The Misbehavior of Markets: A Fractal View of Financial Turbulence annotated edition Edition

Great book (albeit incomplete if you're looking for definitive answers) that discusses the shortcomings of risk assessments for financial products and portfolios. As others have said, the author has posed several questions regarding the validity of financial practitioners' existing tools in corporate finance (valuation), options, and portfolio theory. One answer: multifractal theory; which the author posits could be the foundation for the next class of financial economists (best case).

My key takeaway from this book is that market participants' tools underassess risk and thus market participants should be wary of becoming model-dependent.

Additionally, supporting research and proofs are in the appendix or on the book's designated website for the more curious readers.

Mandelbrot sets out to demolish most of the theoretical bases of financial theory that led to several of the financial crises in the last several decades, foremost of which is that the random motions in prices of commodities and stocks can be assumed to be normally distributed. This sounds like an esoteric sort of argument, but anyone who wishes to win in any game of chance must have some solid notion of how to deal with risk. If one uses the standard model employing the normal (Gaussian) distribution, one will always underestimate the probability of rare events. This can lead to ruin, sometimes on a small scale. As an example, Mandelbrot talks about the rise and fall of the mother of all hedge funds - Long Term Capital Management which took a measly $3.6 billion bailout in the late 1990's because it underestimated risk. But it can happen on a much larger scale as in the crash of 2008 when many large financial institutions in the US held leveraged positions in mortgage security debt instruments. Long story short, everyone underestimated the risk of the unexpected happening, and it nearly crashed western civilization. The cost of that mistake will be measured in the $trillions.

Mandelbrot goes through the models that set up the whole thing: Bachelier, Sharpe, Black-Scholes, and standard portfolio theory. He briefly discusses their power. It's a great, if somewhat sketchy overview of what tools financiers and bankers often use. But in each case, lurking in the background are the assumptions of normality in price movements, and of statistical independence between time periods and between different asset classes.

There is no question that Mandelbrot proves that cotton price fluctuations are badly described by the normal distribution. The quantitative and qualitative information he brings to other asset classes is much less robust. He gives us very good arguments as to why other classes behave as does cotton; but It is hard to say that he brings the same level of quantitative rigor to these. For those of us who want the argument to end with everyone believing the fractal story, it's a bit of a disappointment. What he does do, though, is to describe the Cauchy distribution function which, with some slight generalizations can produce distribution functions that will accurately characterize time series price data whose variation obeys power-laws in the tails of the distribution. The upshot is that anyone with a solid understanding of college level statistics could go on to derive their own Black-Scholes formula.

His publisher appears to have set two rules: 1) no math of any sort in the body of the book, and 2) only simple algebraic equations in the notes. These prohibitions have several consequences. One is that the book is quite readable to anyone, even someone who has not finished eighth grade algebra. A reader can get a vague sense for what Mandelbrot is saying without the math. The flip side is that people who have finished eighth grade algebra may find the arguments hand-wavy when they could be much more solid. Anyone who has a solid background in statistics is likely to be able to fill in the gaps much better, but they will find the arguments fall far short of the kind of proof that one would expect in a 300 page book written by a world-famous mathematician. The people who have studied Black-Scholes, understand its derivation, and use it everyday will likely want a little bit more data and a lot more math before they kill the beast that writes their paychecks. Specifically, they will want a replacement method, which Mandelbrot only hints at.

I found the text here to be a little bit discursive and somewhat repetitive. I often enjoyed his anecdotes, but I did find myself skipping paragraphs, pages, and even chapters. I bought the book knowing that markets have fractal behavior, and hoping to be able to make my own mathematical models based on information in this book. It did allow me to make the intuitive connection between power-law behavior and fractal behavior. And I believe the book has gotten me to the point where I can do all the steps required to price risk and characterize random motions in the prices of assets; although I think a six page monograph that admitted mathematical notation would have been more than sufficient.

Mandelbrot shows that modern finance has a problem.

He examines CAPM, MPT, and Black-Scholes and shows that these models have major issues, mainly rigid assumptions.

He then shows that fractals provide a more realistic approach.

Before reading this book, I have only heard about fractals. It is interesting that fractals can be used in finance.

However, as the other reviews suggest fractals have some issues as well (large subjectivity!).

Overall, the book is still a good read because Mandelbrot shows the issues in modern finance and tries to

suggest a better approach (fractals).

The author shows how modern financial theory underestimates risk in financial markets. Famous as "the father of fractal geometry," Mandelbrot is less well-known for his contributions to financial market theory. He is the tour de force behind Taleb's "Black Swan" writings.

"Misbehavior" is more of an introduction to fractal finance than a textbook about how to implement Mandelbrot's ideas into trading systems. Nevertheless, it provides a foundation and introduction to new methods that many may find useful, with enough detail to begin incorporating same into quantitative models. Other works by Mandelbrot go much deeper into the "how to" side of fractal finance.

Benoît (pronounced "ben-wah") Mandelbrot writes in a clear, conversational style. The text avoids mathematical formulas, using instead a combination of written descriptions and entertaining analogies to explain. Chapter notes in an appendix present the mathematical formulas behind his descriptions, along with further (clear, simple) explanations.

The book divides into three parts: The Old Way, The New Way, and The Way Ahead. The first part describes the history leading up to modern finance as still taught in most business schools. It describes contributions by key figures such as Louis Bachelier, Paul Samuelson, William Sharpe, Harry Markowitz, Myron Scholes, and Fischer Black. I found this summary quite interesting, a valuable lesson history. Although we learned MPT (modern portfolio theory) in my MBA finance classes, it's background and potential shortfalls were not addressed.

The second part steps back to examine the nature of markets (turbulent, not Gaussian), identify contradictions between observation and modern theory (extreme events way more common than predicted), and then develop a better, multi-fractal (i.e. scalable) view of finance. Here Mandelbrot excels. Illustrations ("cartoons") help get points across while entertaining analogies (e.g. "Noah, Joseph, and Market Bubbles") and a true story of engineering genius (H.E. Hurst's analysis of Nile River floods) lead to insight into market trends useful to trend-followers.

The third part looks to the future. It summarizes the previous material in "Ten Heresies of Finance" and points the way for future research.

Overall, I loved this book. Obviously, Nassim Nicholas Taleb did too ("...the first book in economics that spoke directly to me.") It contains valuable information for every investor, professional or amateur, experienced or novice. Rather than something for advanced-level traders, I think it is the first book for anyone interested in investing or trading. It will open your eyes like no other, and inject a dose of realism and humility about money and markets that otherwise might cost a lot more than this book's price.