mandelbrotian randomness in finance, examples of practical uses?

[RicoTubbs]

I was trying to make more of a philosophical point, but failed, I think. You brought up Taleb, which allows me to restate my point, maybe more clearly.

The problem I have with Taleb's writing, albeit based only on Fooled by Randomness - I haven't read Black Swan, is that he seems to pound the table to point out that:
1. People are overconfident about their ability to understand statistics and don't have the ability to estimate or appreciate the true distribution/probability of events. Alternatively, people fail to appreciate the degree to which unexplainable "randomness" exists in data.

2. People underestimate the likelihood of rare events.

These two points seem contradictory to me, at least in the way that Taleb presented them. By simultaneously claiming that the true distribution of some outcome isn't knowable and that people underestimate the extent of rare events, his book came off as almost a religious text where Taleb himself had a supernatural ability to understand the true distribution of events.

Why, for example, couldn't it be the case that people tend to overestimate the occurrence of rare events? As a concrete example, Steve Levitt would say that parents overestimate the probability of guns causing harm to their children.

Unless Taleb knows the actual distribution, which is unlikely given his stance that such things are unknowable, who is he to say whether people are over- or under- estimating the probability of some event. That, for me, was the fatal flaw with “Fooled by Randomness” – he never gave a fundamentally sound reason for why he believed that people underestimate rare events.

Tying back to my original post, I squirm when people simultaneously say:
[1] LTCM was modelling risk in some way (e.g., using some type of VaR metric) when in fact such future risk is simply unknowable.

[2] They underestimated the risk of some event (e.g, a particular liquidity crisis).

I think it's a little weird to simultaneously claim that an event is unmeasurable AND that you know the direction that they misestimated. In my eyes, it suggests an omniscient speaker.


As a side note, where did you get your information about LTCM? You make several very specific statements (they didn't consider the possibility of a 20% loss, they didn't use monte carlo simulations to stress test their models, they made predictions with 100% precision in their shareholder letters) that sound unlikely to me. I’ve read a bit about LTCM and would appreciate any references you have that would support your claims. [I don’t mean this as a dick-waving challenge – I would genuinely like to read any sources that you have.]

[DcifrThs]

Ok, this thread got WAAAYYY off track.

lets bring it back.

the books i ordered are the following:

1) the (mis) behavior or markets: a fractal view of risk, ruin & reward

2) Fractals & scaling in finance by benoit mandelbrot

the first is like a 15 page essay and the 2nd is a textbook w/ both mathematical & non-mathematical treatments on the subject.

the journal of finance had not one reference of "fractal" "non-scalable" "scale invariant" etc. they had about ten million references for "volatility" though.

i've read tons of stuff on NNT's homepage and a lot of good info comes from this article:

Page 1

Page 2

enjoy!

lets get some more thoughts or sources! please!!!

thanks,
Barron

PS- if there are any other Qs about anything then just bump the "ask dcifrths" thread from a while ago

[DcifrThs]

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I thought it was based on a log normal distribution, because it has fatter tails?

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still insanely deficient. the use of the lognormal distribution has to do with the treatment of compounding of returns. it does indeed have fatter tails, but the cumulative effects of massively unlikely events do not wash out in reality (instead they are very important) whereas they are basically assumed to in a lognormal distribution.

the problem w/ any of these distributions is the way the tails are constructed. they exhibit an exponentially increasing decrease in the probability of rare tail events.

Barron

[eastbay]

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dcfr,

what type of trading do you do?

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no particular type, i get my kicks learning.

to be more specific: i just want to learn about how to apply varying tools to the imprecise art + science of financial market research. this one seems key

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Based on what?

eastbay

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i dont' really know what you're asking here.


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You said "mandelbrotian randomness" in finance seems key. I'm asking why you think that.

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first there seem to be more books popping up on the subject.


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In the early 90's there was a rash of books about aliens at Area 51. Did that mean it was more likely that aliens were there then? (only partially tongue in cheek.)

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the academic literature seems to be prodding slowly in that direction.


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for example?

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further, we are experiencing an utterly widespread misuse (though not disillusionment) of financial models that apply notions from the more normally distrubuted physical sciences to those of the jumpy financial markets.


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It is not a new idea that distributions in finance are "fat tailed" and not Gaussian.

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specifically, think about brownian motions. this is a type of randomness generating process that is "the" underpinning of scholes et. al.'s elegant world of options pricing. it is the basis on how the prices of risky assets are assumed to move in time. it is ubiquitous in interest rate models & term structure of volatility models.


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It's called a model. All models are approximate and based on idealized assumptions. This is not a revelation.

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it was (and still is) used with complete faith regarding its ability to mimic moves of risky assets& thus price them based on that voaltility.


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Anybody who uses any model with "complete faith" is an idiot and not worth talking about.

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it seems now to be becomming more accepted (at a VERY VERY early stage) that our current mathematical models aren't robust to reality.


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I don't know what "robust to reality" means, but I don't think it's news to anyone that normal distributions are not often a good model in finance.

Maybe I should start with a simpler question: What do you mean by "Mandelbrotian randomness"?

eastbay

[eastbay]

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the journal of finance had not one reference of "fractal" "non-scalable" "scale invariant" etc. they had about ten million references for "volatility" though.


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Maybe that's because ideas like "fractal" and "scale invariant" are nice mathematical poetry that make for pretty figures, impressive looking equations, and elegant sounding academic journal articles, but don't have much practical application.

eastbay

[edtost]

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the journal of finance had not one reference of "fractal" "non-scalable" "scale invariant" etc. they had about ten million references for "volatility" though.


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Maybe that's because ideas like "fractal" and "scale invariant" are nice mathematical poetry that make for pretty figures, impressive looking equations, and elegant sounding academic journal articles, but don't have much practical application.

eastbay

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not that i have any idea what barron is talking about here besides fat-tailed distributions, but if that were the actual issue here, wouldn't JoF be full of articles with those terms?

[DcifrThs]

i'll answer the main question:

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what do you mean by mandelbrotian randomness

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i mean alternatives to stochastic models where the underlying assumptions are too stringently normal (even when jumps & other variations are introduced).

i am looking for a book i think i found in the book mandelbrot wrote on fractals in finance and that is on order being shipped to me.

the goal is to use power laws instead of the distributions where the probability of highly unlikely events decreases exponentially.

that is what i mean by mandelbrotian randomness.

i think it is key simply because it appears to be the best perspective available from which to view the functioning of financial markets.

i am currently reading an article from the june 2007 issue of journal of finance: "stochastic volatilities & correlations of bond yields." the models fit the data better and better but they can never seem to explain the important big moves. the paper is great & the math elegant and the data supportive.

i still learn from it and enjoy thinking about the traditional methodologies, however, i want to be as widely versed as possible. im' not throwing out the traditional models. i just want to supplement them.

that is all.

Barron

[anklebreaker]

dc,

Have you used metastock or a similar graphical TA platform?
I played around with fractals and price charts there.

[Sniper]

Barron, since this seems to be what you are asking... Can you project what might be practical examples of using mandelbrotian randomness?

In simple and practical terms, what are you hoping to find?

For example, a mispricing at the extremes of tails that might provide an edge in betting on long shots?

[DcifrThs]

[ QUOTE ]
Barron, since this seems to be what you are asking... Can you project what might be practical examples of using mandelbrotian randomness?

In simple and practical terms, what are you hoping to find?

For example, a mispricing at the extremes of tails that might provide an edge in betting on long shots?

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mostly in terms of active management basically.

security valuation, portfolio construction & analysis.

Barron