Mandelbrot on efficient markets
Marko Amnell
See video at FT.com:
"In a fascinating in-depth interview with
John Authers, investment editor, 85-year old
mathematician Benoit Mandelbrot discusses
his now 40-year old groundbreaking critique
of the "efficient markets" hypothesis and why
new theories on price movement discontinuities
are needed after the credit crunch.
Benoit Mandelbrot is an emeritus professor of
mathematics at Yale University."
Marko Amnell
I know it's a sign of creeping senily to reply to
one's own posts, but here goes...
I have gotten some email replies to this post
(dunno why they didn't want to share their
interesting comments with Usenet) and I
should say that I have not read Mandelbrot's
book on the financial markets, _The (Mis)behavior
of Markets_, so I cannot answer any specific
questions that relate to it. I have read parts of
another of his books, _Fractals and Chaos_.
Here is what I said about it four years ago:
> > This is really a nice find, since Mandelbrot tells a lot about the
> > early history of his discoverey of fractals. He has found the original
> > low resolution print outs of the first images of the Mandelbrot set,
> > made at Harvard in 1980 and the first better quality images made at
> > the IBM research center later that year. Also, a lot of interesting
> > things about the history of math in Paris going back to the late
> > 19th century and how this led to his discoveries. The theme is
> > Mandelbrot and his uncle who see math as a collection of
> > special cases vs the evil totalitarian Bourbakists who would
> > do away with these special cases and reduce everything to
> > one abstract system.
http://newsgroups.derkeiler.com/Archive/Rec/rec.arts.books/2005-12/msg00240.html
I can also recommend a lecture Mandelbrot
gave at MIT in 2001 where he talks about
using fractals to model financial prices.
See video here:
![[LINK] == http://www.meami.org's profile photo](http://lh3.googleusercontent.com/a-/ALV-UjUMj6DMRopgfVTx-8XnFnfzm6qz4ujHqiBq2z06lFsw5mxdQg=s40-c)
[LINK] == http://www.meami.org
>
> I can also recommend a lecture Mandelbrot
> gave at MIT in 2001 where he talks about
> using fractals to model financial prices.
> See video here:
>
> http://mitworld.mit.edu/video/52
N[(1/2)-k*(k-1/2)*(-3)/Factorial[k], 10000]
From: "M.MichaelMusatov" <marty.musatov@xxxxxxxxx>; Date: Sun, 20 Sep
2009 05:53:00 .... %C A000045 A relationship between F(n) and the
Mandelbrot set is .
spudnik
and boring; I was the oly one with a technical question
about his M-set.
so, what is the nature of the rlation between F(n) and
the M-set, is?
> > I can also recommend a lecture Mandelbrot
> > gave at MIT in 2001 where he talks about
> > using fractals to model financial prices.
> > See video here:
>
> >http://mitworld.mit.edu/video/52
>
> N[(1/2)-k*(k-1/2)*(-3)/Factorial[k], 10000]
> From: "M.MichaelMusatov" <marty.musatov@xxxxxxxxx>; Date: Sun, 20 Sep
> 2009 05:53:00 .... %C A000045 A relationship between F(n) and the
> Mandelbrot set is .-
thus:
I had at first to laugh, at the idea of the "time dimension"
being curved, although it is probably true, subjectively -- and
does remind of the "4D is expanding at the speed of light,"
pseudo-authorial dude ... but which is also true
in a delimited sense. there's no business like show business.
thus:
Hales' proof is unfinished, as covertly acknowledged
by the existence of his "Flyspeck" program, although
it is actually admitted, here & there (in Szpiro's book
e.g.). I'd already stated this in an item that JSH started, and
abandoned.
"mathematical proof" was defined to most's satisfaction
by Leibniz, as proving "necessity & sufficiency;" at least,
if you can't do that, you'll still have a problem (although
proving only one or the other is also good:
"the tetrahedron" as a neccesity for 4 colors
on a map e.g.).
> Do I show up with the following phrase? define mathematical proof
>
> That's kind of a test one which seems to work around the world. It'd
> be interesting if true that I don't show up in your region with:
> spherical packing problem
thus:
Michelson-Morley was not a null;
there were regular, very small anomalies over a year.
several researchers improved upon M-M's results, at least one
of whom had an accompanying theory.
[this was covered in the Larouchiac science magazine,
ne Fusion, but may not be online:
http://www.21stcenturysciencetech.com/ .-]
thus:
that was really cool, about the zeroes related to 2/epi (or,
one could say, 2*eth*pith, and there is one other possibility,
thereinat).
I don't see why anyone'd posit weightfullness, other
than inertia -- when Moon hits your eye, like -- if
one is already stressing an aethereal theory. anyway,
Newton's corpuscle was burst by Young, a century later. so,
any further attempts by the Copenhagen schoolers to reify
their math of probability, viz-a-vu "photons," is really
just an exercise in mathematical duality (and,
taht is perfectly-well justified, with enough bullets .-)
> e. Learning that Einstein had done calculations based on the
> gravitational diffraction
--Cap'n'trade is an arbitrageur's delight;
an actual tax on imported oil is a tariff e.g..
".... beyond that level (today, it is over 300 ppm),
the effectiveness of carbon dioxide as a greenhouse gas decreases
exponentially (Figure 1). This exponential
decline in the effectiveness of carbon dioxide as a
greenhouse gas is not contested by the believers in
global warming; they simply ignore it.
