The Misbehavior of Markets: A Fractal View of Financial Turbulence [Paperback]

"...forty years after I started battle on the subject, most economists now acknowledge that prices do not follow the bell curve, and do not move independently. But for many, after acknowledging those points, their next comment is: So what? Independence and normality are, they argue, just assumptions that help simplify the math of modern financial theory. What matters are the results. Do the standard models correctly predict how the market behaves over all? Can an investor use Modern Portfolio Theory to build a safe, profitable investment strategy? Will the Capital Asset Pricing Model help a financial analyst, or a corporate financial officer, make the right decision? If so, then stop arguing about it. This is the so called positivist argument, first advanced by University of Chicago economist Milton Friedman."

Isn't it this positivism that the majority of practitioners of finance exhibit? I myself, though not a practitioner, held such thoughts. My reasoning had been based however more upon majority's acceptance -- if everyone else is acting upon the assumptions of normality and independence, I thought, what good will there be adopting a new theory? Isn't finance more akin to social sciences than to natural sciences after all?

It is these beliefs that Mandelbrot sets out to dispel with this monograph. He does so convincingly with great confidence and tenacity. The book consists of three parts, first the examination of the current theories (CAPM, MPT, Black-Scholes), next explanation of his methodology (fractal analysis), and finally of posing questions that should be answered (Mandelbrot asserts that virtually all the current theories should be reexamined under more realistic assumptions). To readers who have followed Mandelbrot's findings even remotely, there are no new advancements recorded in this book per se. He explains with concepts he developed throughout his entire career -- fractals; more specifically self-similarity, long-range dependence (via the Hurst exponent), and fractal decomposition of [trading] time. Mandelbrot's original research without doubt launched an entirely new field of study in science and engineering. Here his objective seems to be persuasion of the general public that an overhaul of existing methods is due. This may be evidenced by the absence of equations in the main text (some are included in the notes/appendix), and by the existence of the second author of this book.

The book is also a trajectory of Mandelbrot's intellectual development. He explains, with characteristic detail, why, how, and when he has become interested in the problems as he did. The result is interesting accounts of historical figures (Bachelier, Hurst, Markowitz, etc) and records of encounters with eminent figures in mathematics and economics (Lévy, Poincaré, Sharpe, and Fama (his student) to name a few).

There has long been a need for mathematical models that reflect the market more accurately. Should the new models be in form of incremental modifications of existing models or should they be based on an overhaul of the foundation as Mandelbrot proposes? Be prepared to be challenged, if not altogether persuaded, by Mandelbrot's arguments.

The author renders a brilliant critique of modern finance theory. He criticizes all its components, including CAPM, the Efficient Market Hypothesis, and the Black Scholes model as being flawed. All these theories rely on two main assumptions. The first one is that market prices are normally distributed. The author, using price charts, demonstrates that market prices do not follow a normal distribution; but instead a Cauchy distribution. Such a distribution is associated with fatter tails. This means that catastrophic drop in market prices happen more frequently than a normal distribution suggests. The second assumption of modern finance is that market prices are independent of each other. Yesterday's prices have no influence on today's. The author makes a case that even if prices are not correlated, their volatility is correlated over time. Thus, big price swings tend to cluster. If a stock moved by 10% yesterday, it is likely it will move by an above average amount today even if we don't know the direction of that change. He calls this correlation of volatility (instead of price) long-term dependence.

Because the two main assumptions of modern finance are flawed, all related models are flawed as they understate risk. If such models understate risk, they actually overprice stocks and underprice options, and also understate the capital financial institutions should hold to withstand market risk.

If the author had stopped there, I would have given him a 5 rating. However, such a rebuttal of finance theory would make no more than a great essay. Instead, he attempts to build an entirely different edifice of modern finance over 300 pages. And, his theoretical foundation lacks any robustness. That's why I call it a castle of cards.

