Jump to content
House Price Crash Forum
Sign in to follow this  
scepticus

Fractal Markets - One For All The Traders

Recommended Posts

The TA types often tell me that 'markets are fractal', by way of explanation for why TA works.

OK great I say, but all life is fractal so how does that help?

Well, fractals have dimension, as explained here:http://en.wikipedia.org/wiki/Fractal_dimension

Here's a great piece that explains about fractal markets and estimates the fractal dimension of financial data. It may take you a while to read it but it will be worth your while.

http://www.triple.net/fractalmarkets.php

My hypothesis is that the particular fractal market structure currently observed is based on the interplay between the so called safe havens and the rest of the asset-sphere. Given that the former are changing I think this will provoke a change in fractal dimension and behaviour. That's what I want to discuss in this thread.

Share this post


Link to post
Share on other sites

The TA types often tell me that 'markets are fractal', by way of explanation for why TA works.

OK great I say, but all life is fractal so how does that help?

Well, fractals have dimension, as explained here:http://en.wikipedia.org/wiki/Fractal_dimension

Here's a great piece that explains about fractal markets and estimates the fractal dimension of financial data. It may take you a while to read it but it will be worth your while.

http://www.triple.ne...ctalmarkets.php

My hypothesis is that the particular fractal market structure currently observed is based on the interplay between the so called safe havens and the rest of the asset-sphere. Given that the former are changing I think this will provoke a change in fractal dimension and behaviour. That's what I want to discuss in this thread.

A long, long time ago, I tried to model a stock price random walk using a set of affine transforms (this was back in the early days when Barnsley hadn't yet published Fractals Everywhere). The conclusion I came to, albeit with only 6 months or research, was that there was almost no compression to be had to doing this implying that the level of self-similarity was fairly low. I also looked at fractal dimension as some kind of measure of volatility and got nowhere with that. I'm not saying there isn't any mileage in it, just that it's not something with some obvious easy results.

Share this post


Link to post
Share on other sites

t there was almost no compression to be had to doing this implying that the level of self-similarity was fairly low.

you'd have to believe in significant self similarity to also believe that TA works wouldn''t you?

I also looked at fractal dimension as some kind of measure of volatility and got nowhere with that. I'm not saying there isn't any mileage in it, just that it's not something with some obvious easy results.

I don't have any particular result in mind, just to be clear.

Probably 1 dimension/exponent is insufficient to properly capture the behaviour. Have you ever come across the Multifractal Model of Asset Returns ?

Share this post


Link to post
Share on other sites

you'd have to believe in significant self similarity to also believe that TA works wouldn''t you?

Not necessarily as repeating patterns at the same scale don't imply self-similarity, you need some evidence of scale invariance for that. Personally I think TA/charting is a pile of crap btw, somewhere at the same level as reading tea-leaves.

I don't have any particular result in mind, just to be clear.

Probably 1 dimension/exponent is insufficient to properly capture the behaviour. Have you ever come across the Multifractal Model of Asset Returns ?

That came along well after I'd moved on to other things so I never looked at it in any detail. IIRC the main thing it had going for it was that it seemed to fit the fat-tail observations of real data.

Share this post


Link to post
Share on other sites

Are there other factors in the market that cause price movements (cost of borrowing/yield curve?) or even 'VaR' in response to volatility. This element to me seems a big factor at the moment. Supposedly a risk adjustment tool - but one where if volatility rises, causes itself to rise by affecting prices and vice versa. Something that certain traders try to use to their advantage.

There are a gazillion factors that might influence prices, hence the prevalence of multi-factor models in automated trading strategies.

Share this post


Link to post
Share on other sites

Not necessarily as repeating patterns at the same scale don't imply self-similarity, you need some evidence of scale invariance for that.

AFAIK the same rules are applied to boith 50 and 200 day MAs are they not?

Also the sampling interval (in this case the time between trades or trades per second) has increased dramatically in the last 10 years, which implies a change of scale,

That came along well after I'd moved on to other things so I never looked at it in any detail. IIRC the main thing it had going for it was that it seemed to fit the fat-tail observations of real data.

Yes that is the main claim of it. I have to confess I don't understand it properly.

Share this post


Link to post
Share on other sites

Interesting thought.

I suppose you may also question the randomness of price movement tbh. Do market participants' minds (or increasingly hft) draw patterns? Do algols use patterns they perceive and proceed to re-write them going forward by their reactions? Are human reactions in response to price movements predictable?

all you are saying here is that prices in one interval are not independent of those in prior intervals - that is, the process has memory, which applies to most all naturally occurring fractal processes such as fluid turbulence and leaf skeletons.

That is not in doubt and is not disputed by any fractal market theory.