There is an experiment anyone can do to understand
this principle: Take a sheet of paper, and place it
over a window with sunlight coming through. You ...."
http://larouchepub.com/lar/Articles_2009/Articles_2009/Cap_and_Trade.pdf
http://larouchepub.com/lar/Articles_2009/Where_Punt_sp09.pdf
Bappa
> On Oct 1, 8:45 pm, Marko Amnell <marko.amn...@kolumbus.fi> wrote:
>
> > See video at FT.com:
>
> >http://tinyurl.com/yawv9ol
>
> > "In a fascinating in-depth interview with
> > John Authers, investment editor, 85-year old
> > mathematician Benoit Mandelbrot discusses
> > his now 40-year old groundbreaking critique
> > of the "efficient markets" hypothesis and why
> > new theories on price movement discontinuities
> > are needed after the credit crunch.
> > Benoit Mandelbrot is an emeritus professor of
> > mathematics at Yale University."
>
> I know it's a sign of creeping senily to reply to
> one's own posts, but here goes...
My sympathies.
> I have gotten some email replies to this post
> (dunno why they didn't want to share their
> interesting comments with Usenet) and I
> should say that I have not read Mandelbrot's
> book on the financial markets, _The (Mis)behavior
> of Markets_, so I cannot answer any specific
> questions that relate to it. I have read parts of
> another of his books, _Fractals and Chaos_.
> Here is what I said about it four years ago:
>
> > > This is really a nice find, since Mandelbrot tells a lot about the
> > > early history of his discoverey of fractals. He has found the original
> > > low resolution print outs of the first images of the Mandelbrot set,
> > > made at Harvard in 1980 and the first better quality images made at
> > > the IBM research center later that year. Also, a lot of interesting
> > > things about the history of math in Paris going back to the late
> > > 19th century and how this led to his discoveries. The theme is
> > > Mandelbrot and his uncle who see math as a collection of
> > > special cases vs the evil totalitarian Bourbakists who would
> > > do away with these special cases and reduce everything to
> > > one abstract system.
>
> http://newsgroups.derkeiler.com/Archive/Rec/rec.arts.books/2005-12/ms...
>
> I can also recommend a lecture Mandelbrot
> gave at MIT in 2001 where he talks about
> using fractals to model financial prices.
> See video here:
>
> http://mitworld.mit.edu/video/52
I first read about his sets in 1983 in Scientific American, and wanted
to implement them. I found them useful to model clouds and clutter,
for computer simulation of tracking with military radar. In those
days memory was scarce and an in-process mechanism that was simple too
made life a lot easier...
Now their main use to the public lies in screensavers, and quite
beautiful they are. I also remember how back in 1990 one of my
colleagues in TRL gave a talk on chaos theory using these sets - the
transformation between order and chaos (or rather randomness).
Cheers,
Arindam Banerjee
Marko Amnell
> the lecture that I saw, at UCLA, was extremely general
> and boring; I was the oly one with a technical question
> about his M-set.
Well, Mandelbrot's MIT lecture is pretty general too.
Here is one exchange that addresses the issue of
trying to predict financial prices in a bit more detail.
It was brought to my attention in an email reply to my post.
Guy Sorman, author of "Economics Does Not Lie:
A Defense of the Free Market in a Time of Crisis"
His presentation at the New York City Harvard Club is available at:
Transcribed starting 42m 15s into the presentation
he is asked a question:
Kay Ajerman? of Commentary Magazine:
"You quoted Mandelbrot twice approvingly in his characterization
of the market and of wild randomness yet in the beginning of
your speech you said that economics grounding as a science has
been solidified by the ability of data and the application of
mathematical and statistical models which I would think
Mandelbrot probably would take contention with. Do you believe
that in addition to helping economists verify their hypotheses
or check them empirically against reality the reliance on, or
should I say over reliance on, mathematical models is a blind
spot in the circles of academia in economics and it fails to
take into account the wild randomness and the unpredictability
of financial and economic cycles and do you think it trumps
sometimes common sense and a healthy account of human nature?"
Guy Sorman:
"Um Hum. Um, there are at least three questions in your
question so I try to make a distinction. Starting with the
notion of wild randomness. What Mandelbrot says and tries to
show is that in nature you don't have wild randomness, you have
what he calls mild randomness. Physical events can be predicted
to a certain extent. And he has built a mathematical model, I
don't want to be too technical there, on the fractal model.
Fractal models show that many chaotic events, like noise for
example, do follow a mathematical pattern and can therefore be
predicted and the consequences have been extremely important,
for example in telecommunication. The Mandelbrot mild
randomness mathematical model applies to nature and physical
events. Okay? Chaos is not that chaotic, that is what he says.
Then he tried and many others tried to transfer his model to the
financial market and when looking at the data, and we have data
since the late 19th century starting with the cotton exchange in
New York which are the oldest financial data which are available
it appears that no pattern ever appears, it is completely
random. And any mathematical model which tried to introduce
kind of a prediction in the evolution of the prices and the
market, all these models have been proven wrong, including many
models which have been used these recent years, at least not to
lose money. And these models were attempt to predict the
evolution of the prices. They all failed. And the conclusion
of Mandelbrot is to say at that stage we have no mathematical
tool or not enough knowledge to predict the financial market,
therefore randomess is mild in the physical nature, in the
financial world randomness is complete or wild. This is what we
know at that stage. Okay? And I won't elaborate, but you have
many mathematical models I am sure which come to your mind
which have been extremely popular until the recent stock exchange
crisis and these models are proved not to be extremely precise.
