Bolzmann and the stock markets

[hallenrm]

I have been lately observing the movements in the Indian stock market, I can feel a kind of similarity in the distribution of velocities of the molecules of a gas and the movement of the individual stocks on a day to day basis.

 

Both are random to a certain extent and predictable also. The velocity of individual molecules in a gas depends on the temperature, similarly the stock prizes depend on the liquidity and also to a certain extent on the sentiments of traders and investors. But, there are soime discernible differences too, Can somebody help me in pointing them out? I feel this can be a lively topic of discussion among scientists.

 

Do you agree?

[Buffy]

How do you want to do your mapping? Each molecule is a stock or each molecule is an investor? The former would be simpler to track, but hides a massive level of complexity that is exposed by the latter. Even then I think what you discover is that this is really like a gas in which every molecule has a different composition, which to me means that Bolzmann's equations probably will only be able to have a very rough approximation of what happens.

 

People have been working on things like this for ages, trying to map various chaotic systems on to each other, and its a very worthwhile endevour if for no other reason that it gives us a better understanding (or rather a better understanding of how little we understand) about such systems.

 

Great thread!

 

Chaotically ordered,

Buffy

[ughaibu]

On one occasion I was talking to a friend of my brother's, an economist, about the use of staking plans in conjunction with statistically based selection systems for horse races. This economist was unimpressed with my ideas and gave me a proof as to why such a strategy necessarily fails. Unfortunately I dont remember the proof and no longer have access to that guy, if anyone can think of what this proof might be I'd be appreciative.

[hallenrm]

How do you want to do your mapping? Each molecule is a stock or each molecule is an investor? The former would be simpler to track, but hides a massive level of complexity that is exposed by the latter. Even then I think what you discover is that this is really like a gas in which every molecule has a different composition, which to me means that Boltzmann's equations probably will only be able to have a very rough approximation of what happens.

 

People have been working on things like this for ages, trying to map various chaotic systems on to each other, and its a very worthwhile endeavor if for no other reason that it gives us a better understanding (or rather a better understanding of how little we understand) about such systems.

 

Great thread!

 

Chaotically ordered,

Buffy

 

Yes every molecule has a different distribution of energy in its different levels, something very similar to stocks, each stock has several characteristics attached to it, e.g its nature (commodity, service, manufacturing, technology etc) the perception how it will perform in short or long, and of course whether it is backed by some wealthy people or not.

 

The reason this idea stuck me, us because I feel that looking it by that perspective it appears that the Boltzmann treatment of molecules in a gas is perhaps over simplistic, although it has been found to be very useful by scientists. But, isn't that true of most theories in economics?

 

I think there is some value in cross examination of theories in both disciplines

[Buffy]

Yes every molecule has a different distribution of energy in its different levels, something very similar to stocks, each stock has several characteristics attached to it, e.g its nature (commodity, service, manufacturing, technology etc) the perception how it will perform in short or long, and of course whether it is backed by some wealthy people or not.

That's why I think you're missing my point here: the actions of molecules are fairly predictable with a few variables. In a market--choose whichever level of mapping you want--the actors are all absolutely unique. They can fall into classes, but are highly susceptible to reactions that are unique to them. Most really do not look like any others and are highly random. An example of this: there are whole classes of companies that defy the usual PE ratio rules of thumb because the they have unique traits (patents, channel control, etc) that lead to higher profit expectations. They can also be blown out of the water by unique traits: GE took a huge hit (over time, because there was speculation that he would) when Jack Welsh resigned--one guy made that company special. That's why its better to go down to the investor level, which have fewer variables, *but they are just as unique*.

 

This just goes way beyond saying, they're a mix of 80% Nitrogen and 20% Oxygen, and they have velocities in these ranges due to pressure. That sort of system is at least several orders of magnitude simpler.

 

Now that's not to say you can't get something useful out of it, but you do have to recognize the limitations.

 

The Uniformity of Billiard Balls,

Buffy

[hallenrm]

That's why I think you're missing my point here: the actions of molecules are fairly predictable with a few variables. In a market--choose whichever level of mapping you want--the actors are all absolutely unique. They can fall into classes, but are highly susceptible to reactions that are unique to them. Most really do not look like any others and are highly random.

Buffy

 

No, I am not missing the point you have in mind, on the contrary that is precisely what I am hinting at:) Yes we believe that the actions of molecules are far more predictable than the individual participants of stock markets, but just think what will be consequences if some people really engaged themselves in a serious scientific study with the premise that molecules have traits like participants of stock markets. I believe it may lead to fresh insight into the behavior of matter.

 

Or, do you believe that the Boltzmann theory in the present form is the ultimate word?

 

Iconoclast

 

hallenrm

[jungjedi]

i thought there were two types of events that seemed similiar.a random and a chaotic event.the random event would be descibed by the rules of monte carlo and a chaotic event would be described by a fractal equation.

