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Benoit Mandelbrot's Contributions to Price Analysis
Before his death, Benoit Mandelbrot was one of the most celebrated mathematicians in the
world, and most of his work was based on the belief that the wider view of price behavior in
financial markets is primitive and in need of large revisions. Mandelbrot's work sought to
update these “medieval” views of market behavior so that economists could update the
ways asset price changes are understood on a fundamental level. Mandelbrot's legacy as
one of the main contributors to the field of technical analysis is firmly established but there
are still some traders that view Mandelbrot's work as being disconnected from the real
workings of asset markets.
Here, we will look at some of Mandelbrot's main contributions to the study of price behavior.
The work started roughly 50 years ago and involved the creation of a new type of
mathematics. Rather than focusing on accounting or simple geometry, Mandelbrot equations
dealt with mathematical shapes rough and complex, rather than smooth and simplistic.
Additionally, the pattern repetition that Mandelbrot found was largely uncommon and
unexpected relative to most of the similarly focused work that had come before him.
Mandelbrot's equations would later be referred to as Fractals and the wider applications for
these equations have been seen in environments that are far-removed from the world of
finance (being used to describe clouds and coastal formations, to forecast the ways rocks
and metals will wear over time, and to generate computer graphics programs.
Mandelbrot’s Approach to Finance Markets
Focusing on how Mandelbrot's work relates to a financial context, specific examples can be
seen in the ways Mandelbrot criticized a large majority of his colleagues attempted to
predict the changes in price activity. Mandelbrot’s initial assertions were that market
participants should be looking to describe market behavior before attempting to forecast or
predict it. While this might sound disappointing to some looking for the “holy grail” of price
forecasting, for Mandelbrot, this was an essential step in the process because accurate
predictions would be impossible without first having accurate descriptions of what exactly is
happening in market environments.
Mandelbrot’s Critiques of Prevailing Ideas
Since Mandelbrot largely disagreed with most of the price forecasting approaches around
him,it should be noted that Mandelbrot's main contention was with the idea that price
activity is determined by dual opposing positions (the decision to either push prices higher,
or to drive them lower). This idea he saw as an overly simplistic view of market activity,
reducing asset valuations to nothing more than the toss of a coin: Heads, markets buy and
push prices higher, Tails, markets sell and drive prices lower. Before Mandelbrot, this idea
reigned as an explanation of how prices remain generally supported: Buyers and Sellers
constantly bump into each other and keep prices suspended with real valuation changes
occurring slowly.
Mandelbrot argued, however, that this view does not adequately account for the occurrence
of major swings in market volatility. Imagine a stock that falls from $50 to 5 cents. Surely,
for Mandelbrot, these suspension ideas (and the binary Coin Toss view) contain some
inefficiencies and cannot be relied upon to forecast all possible price outcomes. According to
Mandelbrot, large increases in price activity should never happen when viewing markets in a
binary, suspension fashion. But, of course, we know that these situations occur all the time
and Mandelbrot main focus was to explain why this is the case.
by RichardCox http://www.traderslaboratory.com/forums/
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Benoit Mandelbrot's Contributions to Price Analysis
Changing the Prevailing Approach
One of Mandelbrot’s suggestions was to modify the binary (Coin Toss) suspension model to
that the equations matched the real world occurrences. When looking at the financial
markets, this modification meant applying Fractals because of the ways they can plot and
describe the rough and seemingly unlevel nature of price activity. Uneven changes in price
activity (or any observable environment) will make it difficult to formulate equations, and
for Mandelbrot, this is the reason simple geometry proved insufficient when describing these
environments.
This is the reason Mandelbrot’s work with Fractal geometry became a primary focus. With
this form of mathematics, he felt he could write equations that mirrored market behavior
but he still found himself confronting problems with the ability to forecast future price
behavior (especially in cases where major swings in price were seen). While many of
Mandelbrot’s critics agreed with the idea that traditional statistics were insufficient when
looking to forecast wild variations in price, some contended that when looking at longer
time frames the market actually does smooth out in ways less rough than Mandelbrot was
suggesting. This debate led many to favor Mandelbrot’s models over short time frames,
while preferring to use more traditional models as durational periods are extended.
Theories Gauging Market Performance
In his 1982 book The Fractal Geometry of Nature, Mandelbrot looked more broadly,
attempting to find evidence continual reappearance of fractals within the universe, and this
is the work that ultimately granted him the notoriety he would later receive. The
appearance of Fractals in many of the patterns we encounter in daily life (in clouds, plants,
geographical formations), can be described by Mandelbrot’s mathematics. This gained him
attention from practitioners of Chaos Theory and computer graphics visionaries and both of
these fields would later draw largely from Mandelbrot’s Fractals equations.
Mandelbrot’s equations for price forecasting evolved later in his life.
The changing approach to price analysis allowed for new ways to measuring market
performance, and in modeling the drastic price swings with a greater level of precision.
Mandelbrot's formulas are now viewed as a means for measuring and assessing the broader
climate seen in the market over a given period. For Mandelbrot’s theories, consequences
must be tested a large number of times and show high levels of accuracy in order to be
applicable to asset trading.
Mandelbrot's central contention is that Coin Tossing approaches are overly simplistic and
almost suggest that the trading outcome of one day is equal to those seen on every other
day. Anyone with any real experience in the markets knows that this just isn’t the case.
Trading with Mandelbrot’s theories typically involves looking at the number of price changes
and then isolating the number of important trading days to small intervals. For Mandelbrot,
it is this significant minority that is the important period, and the other trading days can be
avoided altogether - as the ability to forecast movements is less likely to result in
substantial gains.
by RichardCox http://www.traderslaboratory.com/forums/
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Benoit Mandelbrot's Contributions to Price Analysis
A Summary of Mandelbrot’s Fractals
Benoit Mandelbrot’s Fractal theory has been studied for decades and is based on the idea
that financial markets (and science as a whole) is based on our sensations. Most of these
sensations are commonly understood: When we see something, we recognize this as the
sensation of optics. When we hear something, we recognize this as the sensation of
acoustics. When temperatures rise, we develop theories to explain the sensation of heat.
For Mandelbrot, one of the most fundamental sensations can be described as “roughness.”
Imagine primitive man agitated by roughness in the same way that humans become
agitated by heat. Roughness was difficult for primitive man to overcome, and this, for
Mandelbrot required the use of Fractal geometry to remedy. Mandelbrot argues that the
ability to measure the non-basic sensations (such as Roughness) came relatively recently.
These advances came with ability to make accurate physical measurements, as we
essentially turn sensations into abstract numbers and equations. The patterns that mark
Fractals repeat in a similar fashion, and with this repetition Mandelbrot suggests that we can
gain an accurate description of “rough” and irregular constructions - like a cloud formation,
coastline, plant structure - or the financial markets. For Mandelbrot, it is this description
that is the first step to efficient price forecasting.
by RichardCox http://www.traderslaboratory.com/forums/
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