On the basis of this book and his well respected book on options pricing, I have a lot of admiration for Taleb. This chapter combines the two aspects, dependency and discontinuity and mixes it with trading time, a concept explained in this chapter.

People who helped build the house of modern finance and their theories are mentioned – Markowitz, Sharpe, Black and Scholes. Even though some received Nobel Prizes, they still lost a lot of money in the markets. Furthermore, for a given object, if its “fractal dimension” is greater than its “topographical dimension”, then it is, by definition, a fractal. This book does a decent job providing an overview of this idea . Mandelbrot’s account of this work is extremely fascinating, any other writer would have simply lavished praise on Mandelbrot for his ideas; Mandelbrot in turn told a wonderful story of how these ideas came to fruition. I knew of Mandelbrot in mathematics, computer science, and natural sciences — I had no idea how deep his obsession with economics was till I read this book. A premodern take on time series data, the markets behavious and whether the natural concepts still apply to them.

## Overview

Benoit Mandelbrot has had a remarkable career which includes seminal work in theoretical and applied mathematics. This implies correlation vanishes despite of the strong dependence. Large price changes tend to be followed by more large changes, positive or negative. This section also mentions forex about “Index of Market Shocks”, a scale that is used to measure financial crisis. Mandelbrot incorporates this dependency in his fractal theory and denotes it as H, the Hurst coefficient. For a Brownian motion, H equals ½ and for any other persistent process, H tends to fall between ½ and 1.

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 overall presentation of ideas was lovely and far from the usual stodgy manner of economics books.

Full stop, this is the point where investors usually lose interest. A multifractal object is an object where more than one “fractal dimension” variable is needed to describe the object. This includes magnetic fields, fluid dynamics, and stock prices over time. It wouldn’t have taken someone of Mandelbrot’s intellect to blow these assumptions out of the water – a much lesser mind could have done it. But the key reason that modern portfolio theory took such hold in the 1960s and 1970s seems to be because there was nothing better on offer – or at least, nothing that offered easy answers. Mandelbrot didn’t offer easy answers; but he did offer an explanation of how markets behaved that – unlike MPT – fit the facts.

## Related Reads

Amidst this wave, Mandelbrot’s cotton price analysis did not find the right traction. Modern Portfolio Theory — an idea that markets are efficiently priced for all information, markets are independent with no memory, and variance and standard deviation are now the good proxies for risk. This theory is generally good, but still underestimates the tales of the bell curve. It was his openness to practical problems that led him to the US; when he got his PhD French mathematics was in the grip of the Bourbaki , which was too much “math for math’s sake” for his taste.

- Dig into the math of investment models and understand the assumptions.
- Well, one can only wish a dose of good luck to all who are trying to make money in such wild markets.
- Maybe it’s a side effect of some incident as a child but the author has no reservations about promoting himself.
- The power of chance suffices to create spurious patterns and pseudo-cycles that, for all the world, appear predictable and bankable.
- The cotton market had its own characteristics of volatility, which he could measure and give parameters for.
- They grossly underestimate risk, largely because they insist that data should fit a bell curve, when it simply doesn’t fit.

They are nowhere near close to that generated by a Geometric Brownian motion process that is assumed in finance literature. The second visual has been generated with the assumption of GBM with observed nifty volatility looks too regular as compared to the reality. Efficient Portfolio Theory — this theory, although effective, relies too heavily on the bell curve. VIX hedge – Correlations go out the window when market volatility significantly increases, so we have been diligent in using a VIX hedging strategy to reduce our portfolio risk. Dig into the math of investment models and understand the assumptions. Mandelbrot took this a little further using his fractal geometry and hypothesized that there is something called long memory — things that might have happened 20 years ago in the market still have a very faint echo later on.

Most financial data, such as stock price over time, for example, has a “fractal dimension” greater than 1 . This measurement of “fractal dimension” is stable and well-defined mathematically.

For instance, when wind speeds increase, the air movement in the wind tunnel undulates forward and backward between periods of smooth flow and turbulence, with sudden gusts and complex swirls. Bachelier’s theory stated that prices move up and down randomly, with each variation being completely independent from the last. Thus, changes and price can’t be considered normally distributed. Additionally, they’re all thought The Misbehavior of Markets to have the same time horizon, the point at which they re-evaluate their investment decisions. For example, this could mean that they’ll all hold their stocks for five years before deciding what to do with them. Many of these orthodox theories are rooted in the works of notable economists, like those from the University of Chicago’s Chicago School, a Neoclassical group that produced and attracted many Nobel laureates.

More specifically, he uses multifractal analysis that rests on the assumption that “trading time” is different from “clock time”. In financial markets, prices move in fits and spurts rather than linear increments. As a result, normal time can be converted into “trading time” to model this multifractal complexity. To do this, create a fractal model to convert normal time to trading time, and another fractal model to convert trading time into price. The resulting models can be used to relate normal time with price. What Mandlebrot basically says is that the widely held view that price varies randomly on a trade-by-trade basis is incorrect. If this did happen then a 5% fall in price today should have no effect on how the price changes tomorrow.

## Community Reviews

Having read his student Taleb’s work first, I was aware of the ideas that Mandelbrot proposes. Reading the teacher’s first-hand account improved my understanding of it. I have a feeling, the multifractal world is too important to be left aside. With its spectacular cleverness it is more than just gorgeous Mandelbrot set pictures.

Affinity and walking through a whole maze of philosophical concepts. “If you are going to use probability to model a financial market, then you had better use the right kind of probability. Nevertheless, some labs, financial providers and consultant firms employ these models. For instance, the financial provider Oanda, who offers an online currency conversion platform in addition to information on foreign exchange, uses fractal analysis for its services. As we’ve seen, it’s difficult to find market patterns, as price movement can be distributed with great irregularity. Some days price changes are dramatic and numerous, while on others such changes are slight and scarce.

All rights in images of books or other publications are reserved by the original copyright owners. He has been writing on this for 50 years and was ignored for a majority of this time. Only now in the last couple of decades, and I can imagine even more since 2008, has his academic papers found their way into the major producers of economists who pretend to know whats going on. A fundamental problem is the Black-Scholes assumption of constant volatility—in essence, that the world does not change.

However, it is superior to the mainstream theories, since they dangerously underestimate risk. Mandelbrot forex analytics tries to convince us, that we should be thinking of fractals, when we look at stock charts.

## The 2008 Market Crash

Overall I would recommend this book for someone interested in finance and maths however I would warn you that it is quite tough to finish. forex analytics You pretty quickly get the jist of the book and then it is just endless examples of why he is right and everyone else is wrong.

In most of the phenomena that authors have researched, they have found a surprising convergence for the logarithmic ratio of the two quantities, ruler length and measurement length. This ratio is summarized as a parameter for the scaling law that is put forth in the book.

## The Cotton Market Example

In history, modernists argue that the course of human events is shaped by many trends, economic and social, enacted in the lives of millions of forgotten individuals; the historian’s task is to trace these trends. By contrast, traditionalists, now coming back into fashion, contend that history was shaped and dominated by a few great men, Caesar or Napoleon, Newton or Einstein, for example.