..."
Copyright =A9 2009, National Cable Satellite Corporation.
Powered by Zen Cart
Arindam Banerjee
of markets. Differentiations of the response profiles along various time
trajectories are a reasonably good predictor for singularities, as I found
out to my own benefit, using the tool I constructed for dimensioning and
optimising the performances of call centre networks.
But I doubt if anyone in the world will take me seriously... heh-heh
Cheers,
Arindam Banerjee.
"Marko Amnell" <marko....@kolumbus.fi> wrote in message
news:c2a5b04a-760d-46e5...@r31g2000vbi.googlegroups.com...
Arindam Banerjee
"Arindam Banerjee" <adda...@bigpond.com> wrote in message
news:_Nizm.46170$ze1....@news-server.bigpond.net.au...
> Nothing other than queuing theory is good for commenting upon the
> behaviour of markets. Differentiations of the response profiles along
> various time trajectories are a reasonably good predictor for
> singularities, as I found out to my own benefit, using the tool I
> constructed for dimensioning and optimising the performances of call
> centre networks.
>
> But I doubt if anyone in the world will take me seriously... heh-heh
>
> Cheers,
>
> Arindam Banerjee.
Well, if they don't want to die from bushfires they'd better take me
seriously, so that it will be possible to give reliable early warning as a
result of build-up of phone calls. The rates of increase are a very serious
factor, in order to distinguish between isolated bursts or catastrophic
situations. I was working on that for Telstra, when I got sacked.
I think that a mathematical approach that makes calling such a breeze (who
remembers the foul frustrating engaged ring tones of the past?) should be
taken seriously - but seriousness lies with engineers, not novelists,
economists, beautiful people, ugly pols, etc.
Cheers, and yes I am replying to my own post, so you are not alone in your
senility, Marko.
David Bernier
> On Oct 8, 3:37 am, spudnik <Space...@hotmail.com> wrote:
>> the lecture that I saw, at UCLA, was extremely general
>> and boring; I was the oly one with a technical question
>> about his M-set.
>
> Well, Mandelbrot's MIT lecture is pretty general too.
> Here is one exchange that addresses the issue of
> trying to predict financial prices in a bit more detail.
> It was brought to my attention in an email reply to my post.
>
> Guy Sorman, author of "Economics Does Not Lie:
> A Defense of the Free Market in a Time of Crisis"
>
> His presentation at the New York City Harvard Club is available at:
>
> http://tinyurl.com/yb4lphy
>
> http://www.booktv.org/Watch/10705/Economics+Does+Not+Lie+A+Defense+of+the+Free+Market+in+a+Time+of+Crisis.aspx
I recently had a look at a book on monetary regimes and inflation:
"Monetary Regimes and Inflation: History, Economic
and Political Relationships", by Peter Bernholz.
It was reviewed here by Pierre Siklos:
http://eh.net/bookreviews/library/0649
Also, cf.:
http://books.google.com/books?id=tt8ip6gienYC
One general idea from that is that too much stimulus spending financed
by too large budget deficits will lead to some inflation,
but cutting back stimulus spending will decrease consumption,
and tend to increase unemployment short-term (say when
stimulus spending is used to try to get out of a
recession "faster") ...
David Bernier
Marko Amnell
> ... I should say that I have not read Mandelbrot's
> book on the financial markets, _The (Mis)behavior
> of Markets_ ...
I'm reading this book now. If you want to read this,
get the new 2008 edition (yellow cover) with the
new preface written in October 2008 on the
financial crisis. You can buy a used paperback
copy online very cheap. I got one from
abebooks.com for $4.50.
Here is a short review which I thought was fair:
In 1963 Mandelbrot published research into the distribution of cotton
prices based on a very long time series which found that, contrary to
the general assumption that these price movements were normally
distributed, they instead followed a pareto-levy distribution. While
on the surface these two distributions don’t appear to be terribly
different, (many small movements, and a few large ones), the
implications are significantly different, most notably the pareto-levy
distribution has an infinite variance.
This implies that rather than extreme market moves being so unlikely
that they make little contribution to the overall evolution, they
instead come to have a very significant contribution. In a normally
distributed market, crashes and booms are vanishingly rare, in a
pareto-levy one crashes occur and are a significant component of the
final outcome.
It has taken years for this to be taken seriously, and in the mean
time financial theory has gone on using the assumption of normally
distributed returns to derive such results as the Black-Scholes option
pricing equation, ultimately winning an Nobel Prize in Economics for
the discoverers Scholes and Merton (Black having already died), not to
mention Modern Portfolio theory (also winning Nobels). That modern
finance ignored Mandelbrot’s discovery and went onto honor those
working under assumptions shown to be false has clearly annoyed
Mandelbrot immensely and as mentioned previously he spends much of the
book telling us of his prior discoveries and how he was ignored.
That Black-Scholes has significant short comings due to unrealistic
assumptions is very well recognised. In the market there exists what
is known as a volatility smile, options with strikes not near the
current market (ie. out-of, or in-the-money options) are priced with
different volatilities to at-the-money options. The very existence of
such a thing is a contradiction of the basic assumptions of the B-S
model and one of a number of ways the market in practice tries to
compromise between using equations that roughly works in some
circumstances and getting a fair price. For all known flaws of the
Black-Scholes framework, no one has been able to figure out anything
else that uses improved assumptions and enables calculation of real
prices. GARCH models are an attempt to fix this but embed many of the
same assumptions.