[Buffy]

...but just think what will be consequences if some people really engaged themselves in a serious scientific study with the premise that molecules have traits like participants of stock markets. I believe it may lead to fresh insight into the behavior of matter.

That would be cool! BUT I think that you're going to have to find a lot more variables in the models of matter. I argue that the number of variables in the "stock market" are several orders of magnitude greater than that of the actions of molecules in a gaseous state. Insofar as there are many convergent *and* divergent processes that work in opposite directions in markets, it can appear that it simplifies down to something approximating Boltzmann's equations, when it is in fact more complex. The data for this is not in the averages but in the higher standard deviations of results, because there are far more frequent outlier data points that show hidden complexity in the processes.

 

I don't doubt that there could be a lot more complexity in the activities of gasses, its just that setting the bar of "just as complex as our stock markets" boggles the mind. I cannot say its impossible, but if it turned out to be the case, I think it would end up requiring each quark to be a sentient being with methods of communciation and interaction that are not visible in our "universe." Right now, that's called metaphysics: cool to contemplate, but you're going to have to come up with some astounding data in order to show that it even *might* be true....

 

Merely sublime,

Buffy

[hallenrm]

True! Buffy, BUT don't you think that scientific theories invariably develop by taking into account more variables or merging several variables. The Boltzmann hypothesis was developed in an era when our computation acumen was limited as was our knowledge of observed phenomena. Now, that we know many puzzling phenomena it's time that someone with the genius of Boltzmann comes out and give the knowledge of physics a fresh breeze of life!;)

[Buffy]

Absolutely agree with all that. Models like Boltzmann are cool precisely because they work even though they simplify and approximate. That's brilliance!

 

On the other hand, purely from a mathematical point of view--to use a bit of Abstract Algebra--the formal system defined by the operation of gasses to that of stock markets is not "onto"....

 

Orders of magnitude are really, really big,

Buffy

[hallenrm]

last night I was traveling, and because yesterday was the Holi festival being celebrated today there was no newspaper. Any way I was carrying Bill Bryson with me, that fascinating history of almost all developments in science, so I had a rather comfortable read, and many news ideas had the freedom to sprout. This thread was on the top layer of my mind, so here they are:

 

We all have read about the origin of the life, very many scientists have applied their mind to find a viable theory, but there is always this puzzling question: How could so many free atoms/molecules come together to give rise to organized structures that are so characteristic of life forms? I think scientists often ignore what is visible everywhere, for example superstructures (skyscrapers, big industries, large corporations, cities, networks) that have sprung up in the recent past. Have we ever wondered about the origin of their birth, development and evolution vis a vis that of life forms. If we assume that each human being is like an atom/molecule, then a possible theory comes to mind. These atoms/molecules evolve with time as they assimilate more information about their surroundings and hence develop tools and materials that are necessary to give shape to the artifacts of society. If we really care to think about them, the superstructures are very similar to the life forms, microbes, plants, animals etc. If one concedes this thought for a moment, we can realize the potential foe future growth and development of science by integrating all kinds of information into what was hitherto known as natural philosophy. We may awake into the similar period, about a century ago, when people like Boltzmann were excited to solve many unsolved problems.

 

Thinks creatively,

 

hallenrm

[Qfwfq]

A bit of nitpicking:

That would be cool! BUT I think that you're going to have to find a lot more variables in the models of matter. I argue that the number of variables in the "stock market" are several orders of magnitude greater than that of the actions of molecules in a gaseous state.

Are they in the system or out of it?

 

Consider your box of molecules with ideal walls. The boundary conditions are the point in phase space at the initial time, after which you want to extrapolate the evolution.

 

Consider it with non-ideal walls, which means that these are themselves made of molecules. Are they part of the system? They not only interact with the inside but with the outside as well. The water molecules in the pot will go quite differently, according to the flame being turned of or on. Even sitting in the room at constant temperature, the water molecules aren't an isolated system. Therefore the boundary conditions aren't just the state at the initial time but must include the interactions of the molecules with the wall.

 

Is the stock market an isolated system? As well as the companies being complicated systems, people buying and selling aren't just the guys on the floor. It's a lot of investors and savers that are deciding to buy or sell. Each of these decides according to their own individual purposes. So, what's in the sysem and what's out of it? According to how this is chosen, one must then define the states and the Lagrangian and the boundary conditions.

[Buffy]

A bit of nitpicking:Are they in the system or out of it?

 

Consider your box of molecules with ideal walls. The boundary conditions are the point in phase space at the initial time, after which you want to extrapolate the evolution.

I agree this is a very important issue in determining the complexity of the system.

 

AFAIK, Boltzmann really only deals with "ideal walls" so that certainly limits its extrapolation huh?

 

Now as to comparing the two systems though, I would argue that to make the comparison's "fair" you would have to make the assumption that the "additional complexity" due to boundary interactions was "equivalent," in which case the abstract ennumeration of the variables still is the only relevant factor.