Mandelbrot builds his edifice of modern finance on two new parameters that would replace the mean return and volatility of return or standard deviation (mean and standard deviation being the parameters defining a normal distribution). His first parameter is Alpha, derived from Pareto's Law, is an exponent that measures how wildly prices vary. It defines how fat the tails of the price change curve are. The second one, the H Coefficient, borrowed from a hydrologist named Hurst, is an exponent that measures the dependence of price changes upon past changes.

Well, what is wrong with these two measures? He confesses at the end of the book that no two individuals calculate the same Alpha and H Coefficient when using the exact same historical data! Apparently, there is no one established way to calculate these two parameters. The divergence between the various methodologies can be huge. Using one method, you could derive Alpha and H coefficients that suggest a stock is not risky, using another method you would reach the opposite conclusion. So, after reading nearly 300 pages of intense theories you get that their own foundations are at this stage nonexistent. If Alpha and H are mathematically not replicable and well defined, you can't apply his multifractal geometry model in any meaningful way.

It will be up to someone else to build upon Mandelbrot's work and render it applicable to investment management by firming up the algorithms to calculate Alpha and the H Coefficient. Only then, will fractal geometry maybe turn out into a feasible challenge to the foundation of Modern Finance. But, at this stage contrary to what Mandelbrot pretends, it is not.

If you are interested in investment and finance theory, I strongly recommend other books such as: Robert Shiller's "Irrational Exuberance" and "Market Volatility." Also, Nicholas Taleb's "Fooled by Randomness" is very good. Also, Roger Lowenstein's "When Genius Failed: The Rise and Fall of Long Term Capital Management." This last book is a fascinating account of why a hedge fund failed because it relied excessively on the normal distribution, and used time series that were way too short when building its pricing models.