Are there other factors in the market that cause price movements (cost of borrowing/yield curve?) or even 'VaR' in response to volatility. This element to me seems a big factor at the moment. Supposedly a risk adjustment tool - but one where if volatility rises, causes itself to rise by affecting prices and vice versa. Something that certain traders try to use to their advantage.

Well that brings us to the other part of this thread. When market prices fall the price of money rises, or equivalently its velocity falls (or at least the velocity of money involved in the market vortex falls). But that only happens because money (including bank deposits ) are seen as being nominal risk free. Return of principal is not an issue.

Imagine we previously had only two assets, money at AAA and an AA asset market. This AA market would presumably display cyclical risk on risk off behaviour ith some kind of multi fractal price distribution. Now downgrade money to AA. What happens to price distributions?

Share this post


Link to post
Share on other sites

Imagine we previously had only two assets, money at AAA and an AA asset market. This AA market would presumably display cyclical risk on risk off behaviour ith some kind of multi fractal price distribution. Now downgrade money to AA. What happens to price distributions?

You now have 2 AA asset markets.

But how is that different to, say, currency pairs?

Share this post


Link to post
Share on other sites

You now have 2 AA asset markets.

But how is that different to, say, currency pairs?

stick with my thought experiment. One asset market and one money, with the latter rated the same as the asset.

What happens?

We'll extrapolate to more complex situations later (a currency pair is two mediums of exchange, rather than one medium of exchange and one asset).

Share this post


Link to post
Share on other sites

stick with my thought experiment. One asset market and one money, with the latter rated the same as the asset.

What happens?

We'll extrapolate to more complex situations later (a currency pair is two mediums of exchange, rather than one medium of exchange and one asset).

The asset is now money (equivalent) - the 'money' is now any other AA asset (hence my currency example).

Go on.........what's the answer?

Share this post


Link to post
Share on other sites

Yes - but the mere fact there exist models must mean some element of predictability and therefore cannot be random.

If one thinks that TA is just lines on a page then I agree with your sentiment but if you include certain other factors within the realms of 'TA' such as volatility or coded news or google searches even then clearly certain data can have a probability attached to it.

Clearly you know much more about this than I but if it is not predictable whatsoever such that probabilities cannot be attached nor risk mitigation effected cost effectively, then I don't know why people try. Is it all 'luck'?

There are definitely mean-reverting processes to be found within all the noise so, yes, not entirely random, but you need to look at the differences between things, not the thing in isolation (classic example being the price of pepsi vs the price of coca-cola). TA as a different thing as it, in the general case, only looks at individual prices which really are mathematically indistinguishable from a random walk.

Share this post


Link to post
Share on other sites

AFAIK the same rules are applied to boith 50 and 200 day MAs are they not?

Also the sampling interval (in this case the time between trades or trades per second) has increased dramatically in the last 10 years, which implies a change of scale,

It's not the change of scale which is the issue, it's the visibility of the same pattern at different scales. E.g. if you looked at just closing prices and saw some pattern (e.g. the illusive head and shoulders), you'd need to be reliably seeing the same pattern repeated in prices samples at some smaller interval in order to draw the conclusion that there was something fractal going on.

Share this post


Link to post
Share on other sites

The asset is now money (equivalent) - the 'money' is now any other AA asset (hence my currency example).

Well its still a medium of exchange and the asset is not. Presumably the money would retain a price premium over the asset for that reason.

After that, what we have is the store of value function of the money versus the store of value function of the asset. When the asset is perceived to store value better than the money its price in money would rise.

The problem with all this of course is that the dollar has been AAA for ages yet it has been trashed and is clearly a terrible store of values compared to equities or pretty much anything else.

What this says to me is that the time interval over which the money and the asset's store of value function being compared is very small, most of the time.

Unfortunately none of this answers the question of what the impact of the AA downgrade of the money is.

Share this post


Link to post
Share on other sites

It's not the change of scale which is the issue, it's the visibility of the same pattern at different scales. E.g. if you looked at just closing prices and saw some pattern (e.g. the illusive head and shoulders), you'd need to be reliably seeing the same pattern repeated in prices samples at some smaller interval in order to draw the conclusion that there was something fractal going on.

My point was, decrease of trading interval time over the last 10-20 years would indicate that if we considered the trading year 2010 we would be looking at a different scale to the year 1990. Then if similar patterns are present in both the 1990 and 2010 data then we have a fractal process?

Its good to have an informed sceptic on this thread (no jokes please :) ) so how in your view do we characterise mathematically the behaviour of the market if its not fractal and not just noise? Are you tending to the view that it is some other form of short-range-dependence or long-range-dependence process?

I'm not actually claiming here that markets are fractal - I think they might be but I', very open to alternative theories.

Edited by scepticus

Share this post


Link to post
Share on other sites

Well its still a medium of exchange and the asset is not. Presumably the money would retain a price premium over the asset for that reason.