While the book shows some nice fractal schemes for generating much
more realistic market models than are generated by a straight Brownian
motion scheme and this is all very interesting. The discussion of how
varying time scales may explain some of the observed behaviour is also
good, the speed that trading occurs may be a better measure of market
time than the clock is.
However in the end we are left at the end with a lot of criticism, a
few good ideas but little to show for it. Attempts to try to tinker
with calculations such as VAR to include estimates of fat tails are
dismissed as being like the Ptolemaic system. I don’t disagree with
this analogy, but essentially we are in the situation even worse than
astronomy was after Copernicus. Until Kepler calculated the orbits to
be elliptical, the predictions of the Copernican system were no better
than the Ptolemaic system. Similarly while it is widely recognised
that many of the assumptions of modern finance are wrong it does give
us a framework to make calculations and will continue to be used until
something better comes along.
In the end he calls for research to be done into better developing a
theory to understand market behaviour, which is a good thing. In the
interim though work in the old paradigm will continue with some
recognition that there are flaws which will be dealt with in an ad hoc
way. Continued railing against Efficient Markets, the normal
distribution and the independence of returns this will not change this
without some solid results.
[I thought this comment was interesting]
G Sloane Says:
10 October, 2006 at 12:47 pm
I first read this book during the winter of 2005. Most of my career
has been in the arena of financial analysis, and in that field, I am
not really concerned so much with the purity of mathematical theory as
I am about getting results. But as soon as I picked up the book, I
sensed that it was saying something extremely profound that cut to the
core of what I did for a living. In modern business schools, we are
indoctrinated with concepts of the random walk and the normal
distribution – so much so – that we take them for gospel. But when we
transition from the world of academia to the world of enterprise, we
are consistently confronted by the reality that the models don’t work
as well as they should. We usually chalk this up to being a problem of
implementation rather something fundamentally wrong with our most
basic assumptions. But when I read “Misbehavior of Markets”, I knew
that Mandelbrot was articulating a great truth. Suddenly I could see
dozens of situations from my past, where assumptions about probability
had fallen short of reality – not only in the financial markets, but
also in the metrics of corporate planning. The critic above it correct
in saying that Mandelbrot raises questions without providing the
answers. This book is not a cookbook. It will remain for others to
come up with recipes. But just knowing the short-comings of
traditional models is an important first step. My financial consulting
firm has already begun that process in our own work. This book was the
catalyst for that process.
http://steveedney.wordpress.com/2006/09/26/misbehavior-of-markets-mandelbrot/
Virgil
The Other <ot...@address.invalid> wrote:
> Marko Amnell <marko....@kolumbus.fi> writes:
>
> > Here is a short review which I thought was fair:
>
> [...]
>
> Agreed, but all of this is very old news. People have known for
> decades that distributions of returns are nonnormal. As the guy says,
> the models are used anyway when there's nothing better. It's another
> case of looking for your keys under the streetlight when you dropped
> them in the alley, because the light is better there. The main thing
> is that the people developing and implementing these analytics, the
> "rocket scientists", very rarely have a background in statistics. (I
> think Nissim Taleb emphasizes this fact.) I'm not talking about the
> big names here, but about the ones who actually do the stuff. They've
> typically learned their probability and statistics in physics courses,
> sometimes econometric courses, or sometimes even on their own.
> They're financial *engineers*, and like all engineers, they have no
> patience for "philosophical" questions like whether their models are
> really justified. That's the kind of stuff statisticians worry about;
> it's not what the customer is paying for. Engineers just want to find
> a formula that "works".
But, in this case at least, it appears the formulas don't work!
Even engineers should eventually notice when that keeps happening.
Marko Amnell
> In article <lyk4ynvqii....@circe.aeaea>,
> The Other <ot...@address.invalid> wrote:
Right. I think the key question that needs to be
answered is: To what extent were the incorrect
assumptions underlying modern financial theory
responsible for the severity of the recent (and
ongoing) financial crisis? Mandelbrot and Hudson
claim in their new preface written in October 2008
that "the 2007/08 credit crisis was magnified by
a phenomenon new to our generation: an over-
confidence in our understanding of markets, as
reflected in the industry's increasingly sophisticated
computer models." But they do no substantiate
that assertion. Well, the new preface is only five
pages long, so they can't, but there is a more
fundamental difficulty in answering that question:
lack of data. A large proportion of the financial
instruments responsible for the financial crisis
were not traded on markets for which records
are available.
Arindam Banerjee
"Virgil" <Vir...@home.esc> wrote in message
news:Virgil-64345C....@bignews.usenetmonster.com...
Let us see, in my engineering institute we had separate engineering degree
from different departments in Agricultural, Aeronautical, Electrical,
Electronics and Electrical Communication, Chemical, Mechanical, Civil,
Mining, Metallurgical, Naval Architecture - what the hell is a financial
engineer? Looks like there is an effort in this ng to give genuine
engineers a bad name. Most deplorable!
> But, in this case at least, it appears the formulas don't work!
>
> Even engineers should eventually notice when that keeps happening.
