## Benoit Mandelbrot

05.11.2020

Content

The change in market prices does not follow a Gaussian distribution in a reliable fashion. Like income distribution, market statistics frequently follow a power law. The «fat tails» of the return curve reflect risk, where large losses and profits can be realized. The roots of the book The behavior of Markets go back to 1961 when Mandelbrot was a new researcher at IBM.

Benoît Mandelbrot, was a great mathematician, the inventor of fractal geometry. Those sets is a manifestation of the vast aesthetic power of math – the langue of nature – or the nature https://forexbitcoin.info/ itself as Max Tegmark argues in his book Our Mathematical Universe. Fractal geometry might be the evidence that math is not just a thing that only exists in the brain of humans.

Mathematical superstar and inventor of fractal geometry, Benoit Mandelbrot, has spent the past forty years studying the underlying mathematics of space and natural patterns. What many of his followers don’t realize is that he has also been watching patterns of market change.

For centuries, shipbuilders have put care into the design of their hulls and sails. They know that the sea is typically calm but hurricanes do sometimes happen. Shipbuilders design in case of these storms – despite the construction appearing overkill for the typical day. Mandelbrot’s discovery that prices are not normally distributed means that markets are riskier than previously thought. Most investors are like shipbuilders who ignore extreme weather and optimize a portfolio for the 95% of the time the market is normal.

As the horizon of Mandelbrot’s mortality approaches, he seems to be working to establish his intellectual legacy. He recently publishedFractals and Chaos (Springer-Verlag, 2004), which is a collection of some of his papers from 1979 onward. Mandelbrot’s papers can be difficult reading for anyone who is not a skilled mathematician. His book The Fractal Geometry of Nature can be read by anyone who has a solid high school math background and patience with an academic writing style. In publishingThe behavior of Markets Mandelbrot is writing for the general reader, who usually has no tolerance for mathematical equations. Before engaging in the field of finance, the author Benoit Mandelbrot initially endeavored in researches and academic pursuits relative to the mathematics of space, figures, and natural patterns. Though he is an esteemed figure in the area, he also studies financial landscape and market movements.

## Randomness In Financial Markets

As anyone who has repeatedly put money at risk in a market over a long period of time knows, market behavior does not reflect the well behaved Gaussian models proposed by economists in the 1970s and 1980s. There are far more market bubbles and market crashes than these models suggest. Mandelbrot saw financial markets as an example of «wild randomness», characterized by concentration and long range dependence. He found, for example, that cotton prices followed a Lévy stable distribution with parameter α equal to 1.7 rather than 2 as in a Gaussian distribution. «Stable» distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger scale parameter. Benoit Mandelbrot’s The Behavior of Markets is a splendid read and very informative.

Part of Mandelbrot’s point is that their models are not merely inadequate, they so severely underestimate risk as to be catastrophically dangerous—worse than useless, and not improved by adding epicycles. Even if no one except perhaps some hermetic academics believe in the efficient-market hypothesis, typical analysis continues to rely on tools that make assumptions like normal distribution of returns and the applicability of continuous mathematics. In fact, one could almost say the book is about fractal processes, using the markets as a case study. In this way, it is reminiscent of Nassim Nicholas Taleb’s Fooled by Randomness, which uses the markets largely as a basis to investigate logical fallacies . The third chapter is about Bachelier and his coin-tossing view of finance. According to this theory, the market is so efficient that all information is directly reflected in the price of financial assets.

Basic familiarity with options and mathematics is extremely helpful and understanding this book, but it is overall quite approachable. With his fractal tools, Mandelbrot has gotten to the bottom of how financial markets really work, and in doing so, he describes the volatile, dangerous properties that financial experts have never before accounted for. The result is no less than the foundation for a new science of finance.

And through this book, he collected and delivered advanced mathematical tools for market participants’ usage. Equipped with Mandelbrot’s mathematical principles, one will never look at markets the same way again. Interesting discussions of price distributions, path dependency, fractals, and market risk. Marred by poor copy editing (it’s «Chicago Board Options Exchange») and the reader’s mipronunciations of non-English names and terms. XRP (Ripple) Trading The authors’ conclusion, in which they express hope that more-enlightened academic research into market behavior will make the world a better place, is naive but doesn’t much detract from the better ideas in the book. Excellent book by Mandelbrot himself on markets and why they aren’t brownian and how fractals can be used to represent markets. He goes into volatility and how a Gaussian distribution cannot properly describe markets.

The Misbehavior of Markets The reason people lose money in markets is that they underestimate the risk. The mathematical and financial models that are most commonly used by banks and investment firms around the world are based on faulty assumptions. I can very well see why Taleb considers this as the deepest and most realistic book on finance, since I occasionally felt that I was reading Taleb, not Mandelbrot. It is frightening to read books like these, since you become more and more convinced that what you learned in university was bunk. Financial markets do not follow bell curves, and standard risk measurements are plainly wrong.