After that, what we have is the store of value function of the money versus the store of value function of the asset. When the asset is perceived to store value better than the money its price in money would rise.

The problem with all this of course is that the dollar has been AAA for ages yet it has been trashed and is clearly a terrible store of values compared to equities or pretty much anything else.

What this says to me is that the time interval over which the money and the asset's store of value function being compared is very small, most of the time.

Unfortunately none of this answers the question of what the impact of the AA downgrade of the money is.

You're flipping between dollars and treasuries of various maturities.

S&P have put US treasury debt on negative outlook.

Dollar is the unit of account and currency, USTs are an asset class.

USTs are bid/sold independently of the price of the dollar (though of course there is an interplay).

As far as I'm aware S&P don't rate the dollar as a unit of account, store of value or medium of exchange, just the debt.

I suppose it depends which price you consider is moving - the unit of account or the debt.

Share this post


Link to post
Share on other sites

You're flipping between dollars and treasuries of various maturities.

No, when I said the money is downgraded I meant the money, in my thought experiment.

Back in the real world, a downgrade of the US treasury must also be a downgrade of the FEDs notes since the FEDs notes are backed by US treasury assets.

Share this post


Link to post
Share on other sites

So you do hedges? Looking for 'price anomalies' when simple ratios get out of kilter? What sorts of ratios do you look at?

Me personally, no, I buy and hold index tracking funds, I never actively trade single stocks on my own account (I work for a bank so compliance makes it too bureaucratic and, in any case, it's a bit of a mugs game really). However, in the past, in a work capacity, I've been involved with various equity long/short trading strategies and they were all looking for different things. The simplest one was pairs trading where, and this was a long time back so almost certainly wouldn't work now, the group I was with looked for correlation between the prices of pairs of stocks using SLR. Where there appeared to be a meaningful correlation and where the relative price of the two had diverged for something other than an obvious reason (dividend payment, takeover approach etc), we'd go long the one currently underperforming, short the other and wait for the divergence to correct itself. You can extend that to use other, more complex, statistical techniques (non-linear regression, groups of stocks rather than just 2 etc). This is different from hedging which, generally, is more about putting a floor under your potential losses.

Share this post


Link to post
Share on other sites

My point was, decrease of trading interval time over the last 10-20 years would indicate that if we considered the trading year 2010 we would be looking at a different scale to the year 1990. Then if similar patterns are present in both the 1990 and 2010 data then we have a fractal process?

Its good to have an informed sceptic on this thread (no jokes please :) ) so how in your view do we characterise mathematically the behaviour of the market if its not fractal and not just noise? Are you tending to the view that it is some other form of short-range-dependence or long-range-dependence process?

I'm not actually claiming here that markets are fractal - I think they might be but I', very open to alternative theories.

Sorry, I'm not saying there definitely isn't any kind of process going on that could be fractal in nature, just that I don't think it's discernible by looking at a single stock price. If I were going to go looking again, I'd be inclined to look at the differences between a stock and an appropriate benchmark (e.g. IBM vs. S&P 500). For me though, the markets are definitely chaotic rather than truly random. Think of a share as being a blob of smoke being buffeted around by the molecules of gas in a demonstration of Brownian motion and you're about there. If only we could plot the trajectories of all the gas molecules we could figure out exactly where the blob of smoke was going to end up...

Share this post


Link to post
Share on other sites

Sorry, I'm not saying there definitely isn't any kind of process going on that could be fractal in nature, just that I don't think it's discernible by looking at a single stock price. If I were going to go looking again, I'd be inclined to look at the differences between a stock and an appropriate benchmark (e.g. IBM vs. S&P 500).

why not look at the price of the whole index?

obviously we can price any stock in terms of all the others but what are the metrics that govern stock buying behaviour, stock vs stock or stock vs money. Both, obviously but does one metric dominate over the other or perhaps the dominant metric changes at key times?

For me though, the markets are definitely chaotic rather than truly random. Think of a share as being a blob of smoke being buffeted around by the molecules of gas in a demonstration of Brownian motion and you're about there. If only we could plot the trajectories of all the gas molecules we could figure out exactly where the blob of smoke was going to end up...

brownian motion is random though isn't it? or at least as only short range dependance?

fractional brownian motion from what I have read does have more memory to it.

Share this post


Link to post
Share on other sites

why not look at the price of the whole index?

Because it too, being an additive thing, is as near to random as makes no difference.

obviously we can price any stock in terms of all the others but what are the metrics that govern stock buying behaviour, stock vs stock or stock vs money. Both, obviously but does one metric dominate over the other or perhaps the dominant metric changes at key times?