A few months ago, I found almost casually an editorial by Nassim Nicholas Taleb, introducing this essay by Benoit Mandelbrot (you can find it on Wilmot Magazine,2005 pag.50-59 - downloadable from his webpage)
As most readers, I vaguely knew about Mandelbrot and his studies on fractal geometry - but simply it was not my peculiar field of interest, so when I saw the ad of his new book, it went ignored.
*
Taleb's editorial aroused my curiosity.
He was stressing the significance of this essay in challenging the current orthodoxies on finance and in recommending new tools for risk management.
*
In a sense Taleb's recommendation represents a guarantee.
He is a famous edge fund manager and the author of "Fooled by Randomness - The hidden role of chance in the Markets and in life", a book that impressed me with the wide culture, multi-disciplinary approach and the sheer acumen.
*
"The (mis)Behavior of the Market" was up to my expectations.
The book is interesting, and not just for the economic views it advances. Mandelbrot is extremely learned - not just in his field of expertise - and his approach is challenging while retaining great plainness of exposition.
*
The book is organized in three parts.
The first part deals with the old theories of finance and with the state of the art, to show how all of the old tools are mostly inadequate to control investment risk and how they leave investors with a false sense of safety.
In the second part - the most specific and technical - Mandelbrot proposes his view of how the markets behave, suggesting a multi-fractal approach as a substitute for the random walk/efficient market theory.
The third part proposes some conclusion based both on Mandelbrot's views and common sense.
*
The first part is probably the most interesting and also the most cogent.
Modern orthodoxy of finance (Capital Asset Pricing Model or CAPM) is based on the shaky assumption that financial phenomena can be described according to a Gaussian normal distribution, that is they claim to be able to eliminate the possibility of extreme un-forecasted events with a 99 percent probability and to indicate for each level of risk an efficient portfolio maximizing return.
Mandelbrot demonstrates rather conclusively that Gaussian normal distribution of financial prices has been subject to oversimplification to make the data fit in the model, because of "fat tails", concentration and extreme events.
This means that CAPM is useful only when there is less need of it - that is when markets are calm, while is of no utility with extreme events.
Exposing weaknesses in the orthodoxy is not an intellectual pastime, since everyone can still remember the crash of 1987, the many financial crises from 1992 (the disruption of the European exchange rate mechanism, the crises of Mexico, South East Asia, Russia, Argentina,...), the disaster of LTCM in 1998 (it employed 25 PhD and 2 Nobel medalist in economics for their works in finance) and lastly the financial crises after the buoyant markets and high tech bubbles of 2000.
*
By mismanagement and ignorance great fortunes are created but many more are wasted, so the need of a new more efficient tools is imperative.
*
The second part is much more specific and technical.
It explains Mandelbrot's multi-fractal approach, but is still a series of proposals for further inquiries, more than a comprehensive theory of market behavior.
*
In this second part, I sensed some minor inconsistencies, but since I'm not a mathematician and even less a scientist, I can be - and probably am - mistaken.
*
Mandelbrot seems to overlook that finance, unlike natural phenomena, is subject to a very specific epistemological problem. A theory of market behavior - if widely used - can cause alteration in that same behavior previously described and now forecasted (it happened - for example - in 1987 with portfolio insurance strategies and again with the January effect, that disappeared once it was discovered).
*
A relevant problem is also the interpretation of the financial data. His analysis of the prices of cotton over more than a hundred years is using raw data, apparently without taking any consideration for the underlying changes in production, distribution, commerce and use of financial instruments (options and futures). This is even more complex for stocks, since we have different markets, different regulation and different economic situations.
*
While in the first part Mandelbrot cites studies indicating that shares with low p/e and low p/b have shown higher returns over long time-spans, in the second part he declares that returns appear to be independent from time spans. Now this is a classic case of either .. or...
*
Also rejection of the concept of value ("In financial markets, the idea of "value" has limited value") in part three can be misleading.
True, volatility may be high and prices may be swinging wildly, but none the less a theory refusing to guess a fair value based on conservative estimates, can be extremely dangerous.
*
Previous remarks converge on the main weakness of the essay: pretension to describe financial phenomena ex post, that is to find an elegant mathematical model that easily explains the "(mis)behavior", with scarce attention to the underlying causes.
But if underlying causal events should be working no more, we can theoretically believe also effects will be different and we will be left with a new obsolete theory of market efficiency.
*
The third part is rather average.
There are chapters with sensible advice ("markets are turbulent", "more risky than the standard theories imagine ", "market timing matters greatly" ... and so on)
Chapter XIII is a rather gratuitous ad to financial wizards who are said to be using multi-fractal models. No proof is given of this instance - since most of these models are reputedly secret - and sincerely I cannot understand the relevance to mention them in the essay.
*
Because of my work and personal curiosity, I'm fascinated by financial risk and risk management.
If you happen to be fond of these themes, you may be interested in other works I chanced to read about the same topic:
"Against the Gods" by Peter Bernstein - very entertaining history of the human struggle in confronting chaos and randomness. He is also the author of "Capital Ideas. The Improbable Origins of Modern Wall Street".
"Fooled by Randomness - The hidden role of chance in the Markets and in life" by Nassim Nicholas Taleb, one of the most interesting essay on these argument.
"Randomness" by Deborah J. Bennett -intelligent small book whose thesis is that human mind has not evolved to cope instinctively with probability: the same market volatility could be ascribed to this evolutionary incapacity. She is also the author of an other small book - with a rather repugnant title: "Logic Made Easy", that is a serious and fascinating excursus in the history of Logics and an attempt to analyze how the mind works.
"Irrational Exuberance" by Robert Shiller. One of the best books published in the last years: behavioral finance is not of my taste, yet the first 50 pages (a good example of sensible fundamental analysis written before the great bust of the year 2000) are well worth many times the book price.
"The intelligent Investor" by Benjamin Graham. This is an evergreen. I insert it here because of his interesting remarks about variation of share-prices and return of shares during his long life.
"A Random Walk down Wall Street" by Burton J. Malkiel - probably the best non academic introduction to financial theories on the market.
*
You are most welcome if you can suggest other books about the same theme or just share ideas and comments!
Thanks for reading.