True, which is why *WE* from IIT Kharagpur say that e=mcc is the most
absolute bollocks, and all peoples in all nations that *believe* in that
sort of crap should not get any sympathy when their economies, morals,
health, etc get busted.
Cheers,
Arindam Banerjee.
Les Cargill
> They're financial *engineers*, and like all engineers, they have no
> patience for "philosophical" questions like whether their models are
> really justified. That's the kind of stuff statisticians worry about;
> it's not what the customer is paying for. Engineers just want to find
> a formula that "works".
I dunno - I have always been interested in the philosophy behind
software engineering. And it's been fruitful.
--
Les Cargill
Les Cargill
> On Oct 7, 9:48 pm, Marko Amnell <marko.amn...@kolumbus.fi> wrote:
>
>> ... I should say that I have not read Mandelbrot's
>> book on the financial markets, _The (Mis)behavior
>> of Markets_ ...
>
> I'm reading this book now. If you want to read this,
> get the new 2008 edition (yellow cover) with the
> new preface written in October 2008 on the
> financial crisis. You can buy a used paperback
> copy online very cheap. I got one from
> abebooks.com for $4.50.
>
Marko, how *exactly* does this negate the Efficient Markets
Hypothesis? All the EMH says is "you can't out crazy
the market." - that the market and you have roughly
the same information.
--
Les Cargill
Les Cargill
I don't agree with your assessment - "financial engineering" isn't
actually engineering, and most engineers care a great deal about
philosophy.
>> But, in this case at least, it appears the formulas don't work!
>>
>> Even engineers should eventually notice when that keeps happening.
>
> True, which is why *WE* from IIT Kharagpur say that e=mcc is the most
> absolute bollocks, and all peoples in all nations that *believe* in that
> sort of crap should not get any sympathy when their economies, morals,
> health, etc get busted.
>
> Cheers,
>
> Arindam Banerjee.
>
>
--
Les Cargill
spudnik
just attended a promulgation of "free markets"
re _Turning Oil into Salt_ -- look it up,
in which (I think) the head of the institute,
where it was given, suggested a "floor price"
for "alternative energy," which was immediately
confuzed with one for oil ... so, I asked,
with a resounding non-response, if that latter was not
the same as applying a tariff to imported oil; b)
just read that mister Merriwether,
who started the ill-fated LTCM hedgie,
based upon the Nobel Prize-winning (sic) formula
of Scholes et al, is starting a new one, his third
(it (FT) also said that the average hedgie was
only about two to three times leveraged,
which I guess was "bollocks," what ever that is.
now, as for E=ccm, it is just an extension
of Leibniz'z well-known formula from *vis-viva*
(sp.?), and not so earth-shattering ...
no matter what Leo "doc strangelove" szilard did with it!
(things, only the Larouchiacs know .-)
> > True, which is why *WE* from IIT Kharagpur say that e=mcc is the most
> > absolute bollocks, and all peoples in all nations that *believe*
--Cap'n'trade is an arbitrageur's delight;
an actual tax on imported oil is a tariff e.g..
http://wlym.com/~animations/fermat/index.html
".... beyond that level (today, it is over 300 ppm),
the effectiveness of carbon dioxide as a greenhouse gas decreases
exponentially (Figure 1). This exponential
decline in the effectiveness of carbon dioxide as a
greenhouse gas is not contested by the believers in
global warming; they simply ignore it.
There is an experiment anyone can do to understand
this principle: Take a sheet of paper, and place it
over a window with sunlight coming through. You ...."
http://larouchepub.com/lar/Articles_2009/Articles_2009/Cap_and_Trade.pdf
http://larouchepub.com/lar/Articles_2009/Where_Punt_sp09.pdf
Marko Amnell
Mandelbrot takes the Efficient Markets Hypothesis
to include the claims that:
1) Financial markets are efficient. In an efficient
market, all the relevant data are already priced
into the price of a security right now.
2) Price changes are statistically independent.
3) Price changes are normally distributed.
Mandelbrot argues that price changes are dependent
and that price changes are not normally distributed.
Prices have memories. If the Efficient Markets
Hypothesis is correct, then the market equilibrium
is up-to-date and correct and very quickly adjusts
to incorporate new information, so it is impossible
to beat the market long-term. But if, as Mandelbrot
argues, price series exhibit various degrees of memory
(so that there is long-term dependence) then it is
possible to gain an advantage from actively selecting
securities over the long term.
Let me quote from Mandelbrot and Hudson's book
_The Misbehavior of Markets_ (p. 12):
"My heresy is a different, fractal kind of statistical
relationship, a 'long memory'. This is a delicate
point to which a full chapter will be devoted later.
For the moment, think about it by observing that
different kinds of price series exhibit different
degrees of memory. Some exhibit strong memory.
Others have weak memory. Why this should be is
not certain; but one can speculate. What a company
does today -- a merger, a spin-off, a critical product
launch -- shapes what the company will look like
a decade hence; in the same way, its stock-price
movements today will influence movements tomorrow.
Others suggest that the market may take a long time
to absorb and fully price information. When
confronted by bad news, some quick-triggered
investors react immediately while others, with
different financial goals and longer time-horizons,
may not react for another month or year. Whatever
the explanation, we can confirm the phenomenon
exists -- and it contradicts the random-walk model."