A gazillion different things, the predominant one varying with time as you say. If you could reliably predict which one was going to be dominant then you might be able to use that to make some kind of prediction that could be traded off. I know of some hedge funds trying to do this sort of thing by analyzing social media feeds for example.

brownian motion is random though isn't it? or at least as only short range dependance?

Presumed random, I think is the phrase. Unlike the decay of radioactive elements though, I assume it's predictable to within planck's constant if you have enough information about the state of the system. A bit like a share price would be if you knew the exact motion of all of the players an instant before they placed their orders.

fractional brownian motion from what I have read does have more memory to it.

I guess that fits the fat tail observation. I can see that maybe it could give you some small edge in predicting volatility which you could then maybe trade off if you could find a suitably dated/timed volatility contract.

Share this post


Link to post
Share on other sites

Because it too, being an additive thing, is as near to random as makes no difference.

define additive?

A gazillion different things, the predominant one varying with time as you say. If you could reliably predict which one was going to be dominant then you might be able to use that to make some kind of prediction that could be traded off. I know of some hedge funds trying to do this sort of thing by analyzing social media feeds for example.

Thought experiment. Imagine you attach an electronic tracer to each unit of fiat money worldwide. Then visualize the results on some surface speeded up by several orders of magnitude. Would we see all money moving at V? No, we'd see money sat in grannie's bank account that never moves and a whole load of slow moving money glaciers and then a few vortexes or great spots presumably circling financial markets.

Now if you could actually observe those vortexes while ignoring the rest of the cold money would changes in these vortexes allow you to predict imminent volatility spikes?

Presumed random, I think is the phrase. Unlike the decay of radioactive elements though, I assume it's predictable to within planck's constant if you have enough information about the state of the system. A bit like a share price would be if you knew the exact motion of all of the players an instant before they placed their orders.

Brownian motion among other things is the means by which physical systems obey the second thermodynamic law, do you think markets follow an analogous process (e.g. two bodies in thermal contact will reach thermal equilibrium)?

Share this post


Link to post
Share on other sites

define additive?

Formed by the sum of one or more other things - in this case essentially random variables representing a weighted value for stock prices. Having said that, and thought about it some more, I need to go away and read one of my books on time series analysis to figure out if I'm actually talking crap there!

Thought experiment. Imagine you attach an electronic tracer to each unit of fiat money worldwide. Then visualize the results on some surface speeded up by several orders of magnitude. Would we see all money moving at V? No, we'd see money sat in grannie's bank account that never moves and a whole load of slow moving money glaciers and then a few vortexes or great spots presumably circling financial markets.

Now if you could actually observe those vortexes while ignoring the rest of the cold money would changes in these vortexes allow you to predict imminent volatility spikes?

Maybe not volatility spikes, but certainly volume spikes (not always the same thing).

Brownian motion among other things is the means by which physical systems obey the second thermodynamic law, do you think markets follow an analogous process (e.g. two bodies in thermal contact will reach thermal equilibrium)?

I don't think the analogy works as markets aren't merged in isolation, there's too much leakage in and out. I think there are definitely cases that have some of the characteristics of thermal equilibrium (e.g the way that the correlation between the prices of shares globally has increased enormously over the last 20 years) but, at the high level, I'd say markets look as if they contain strange attractors (so I certainly agree with you that they appear fractal in some respects).

Share this post


Link to post
Share on other sites

Formed by the sum of one or more other things - in this case essentially random variables representing a weighted value for stock prices. Having said that, and thought about it some more, I need to go away and read one of my books on time series analysis to figure out if I'm actually talking crap there!

Don't forget to pop back when you have confirmed (or discounted) the above!

I don't think the analogy works as markets aren't merged in isolation, there's too much leakage in and out. I think there are definitely cases that have some of the characteristics of thermal equilibrium (e.g the way that the correlation between the prices of shares globally has increased enormously over the last 20 years) but, at the high level, I'd say markets look as if they contain strange attractors (so I certainly agree with you that they appear fractal in some respects).

So what are the financial attractors and from what matter are they formed? Sorry to stretch the analogy but sometimes its easier to find common ground that way...

To further push the analogy, our actual universe contains both dominant thermal equilibrium dynamics but also local attractors (e.g. gravity) that create localised lumpyness. But the second law implies that all lumpiness eventually decays to equilibrium (e.g. black holes evaporate via hawking radiation.

I guess what matters here is the time constant for the decay of the existing attractors, both the big ones and the smaller ones that come and go as the market ebbs and flows.

Share this post


Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
Sign in to follow this  

  • Recently Browsing   0 members

    No registered users viewing this page.

  • 338 Brexit, House prices and Summer 2020

    1. 1. Including the effects Brexit, where do you think average UK house prices will be relative to now in June 2020?


      • down 5% +
      • down 2.5%
      • Even
      • up 2.5%
      • up 5%



×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.