As many reviewers have noted, Mandelbrot invented fractal geometry. He has also been on the cutting edge (some would say fringe, but he’s thinking and questioning) in multiple disciplines, as his curiosity seem to know no bounds. Mandelbrot does a good job of describing the inadequacies of the efficient market hypothesis and CAPM and other sacrosanct theories in finance, and he offers for our consideration an alternative view. His view is based on his assertion of reality; namely that the world of finance is turbulent , and linear tools relying on reliability and rational man will never tell the full story. The power of chance suffices to create spurious patterns and pseudo-cycles that, for all the world, appear predictable and bankable. But a financial market is especially prone to such statistical mirages. My mathematical models can generate charts that—purely by the operation of random processes—appear to trend and cycle.

Markets are much more risky than we make them to be, and lives can be ruined as a result. As Mandelbrot put it, this book will not make you rich, but it may save you from ruin. The theory goes that the markets already consolidate all the information available to them, so that price already incorporates all the information available to the market. From there, we get the random walk theory — that prices will move in a random fashion, so that each price move is basically the flip of a coin.

As this math genius and fractal geometry developer continued to observe shifts and persisting trends present in the financial world, he decided to team up with Richard L. Hudson in magnifying the overall financial landscape through a fractal lens. This book should be required reading for anyone interested in investing, markets, or finance.

## About Benoît B Mandelbrot

His interest is not of a speculator, but a mathematical modeller. Forecasting models are not the same as risk models and stock option pricing.

Perhaps at the behest of his co-author, Richard Hudson, there are no equations in the main body of the book and only a few in the notes at the end. This leaves the reader with only Mandelbrot’s articles for reference and these do not make easy reading. At least one book, Iceberg Risk by Kent Osband has managed to mix a very readable narrative with sections of mathematics. For those readers who would like to explore Mandelbrot’s ideas in more depth, it is to bad that Mandelbrot and Hudson did not do something similar. In The behavior of Markets Mandelbrot argues that the Gaussian models for financial risk used by economists like William Sharpeand Harry Markowitz should be discarded, since these models do not reflect reality. Mandelbrot argues that fractal techniques may provide a more powerful way to analyze risk. Unfortunately, as Mandelbrot points out in The behavior of Markets, the foundation of this new era of economics was rotten.

## Booksellers Recommend

Among other things, he was working on using computers to analyze the distribution of income in a society. Mandelbrot’s work echoed the work of Vilfredo Pareto and showed that many economic factors, including wealth, are distributed according to an inverse power law. While at Harvard to give a talk on his work, Mandelbrot saw a diagram on a chalk board that mirrored the distributions he was seeing for income. With access to IBM’s computers Mandelbrot started studying cotton prices. In his most provocative and practical book yet, one of the foremost thinkers of our time redefines what it means to understand the world, succeed in a profession, contribute to a fair and just society, detect nonsense, and influence others. Citing examples ranging from Hammurabi to Seneca, Antaeus the Giant to Donald Trump, Nassim Nicholas Taleb shows how the willingness to accept one’s own risks is an essential attribute of heroes, saints, and flourishing people in all walks of life.

- The result is a revolutionary reevaluation of the standard tools and models of modern financial theory.
- Mathematical superstar and inventor of fractal geometry, Benoit Mandelbrot, has spent the past forty years studying the underlying mathematics of space and natural patterns.
- What many of his followers don’t realize is that he has also been watching patterns of market change.
- In The Behavior of Markets, Mandelbrot joins with science journalist and former Wall Street Journal editor Richard L. Hudson to reveal what a fractal view of the world of finance looks like.
- With The Behavior of Markets, he puts the tools of higher mathematics into the hands of every person involved with markets, from financial analysts to economists to 401 holders.
- Markets, we learn, are far riskier than we have wanted to believe.

He calls it «dependence,» an hitherto underappreciated quality. The standard model of market behavior insisted that today’s price movement is an independent event. Personally, I think most experienced traders know that today’s price is affected by price movements in the past if only because traders themselves have memories. But more than that market prices seem influenced by the past because some of the same mechanisms, phenomena and conditions still prevail. What celebrated mathematician Benoit Mandelbrot discovered when analyzing market behavior is that the markets tend to go to extremes.

## Market Valuation

For example, on pages Mandelbrot recalls that in 1982 IBM hired then small Intel to make its microprocessors and a company headed by the unknown Bill Gates to provide its software. If IBM had started up a pretzel factory in 1982 would their stock prices be correlated? Mandelbrot seems to imply that they would; but I think it may be that he is so enamored of the magic of his fractals that he sees what he wants to see. Bubbles develop and burst and individual stocks have market values totally out of line with their assets, revenue and profits. One had only to live through the go-go high tech market of the 1990s to know that. Mandelbrot claims that part of this inexplicably erratic behavior is due to the markets having a memory of sorts.

The latter two are absolutely essential to a sustainable market, the first one is wishful thinking for relative wealth (that is, making easy money when Foreign exchange autotrading other investors didn’t). Unfortately, most of the effort in finance is put into forecasting stock prices rather than risk modeling or option pricing.

## Essentials Of Risk Management In Finance

It’s at this stage it is easy to get lost — I had to read the crucial chapter a few times. What he does is marry together his notion of the way prices change with his notion of trading time to produce a realistic model of a price chart, where time travels sometimes slow, sometimes fast. The book is very well written, and easy to understand, especially since it deals with a field where people tend to be abstruse and to obfuscate whenever possible.