There are 2 basic reasons that "modern" portfolio theory is no longer "modern". While the basic idea is still golden, diversity lowers risk.

First, there has been an explosion of asset classes in which one can diversify into, which are traded. However, the data on these classes are not long enough to have stood the test of time. For example do high yield bonds diversify or are they simply a mix of bond risk and equity risk with liquidity risk thrown in?

Second there has been an explosion of ways to game the model to make the manager appear to have added Alpha, but really has loaded up on some other risk not measured in the model, like liquidity risk (real estate for example) or model risk (MBS for example) or simply taking other risk besides measurable volatility risk. When the MPT is taken as gospel it often is taken to extremes leaving one vulnerable to misinterpretation, like any other scripture, one should beware of those claiming to help one understand that scriptures fine points, especially when money is involved.

Ralph Vince writes: 

I think there's a bigger question here, and that is, why hasn't MPT been applied to other similar processes (as that of the equity curve of a trader in capital markets or gambler) in the natural world.

This is the question I find most baffling — why, 75 years later (at least with regards to the Markowitz subset or geodesic) are the models floundering solely in these equity curve style exercises. There are more exercises and more important exercises where this can and by now, ought be applied to, specifically exercises in the natural world with respect to many things — some of which I have mentioned here in the past such as deficit reduction sans tax hikes or budgetary cuts, chemotherapy or other pharmacological dosing, spread of pathogens, etc. etc. any growth-feedback function wherein we seek to diminish growth in the natural world.

Given that MPT resides in the Leverage Space Manifold, and that each axis along each dimension in that manifold (minus 1) varies in the domain 0..1 representing, in the exercises we are more familiar with, the percent of stake being risked on that component, MPT itself, at 75 years old could, conceivably, be applied to such growth-diminishing exercises. The axes which each range from 0..1 in value can be transposed to reflect the cosine of the variance to the mean growth of the data used for that axes. Thus, any growth-feedback function can be mapped to the Leverage Space Manifold, and in turn, mapped to Markowitz's Efficient Frontier (the geodesic) provided the variance can be altered by human intervention (such as dosings, national debt accumulation rates, etc. there are some functions, like Sir Ronald Fisher's fundamental theorem of natural selection, which states, "The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time," maps to this model even though we are not seeking to tweak an organisms genetic fitness).

And yet, dosages are not considered under such a model (and contemporary medicine itself stands accused of dosing in manners opposite those which this model might often suggest) , deficits continue amidst a seemingly intractable tug-of-war between budgetary cuts vs. increased taxes, and all of these can be addressed, improved, through the implementation of some relatively simple mathematics. There are ample meals here and research ideas.

The tragedy of MPT, and more generally (and to me, personally), the hyaline manifold of leverage space, is not that it is not seeing full employment in financial markets, but that it is not being used for beneficial ends in other physical and social sciences.

I'll shut up about it now.





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