 

In the real world however, it would be important to next guage the relative complexity of the "walls" themselves, and here I would at least argue that the walls on the stock market are *at least* as complex as the walls on your gas container, and arguably could *also* be considered to be orders of magnitude more complex: You've mentioned outside heat sources/sinks, there's motion, there's at least a few more. The "walls" on the stock market at least include the entire economic activity of the world, as well as all environmental factors that affect economic activity. Which of those two represents more variables? Is it apparently more than a single order of magnitude difference? I'd argue so...

 

I don't know if its 487 or 488 angels there,

Buffy

[hallenrm]

I agree this is a very important issue in determining the complexity of the system.

 

AFAIK, Boltzmann really only deals with "ideal walls" so that certainly limits its extrapolation huh? :eek2:

 

Now as to comparing the two systems though, I would argue that to make the comparison's "fair" you would have to make the assumption that the "additional complexity" due to boundary interactions was "equivalent," in which case the abstract ennumeration of the variables still is the only relevant factor.

 

In the real world however, it would be important to next guage the relative complexity of the "walls" themselves, and here I would at least argue that the walls on the stock market are *at least* as complex as the walls on your gas container, and arguably could *also* be considered to be orders of magnitude more complex: You've mentioned outside heat sources/sinks, there's motion, there's at least a few more. The "walls" on the stock market at least include the entire economic activity of the world, as well as all environmental factors that affect economic activity. Which of those two represents more variables? Is it apparently more than a single order of magnitude difference? I'd argue so...

 

 

Thar's precisely the point I am driving at! The Boltzmann treatment of an ensemble of particles that are moving freely and randomly is at best an idealization, that can be improved upon taking into cognizance the influences from the walls or from other members of the ensemble, to get closer to an mathematical treatment of systems that are closer to real life situation. Boltzmann treatment is a good starting point perhaps:)

 

There are of course walls, even in the stock market, and rhe energy flpw fom outside is in the form of FII's.

[Buffy]

We're mostly in violent agreement except for this issue of order of magnitude differences in complexity.

 

Let me put it this way. Would you argue that the game of Chess is a sufficiently powerful model that no other planning or simulation model was necessary in order to model all of World War II?

 

That's all I'm trying to say: Sure you can make simplifcations for your model, but if you use one that is wholly inadequate to the task, you're not going to see much that is interesting or useful!

 

Not just a little different,

Buffy

[Qfwfq]

FAIK, Boltzmann really only deals with "ideal walls" so that certainly limits its extrapolation huh?

Noch mehr, Boltzmann does a completely different thing, much less hopeless than integrating the dynamics of the microstate. :) It works, of course, when the macrostate is well enough defined.

 

In the real world however, it would be important to next guage the relative complexity of the "walls" themselves, and here I would at least argue that the walls on the stock market are *at least* as complex as the walls on your gas container, and arguably could *also* be considered to be orders of magnitude more complex: You've mentioned outside heat sources/sinks, there's motion, there's at least a few more. The "walls" on the stock market at least include the entire economic activity of the world, as well as all environmental factors that affect economic activity.

Yup! Have you been watching the Chinese bear?

 

Boltzmann is analoguous to when you can sum everything up into an idea of how those bids and asks are gonna balance or sway, at the righ time scale, at least until a couple of airliners crash into skyscrapers, or a CEO gets arrested for accounting fraud or whatever.

[LaurieAG]

Noch mehr, Boltzmann does a completely different thing, much less hopeless than integrating the dynamics of the microstate. :shrug: It works, of course, when the macrostate is well enough defined.

 

Yup! Have you been watching the Chinese bear?

 

Boltzmann is analoguous to when you can sum everything up into an idea of how those bids and asks are gonna balance or sway, at the righ time scale, at least until a couple of airliners crash into skyscrapers, or a CEO gets arrested for accounting fraud or whatever.

 

Hello Q and Buffy,

 

I have been following your discussions and can relate a bounded stock system I developed for clients in the mid 90's.

 

The system followed the usual trading rules but extra interractions were bounded by a mathematical oval (upper and lower curved boundaries) that stayed constant until the share price 'broke out' of the oval and a new one was required. The percentage proximity of the actual market price to this boundary was one of the extra criteria used to determine entry and exit points for trading. (talk about complex virtual geometry)

 

BTW, I agree with your analogy of Boltzman. It's similar to the ancient greek roots of 95% confidence. In Homers 'Odyssey', after 19 years since Odysseus left to fight the Trojan wars, the suitors (to Odysseus wife and property) and their girlfriends had 95% confidence that Odysseus would not return home in the 20th year. One of the western worlds earliest pieces of recorded prose, ends as a bloodbath for the suitors and their girlfriends.

 

In the end I could duplicate my clients results exactly and consistently for 75% of trades across 10 major companies (all over 12 month periods) but found difficulty in matching their beginning and ending transactions. When I questioned my clients about how the angles and start points of their ovals were determined (step one was to model their 'paper' results) they told me that 'the positions of the stars at the incorporation of the company determined all of that'. It's needless to say that, within 1 month of my departure, their advisers license was cancelled.