in practice. Without numerous constraints, the procedure is typically unstable and often leads to unintuitive and unmarketable portfolios. 

Markowitz efficiency, while theoretically sound, is limited in practice by how information is used in modern computers. Optimizers assume that risk-return inputs are accurate to 16 decimal places. While such precision is essential for many scientific and engineering applications, it is absurd for finance. The mismatch between optimization precision and level of investment information certainty results in portfolios that have limited, if any, investment value. 

Resampled Efficiency optimization, invented and patented by Richard Michaud and Robert Michaud, addresses information uncertainty in risk-return estimates.  The procedure utilizes Monte Carlo simulation methods to produce multiple sets of statistically-equivalent risk-return estimates based on the original estimates.  These estimates are then used to compute multiple efficient frontiers, representing the many possible ways in which assets may perform relative to estimation error in the inputs. The figure shows various possible efficient frontiers developed from statistically equivalent risk-return estimates.  Each alternative frontier is drastically different from the others, even though they are all statistically equivalent and based on the same risk-return estimates.  As each frontier represents many portfolios, the variability exceeds what is immediately apparent in the figure. If two investors both want high risk portfolios, one could invest in portfolio A, while the other could choose portfolio B, despite starting with statistically equivalent risk-return estimates.Original and Simulated Efficient Frontiers
(A similar figure appears in Efficient Asset Management by Richard Michaud and Robert Michaud, published in 2008 by Oxford University Press.  This version of the figure is for illustrative purposes only.)

New Frontier develops its efficient frontier by averaging all of the frontiers developed from the statistically equivalent risk-return estimates.  For example, the high risk portfolio on the Michaud Resampled Efficient Frontier is created by averaging the high risk point on all the efficient frontiers shown in the figure.  Michaud Resampled Efficiency is an averaging process that distills all the alternative efficient frontiers into a new efficient frontier and set of optimized portfolios. 

Harry Markowitz, the Nobel prize-winning father of traditional optimization and modern portfolio theory, tested Michaud optimization in an independent academic experiment in 2003. 

Many different aspects of Michaud Optimization are further explored in our publications: Michaud Optimization Articles
NF Patented Research
Presentation