Mar

9

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.

Orson Terrill writes: 

"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." Could you elaborate on this?

Ralph Vince writes: 

We have a manifold of N+1 dimensions where N is any seperate set of outcomes affecting what we are observing (these could be individual stocks in a portfolio, or anything else for that matter) and bound in each dimension between {0,1} (or whatever scale you care to provide, where we scale it to {0,1}).

The N+1th dimension is the growth (after Q trials, or Q elapsed periods, Q{0, infinity} at each value for each of the N dimensions, and thuse gives as an N+1 dimensional "surface" in this manifold.

You look inside this manifold and you see some very interesting contours on the surface across it's field bound by each axis, but also as these contours chage with respect to Q. Tht's a description of the thing but here is what it does. In the context of capital markets, any portfolio construction mechanism (e.g. MPT, CAPM, portfolio insurance and levered ETF constructions, etc.) or "staking system" (e.g. Kelly, antimartinglae, "never risk more than 2% on a trade," etc") map to this surface in ths clear manifold. And from that, given the "chronomorphic" character of the curve (i.e. that it changes as Q gets larger) we can see the effects of these different applications in a manner bigger than the aplication itself. For example, we can see the effect of implementing MPT upon the countour of ths surface, and the benefit of this is that the counters, these geometrically significant points, give us information about our actions and how we might amend them to vastly improve what we seek to acheive, our "criteria." (Absent criteria, we are looking inside of a glass box, mouth agape, like Piltdown man - it is of no use to us despite the fact that all models map to the surface in this manifold).

Here is where there are great insights to be had in my opinion. Each axis, which, in caital markets orgambling parlance represents a percentage of risk, can also be mapped to the cosine of the mean outcome and standard deviation of outcomes of the sample used to construct inputs along that axis. Thus, for any growth function, we can look at what occurs with it with respect to changes mean or standard deviation (see the previous post re: Fisher's Fundaental Theorem) but far more beneficially, if we can affect the mean or standard deviation (as, say, with a nation's period-on-period borrowings, or biological growth rates) we can affect these systems in manners not yet even attempted (or perhaps dreamed of). For example, along the countour of the surface, along every axis, as we move towards 1, there is a point where the grwoth rate drops below 1. Always. This means there is a point, along any axis, where the aggregate growth rate at those values, insures the entire system cannibalizes itself (multiplying an account by a number less than 1 with each passing period, each increase in Q, and the account value approaches 0).

To the notion of MPT, it means that regardless of how may components you have in your portfolio, it takes only one component whose allocation is too high, regardless of he allocations to all others, to insure ruin.

In the natural sciences or other matters where we wish to diminish growth, or affect it in manners opposite those which our criteria call for in capital markets applications, the principles hold again. Any growth rate that has variance in it's growth or where variance may be induced, maps to the surface of this hyaline manifold, and the implications of where we are on that surface and its counters apply. If we can affect the mean and/or variance, we can position ourselves wherever we want on that surface and achieve whatever criteria we seek. If you are near Kalamazoo, Michigan on Thursday, I have to go there and speak about this at Western Michigan University and it is open to anyone.

Stef Estebiza writes:

I'm not sure I understand, but it seems you need a main manifold, for controlling, managing, the overall view, but also serves an independent process for each component of the mainfold, to handle exceptions, those situations where, contrary to the "market efficiency", a market, apparently in "harmony" that responds in a way related, to rule connected, it disconnects (singles part of it) … and every process must be able to manage themselves, monitored, to not degrade the performance of the "mainfold". to understand each other, regardless of the relationship, if a process is disconnected from reality (manifold idea), degrading the overall performance, it must be disconnected (you must atoscollegare) or managed (inverse relationship), or avoided, until he "recovers". .. the main manifold must provide the general idea of what you would like … but if the process is irrational and responsive to subjective rules, then any subjective process must have its own mainfold, "object", which defines the rules of the single object, and may depend on the general idea (mainfold). the main mainfold can provide the basic idea, the limits, but in reality, each "object" must be able to log out( or reverse) to prevent damage to the main idea(mainfold). especially in situations like this, where economic policies and "latency" in fiscal policy can fully determine "new situations", unforeseen, not covered by our "manifold".  

Russ Sears writes: 

If I am following the logic of Stef and Ralph correctly, I would add that if there is a space where the overall market is not aware of or such as a "new market" and one inputs this new market's data into the fixed system one finds an arbitrage advantage. If however, this new market and arbitrage is discovered by all using a similar fixed system, the market will form a "bubble" and hence is headed for ruin. A lack of dynamic inputs into a dynamic system can be worse than no system at all. Such is what appears to have happened with sub-prime loans. One of the biggest problems with the current stress testing system in my opinion is that one must "disclose" any relevant changes to your stress testing model. The regulators look at these disclosure more as an admission of bad modeling or model "error" than as a necessary part of a modeling system. Hence the modelers are not going to do this unless forced to.

Orson Terrill writes: 

Ralph, thank you for the expansive explanation. So, you feel that your work with the Leverage Space Model offers optimization beyond what portfolio managers are currently using? What is the hold back, learning costs?

Is there a video of your talk?

Ralph Vince responds: 

Orson, I'm afraid there's no video. Widespread acceptance is at least a generation away, and I see many depts now teaching it, their professor's sold on it. People remember what their nsteuctora believe and tend to accept it.

Most of the work in this manifold and what is going on in there at this point has not been done by me but quite a few academic others. I try to keep a repository of what they VW written on my website under
*related papers." Zhu and Maier-Ppaape are working now on the most amazing capital market applications of it and will likely publish it in the next year or three. I can understand the concepts…The actual symbol legardemain far beyond me


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