Mandelbrot and Hudson devote chapter 9 to the
subject of long-term memory. The chapter is entitled
"Long Memory, from the Nile to the Marketplace."
The title alludes to Harold Edwin Hurst, who
first developed the necessary statistical methods
while studying the flooding of the Nile River in
Egypt in the early 20th century.
There is a short description of the approach of
Hurst and Mandelbrot in the book _Information
Efficiency in Financial and Betting Markets_ (2005),
ed. Leighton Vaughan Williams (p. 18):
"The idea of rescaled range analysis was first
proposed by Hurst (1951), as a result of his
observations of natural phenomena. The statistics,
since refined by Mandelbrot (1972, 1975),
Mandelbrot and Taqqu (1979) and Lo (1991),
can be used to test for long-term dependence.
Essentially it is a method of measuring how the
path of a time series varies over various timescales.
Specifically, the rescaled-range statistic is the
range (i.e. high minus low) of partial cumulative
sums of deviations of a time series from its mean,
rescaled by its standard deviation. A convenient
way of viewing its application is through an
examination of the so-called Hurst exponent.
Named after H.E. Hurst, who first developed its
use in studies of the Nile river dam project, it
is a measure of correlative persistence.
"The correlation can be derived from the
following equation:
C = 2^(2H-1) - 1
where C is the measure of correlation and H
is the Hurst exponent.
"Thus, if the Hurst exponent equals 0.5, C = 0
and the probability that a move in one direction
will be followed by a move in the same direction
(e.g. positive followed by positive) is 50 per cent.
If the Hurst exponent is less than 0.5 the system
can be characterised as mean-reverting
(sometimes termed anti-persistent or ergodic), if
greater than 0.5 it is correlative or persistent
(also sometimes termed trend-reinforcing).
The period of time over which H is greater than 0.5
is a measure of the _memory cycle_ of the system,
and so measures the time period over which
information can be used predictively. This approach
is particularly useful in the context of non-normal
distributions. The reason is that the variance of
such distributions may not exist (i.e. the expected
value of the variance may be infinite). The essential
intuition behind this is that the tails of the distribution
decay too slowly."
The text goes on to describe research which showed
that from January 1950 to July 1988 "S&P 500
prices were found to increase with the 0.78 root
of time, in contrast to the square root configuration
which would be consistent with a random walk."
Pubkeybreaker
> See video at FT.com:
>
> http://tinyurl.com/yawv9ol
>
> "In a fascinating in-depth interview with
> John Authers, investment editor, 85-year old
> mathematician Benoit Mandelbrot discusses
> his now 40-year old groundbreaking critique
> of the "efficient markets" hypothesis
The "efficient market" hypothesis is horseshit.
The real markets (as opposed to the fantasy markets
of economists, mathematicians and financial 'analysts')
work on INSIDE INFORMATION.
Anyone who believes otherwise is living in fantasy land.
Patok
> On Oct 23, 5:07 am, Les Cargill <lcargil...@comcast.net> wrote:
>> Marko, how *exactly* does this negate the Efficient Markets
>> Hypothesis? All the EMH says is "you can't out crazy
>> the market." - that the market and you have roughly
>> the same information.
>
> Mandelbrot takes the Efficient Markets Hypothesis
> to include the claims that:
>
> 1) Financial markets are efficient. In an efficient
> market, all the relevant data are already priced
> into the price of a security right now.
>
> 2) Price changes are statistically independent.
>
> 3) Price changes are normally distributed.
Thanks for this very interesting information, Marko. The way the
financial world works continues to amaze me with a constant display of
savant idiotism. Apparently, they use advanced statistical and
mathematical models to implement policies that defy common sense and are
based on wrong assumptions. Even I, having nothing to do with markets
and finance, could have told you that the Efficient Markets Hypothesis
is completely wrong, exactly for the reasons Mandelbrot gives. It is so
blindingly obvious; how could they believe in it? Could it be a case of
professional desensitization, where working in a familiar environment
makes them miss the obvious defects that someone from the outside would
instantly notice? Like sometimes happens when shadetree builders build a
house without a plan, and forget to include stairs from the ground floor
to the one above, because during building they use the scaffolding and
never notice the omission.
Another thing that I find myself wondering about financiers is why
don't they use the Marxist theory of added value, together with laws
from electrodynamics to do their calculations? Markets quite clearly
behave much more like an electrical system than like anything else;
value (money) and goods are generated and consumed and move around much
like electricity. Another analogy, that I think the financiers don't
understand (but maybe I'm wrong, and they do), is that you can't
generate more wealth out of thin air than the generators in the system
(producers of goods and services) can generate. Thinking that you can,
leads to things like last year's lending crisis (if I correctly
understood what and why happened in it). Of course the analogy with
electrodynamics can't be full, because of human participation in price
formation, that makes the Efficient Markets Hypothesis wrong in the
first place, and will need to be accounted for in some manner.
Interesting stuff.
--
You'd be crazy to e-mail me with the crazy. But leave the div alone.
Marko Amnell
The wikipedia page for "Efficient-market hypothesis" seems worth
quoting:
The hypothesis has been attacked lately by critics who blame belief in
rational markets for much of the current financial crisis,[1][2] with
noted financial journalist Roger Lowenstein recently declaring "The
upside of the current Great Recession is that it could drive a stake
through the heart of the academic nostrum known as the efficient-
market hypothesis."[3] [...]
