Portfolio Optimization: A General Framework for Portfolio Choice

It is widely accepted among investment professionals that, while portfolio optimization has compelling theoretical merit, it is not useful in practice. Practitioners are concerned that optimization is an “error maximizing”1 process fraught with insurmountable estimation issues. The abstract of an early academic critique of mean-variance optimization, (Michaud 1989) states:

The indifference of many investment practitioners to mean-variance optimization technology, despite its theoretical appeal, is understandable in many cases. The major problem with mean-variance optimization is its tendency to maximize the effects of errors in the input assumptions. Unconstrained mean-variance optimization can yield results that are inferior to those of simple equal-weighting schemes.

Many nay-sayers selectively quote the above passage as reason to dismiss optimization altogether. However, this same abstract continues with the following thoughts:

Nevertheless, mean-variance optimization is superior to many ad hoc techniques in terms of integration of portfolio objectives with client constraints and efficient use of information. Its practical value may be enhanced by the sophisticated adjustment of inputs and the imposition of constraints based on fundamental investment considerations and the importance of priors. The operating principle should be that, to the extent that reliable information is available, it should be included as part of the definition of the optimization procedure.

It’s clear that portfolio optimization is a powerful tool that must be used thoughtfully and responsibly. However, even the critics agree that optimization is the only mechanism to make best use of all the information available to investors.

In this paper, we will first build a theoretical framework that will enable us to determine the most appropriate method of portfolio construction for most situations. We’ll introduce the Portfolio Optimization MachineTM and suggest how an investor might decide which type of optimization is most consistent with the qualities, beliefs, and assumptions he holds about the assets under consideration.

portfolio optimization
¹ Michaud (1989)