mandelbrotian randomness in finance, examples of practical uses?

[DcifrThs]

i just ordered a few books on this but want to see if anybody has seen more empirical (though not necessarily precise) practical uses of scalable distributions for the purposes of trading, investing, portfolio construction, etc.

any clarifying questions, please ask.

thanks,
Barron

[hawk59]

dcfr,

what type of trading do you do?

[DcifrThs]

[ QUOTE ]
dcfr,

what type of trading do you do?

[/ QUOTE ]

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 and after reading 95% of the black swan and reading some philosophical works by benoit mandelbrot, i think this will soon be the next wave of financial market analysis. if not, it will still give me a better idea than my competition into varying methodologies available to the astute mind.

so i'd love eto hear from anybody who knows of or could link/recommend some real time type experiments or any type of application of this stuff.

thanks,

Barron

[eastbay]

[ QUOTE ]
[ QUOTE ]
dcfr,

what type of trading do you do?

[/ QUOTE ]

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

[/ QUOTE ]

Based on what?

eastbay

[DcifrThs]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
dcfr,

what type of trading do you do?

[/ QUOTE ]

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

[/ QUOTE ]

Based on what?

eastbay

[/ QUOTE ]

i dont' really know what you're asking here. are you asking what my "this is key" assumption is based on as it relates to using varying tools to analyze financial markets?

or are you asking about the "key" assumption as it relates to the actual tools i'm looking to learn.

i'll assume from here on out that it is the latter b/c the former seems fairly obvious.

first there seem to be more books popping up on the subject. the academic literature seems to be prodding slowly in that direction. 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. note that while the misuse offers returns, irrespective of large blowups, they'll probably continue to be used. we aren't sold portfolio insurance anymore, but we are still taught the options pricing that was its brainchild.

i remember moving through my math-fin courses thinking, "hey, this mumbo jumbo seems to work, except when it doesn't...but that can't be too big a deal, can it?"

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.

but, it has it's initial home in the physical sciences (IIRC it has to do with how particles dissipate in different environments). the resulting (mis)use of it leads to audacious statements like those that came out of LTCM's shareholder letters (predicting with 100% precision the probability of losing $X/mo/year/5year periods).

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. i was shown nice time period graphs of how this normally-esque distributed randomness produced return streams that looked like those of risky assets.

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

MBAs will still teach this stuff (for those who elect to take it) & MS Fin students will need to understand it. PhDs are going to publish paper after paper applying it as it has been applied (or coming up w/ new and itneresting applications)....but not 10-20yrs from now (if i had to guess).

thus, i want to learn as much about it as possible.

i'm not throwing out the old methodologies, i'm just becomming more aware of their limitations and would like to add more tools to my arsenal of understanding.

Barron

[hawk59]

ok maybe i should ask then do you really think all this stuff is out there because academics want to sound smart or because there is a practical way to make money off of it. you know it's possible to just buy undervalued stocks with a minimum of complication.

[DcifrThs]

[ QUOTE ]
ok maybe i should ask then do you really think all this stuff is out there because academics want to sound smart or because there is a practical way to make money off of it. you know it's possible to just buy undervalued stocks with a minimum of complication.

[/ QUOTE ]

if i were to want to manage my own portfolio then i'd look more into value investing.

however, i'm looking to work at some of the most competitive places out there where equities are a wee tiny part of the overall portfolio simply b/c you run out of undervalued stocks to buy (unless you're private equity) w/ $30billion.

the techniques used are very quant heavy adn i'd like to be more than prepared should anything come up w/ an interview. one question would be like "so what do you find interesting?"

also, the more i know about the structure of the marketplace, the more i'll feel comfortable analyzing it.

hope that makes sense,
Thanks,
Barron

[RicoTubbs]

[ QUOTE ]
but, it has it's initial home in the physical sciences (IIRC it has to do with how particles dissipate in different environments). the resulting (mis)use of it leads to audacious statements like those that came out of LTCM's shareholder letters (predicting with 100% precision the probability of losing $X/mo/year/5year periods).

[/ QUOTE ]

Barron,
What makes you so sure that the probabilities were wrong or that the LTCM guys were not capable of calculating them?

[DcifrThs]

[ QUOTE ]
[ QUOTE ]
but, it has it's initial home in the physical sciences (IIRC it has to do with how particles dissipate in different environments). the resulting (mis)use of it leads to audacious statements like those that came out of LTCM's shareholder letters (predicting with 100% precision the probability of losing $X/mo/year/5year periods).

[/ QUOTE ]

Barron,
What makes you so sure that the probabilities were wrong or that the LTCM guys were not capable of calculating them?

[/ QUOTE ]

the LTCM guys were 100% capable of calculating those probabilities. they probabilities were 100% correct. but they were also 100% based on a model that was 1000% wrong/incomplete/used w/o thought as to its application.

the model was/is based on historical prices and correlations. it ASSUMED that those prices & correlations were both stable (i.e. that they don't change over time) and that they were 100% correct (i.e. the #s they plugged into the models couldn't be wrong). nothing is certain in finance. even using a monte carlo sim of ranges around those #s would be better than what LTCM did, but they didn'te ven do that (it would still be woefully decifient thought).

the example that NNT gives in his books is simple.

if you have a son and the doctor sends him home from school saying that he has chicken pox and may infect the other children, that would be fine.

but if the doctor went on to say that you son has a .218% chance of dying, a 1.1835% chance of losing a limb, and a 62.5381% chance of infecting the other children, you'd be very interested to know what kind of crack medicine the doctor was practicing.

basically, knowing the probability of loss with precision (which is what LTCM claimed) is ludacris.

Barron

EDIT: Oh, by they way, i KNOW the probabilities were wrong because they didn't even CONSIDER the loss of >20% in a year. that probaility itself was reported to be on the order of less than .05% or less than 1 in every 2000 years! but they lost NEARLY 80% (or more depending how you calculate it) of their value IN ONE FREAKING YEAR!!!! and that occured ONCE in EIGHT years. so i'm pretty damn sure those probabilities were wrong.

EDIT 2: more specifically, everything in all of those models works due to the reliance on the normal distribution. Brownian motion (stochastic volatility) is modeled on that gaussian framework. this distribution assumes that the probability of outliers decreases at an increasing rate. so the probabilty of a $1mil loss is maybe 1 in 100, the probability of a $10mil loss is like 1 in 100,000 and the probaility of a $100mil loss is like 1 in 1,000,000,000 (i.e. very fast exponential decrease in probabilities of outliers). the model assumes that the difference between the extremely unlikely to the unlikely is massively bigger than the difference between the unlikely & the possibly unlikely (assuming the scale between them is the same). this translates to an unscalable probability distribution. instead, mandelbrotian distributions allow for more realistic & scalable power law distributions (but can't be used precicely b/c small changes in the estimated scaling factor or exponent result in huge changes in the distribution)

in finance, though, the tails of the distributions are way fatter and can't even be modeled using that framework. according to expectations, a 5% move in the dow should have occured only 34 times in the 100 years till today. instead, it occured like 1000 times. that means themodel is very likely to be pretty freaking wrong imo.

THUS this post. i want to learn more and more about alternatives for risky asset pricing via scalable (or scale invariant) distributions rather than the non-scalable (scale invariant) normal distributions used in many applications.

[RedJoker]

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