The recent global financial crisis has led to renewed scrutiny and
criticism of the hypothesis.[30] Market strategist Jeremy Grantham has
stated flatly that EMH is responsible for the current financial
crisis, claiming that belief in the hypothesis caused financial
leaders to have a "chronic underestimation of the dangers of asset
bubbles breaking".[2]
At the International Organization of Securities Commissions annual
conference, held in June 2009, the hypothesis took center stage.
Martin Wolf, the chief economics commentator for the Financial Times,
dismissed the hypothesis as being a useful way to examine how markets
function in reality. Paul McCulley, managing director of PIMCO, was
less extreme in his criticism, saying that the hypothesis had not
failed, but was "seriously flawed" in its neglect of human nature.[31]
Les Cargill
Thank you for your efforts. Makes perfect sense. Yes, I'd read
Grantham and Martin Wolf, but didn't understand the derivation of
this. Now I do.
--
Les Cargill
Arindam Banerjee
To put it another way, the real markets actually work (by taking money
from the suckers, like in any horse race) is by trying hard to make
the suckers believe that it does *not* work on inside information (and
manipulation), and one way to get credibility is by sacrificing some
Madoffs from time to time.
So there is a tradeoff - markets will rise so long as people are
fooled, but at some time when they are not fooled they stop buying,
and after that depending upon some random or contrived factors they
may panic or they may keep on buying. Greed vs panic here - just as
there is the need vs capacity situation in the telecom networks.
It used to be that markets were a measure to help fund good people
start good business, but now in our Einsteinian world all these high-
minded ideals (if they ever existed) have long gone down the
drainpipes. Will anyone fund a Hydrogen Transmission Network, or the
development of the Internal Force Engine?
Arindam Banerjee
spudnik
the hogs always get slaughtered; that is,
market "up" or "down" makes no difference
to the physical economy, if they are raking it all of
in the "voluntary CO2 emmisions-trading scheme;"
does it?
> start good business, but now in our Einsteinian world all
> of these high-minded ideals (if they ever existed) have
> long gone down the drainpipes. Will anyone
> fund a Hydrogen Transmission Network, or the
> development of the Internal Force Engine?
thus:
that is the penintimate waffle.
> than it, so the rest mass of a photon as a particle of aether, if a
> photon is a particle of aether, would be 'zero', as in nothing has
> less mass than the aether itself.
thus:
distant action by a bunch of British spooks, like Newton,
who wouldn't "share" with Hooke, the first head
of the Royal Society?
this is a groovy thread, although Hawking, MoU, gets it wrong
about M&M, even by the usual "null" say-so;
the speed of light depends upon the index of refraction,
even in a relative vacuum, such as air at sea-level (NB:
there is some heighth, where the air is half dihydrogen).
Davies is more-correct then Smolin:
since stringtheory subsumes most of the math
of the older stuff, it really is not controversial;
Penrose has yet, AFAIK, to address plasma physics,
which is the "9" of Universe beyond the Department
of Einsteinmania, the Musical Department.... but,
he is so brave, to take the suit to the array
of lawyers on the estate of Schroedinger's joke-cat ...
even though, as pertains USA academe, the Department may
as well be run by the Lucasian Chair-sit! (also note,
Smolin is at the "Perimeter Institute,"
supposedly named after a constant, the ratio
of the diameter of the sphere to either its circumference, or
its area.)
thus:
photon hath no restmass, precisely because
it is not a coorpuscle -- it am what it am,
"least action in least time" a la Fermat!...
the photon is a figment of Einstein's photo-electrical effect.
Descartes to Fermat
Tuesday, July 27, 1638
http://wlym.com/~animations/fermat/august08-fermat.pdf
http://wlym.com/~animations/fermat/index.html
Marko Amnell
> Thank you for your efforts. Makes perfect sense. Yes, I'd read
> Grantham and Martin Wolf, but didn't understand the derivation of
> this. Now I do.
There is a lot more information about Hurst at the following website:
http://www.bearcave.com/misl/misl_tech/wavelets/hurst/
I will just give two quotes, which I found interesting:
"I have had a hard time finding an intuitive definition for the term
long memory process, so I'll give my definition: a long memory process
is a process with a random component, where a past event has a
decaying effect on future events. The process has some memory of past
events, which is "forgotten" as time moves forward. For example, large
trades in a market will move the market price (e.g., a large purchase
order will tend to move the price up, a large sell order will tend to
move the price downward). This effect is referred to as market impact
(see The Market Impact Model by Nicolo Torre, BARRA Newsletter, Winter
1998). When an order has measurable market impact, the market price
does not immediately rebound to the previous price after the order is
filled. The market acts as if it has some "memory" of what took place
and the effect of the order decays over time. Similar processes allow
momentum trading to have some value."
[...]
"Looking back over the results, it can be seen that the Hurst exponent
of 1-day returns is very near 0.5, which indicates a random walk. This
corresponds with results reported in the finace literature (e.g., 1-
day returns have an approximately Gaussian normal random
distribution). As the return period gets longer, the Hurst exponent
moves toward 1.0, indicating increasing long memory character.
In his book Chaos and Order in the Capital Markets, Edgar Peters
suggests that a hurst exponent value H (0.5 < H < 1.0) shows that the
efficient market hypothesis is incorrect. Returns are not randomly
distributed, there is some underlying predictability. Is this
conclusion necessarily true?
As the return period increases, the return values reflect longer
trends in the time series (even though I have used the log return).
Perhaps the higher Hurst exponent value is actually showing the
increasing upward or downward trends. This does not, by itself, show
that the efficient market hypothesis is incorrect. Even the most
fanatic theorist at the University of Chicago will admit that there
are market trends produced by economic expansion or contraction.
Even if we accept the idea that a non-random Hurst exponent value does
damage to the efficient market hypothesis, estimation of the Hurst
exponent seems of little use when it comes to time series forecasting.
At best, the Hurst exponent tells us that there is a long memory
process. The Hurst exponent does not provide the local information
needed for forecasting. Nor can the Hurst exponent provide much of a
tool for estimating periods that are less random, since a relatively
large number of data points are needed to estimate the Hurst
exponent.
The Hurst exponent is fascinating because it relates to a several
different areas of mathematics (e.g., fractals, the Fourier transform,
autocorrelation, and wavelets, to name a few). I have to conclude that
the practical value of the Hurst exponent is less compelling. At best
the Hurst exponent provides a broad measure of whether a time series
has a long memory character or not. This has been useful in research
on computer network traffic analysis and modeling. The application of
the Hurst exponent to finance seems more tenuous."
Arindam Banerjee
> the bulls make money, the bears make money, and
> the hogs always get slaughtered; that is,
> market "up" or "down" makes no difference
> to the physical economy, if they are raking it all of
> in the "voluntary CO2 emmisions-trading scheme;"
> does it?
Racial, cultural, national, institutional, personal, career factors
count rather more than some moneys gained or lost in the share/
property markets. Moneys come and go, but prejudices linger.
> > start good business, but now in our Einsteinian world all
> > of these high-minded ideals (if they ever existed) have
> > long gone down the drainpipes. Will anyone
> > fund a Hydrogen Transmission Network, or the
> > development of the Internal Force Engine?
>
> thus:
> that is the penintimate waffle.
I don't know if this is a put-down, but to stick to my earlier point,
only the truly scientific methods/approaches can conquer prejudice,
over the long term.
Arindam Banerjee
Arindam Banerjee
"Les Cargill" <lcarg...@comcast.net> wrote in message
news:hbr3p1$r9h$1...@news.eternal-september.org...
I don't see how you are disagreeing with my assessment, when you yourself
say that "financial engineering" isn't actually engineering. You are only
making my point.
Arindam Banerjee
"spudnik" <Spac...@hotmail.com> wrote in message
news:bf57be45-ca91-4898...@m33g2000pri.googlegroups.com...
> two things: a)
> just attended a promulgation of "free markets"
> re _Turning Oil into Salt_ -- look it up,
> in which (I think) the head of the institute,
> where it was given, suggested a "floor price"
> for "alternative energy," which was immediately
> confuzed with one for oil ... so, I asked,
> with a resounding non-response, if that latter was not
> the same as applying a tariff to imported oil; b)
> just read that mister Merriwether,
> who started the ill-fated LTCM hedgie,
> based upon the Nobel Prize-winning (sic) formula
> of Scholes et al, is starting a new one, his third
> (it (FT) also said that the average hedgie was
> only about two to three times leveraged,
> which I guess was "bollocks," what ever that is.
>
> now, as for E=ccm, it is just an extension
It is more than a wrong formula, derived from a bungle. It is much more
disastrous. It is a wrong ideology, that appearance is actually reality,
that the Earth is standing still... it is the height of anti-science.
Arindam Banerjee
Les Cargill
Ah. Violent agreement, then!
>>>> But, in this case at least, it appears the formulas don't work!
>>>>
>>>> Even engineers should eventually notice when that keeps happening.
>>> True, which is why *WE* from IIT Kharagpur say that e=mcc is the most
>>> absolute bollocks, and all peoples in all nations that *believe* in that
>>> sort of crap should not get any sympathy when their economies, morals,
>>> health, etc get busted.
>>>
>>> Cheers,
>>>
>>> Arindam Banerjee.
>> --
>> Les Cargill
>
>
--
Les Cargill
spudnik
to "E=cmc," it is just the short version, and
it may not be in the best form, but it is *still*,
essentially, Leibniz's *vis viva*, which corrected
someone's "linear" formula (I think, Poor Galileo's).
> It is more than a wrong formula, derived from a bungle. It is much more
> disastrous. It is a wrong ideology, that appearance is actually reality,
> that the Earth is standing still... it is the height of anti-science.
thus:
holy grapes; M&M's experiment was *not* a null; although
the annual anomaly was rather small, it was regular enough.
Miller's result confirmed this. the write-up was brought
to Einstein, at one of hte few times that he was
at his office at Caltech, and he poo-pooed it (according
to I. 4 Gott).
and one *still* has to account for all of the actual results
"proving relativity & so on."
> You do realize this is the aether Michelson and Morley, and Miller,
> and countless others looked for and did not find?
--Sir Dirty Harry Potter & Trickier Dick Cheeny want you:
Sudancrusade!
http://wlym.com/~animations/fermat/Observations%20on%20Diophantus.pdf
1. Yes, this is his statement of what has come
Arindam Banerjee
bottom. e=mcc was derived from this bungle. I have analysed all this
thoroughly.
"spudnik" <Spac...@hotmail.com> wrote in message
news:3a1da2e9-7ffe-49c4...@x15g2000vbr.googlegroups.com...