Benoit Mandelbrot’s “The (Mis)behavior of Markets”

Mandelbrot’s book is both interesting and disturbing. Interesting because he not only takes the reader through the basic ideas behind the history/evolution of finance theory as practiced today, but also some of the stories of the people who were the originators of the ideas; disturbing, because he asserts (reminds us) that everything in modern finance is built on a foundation of sand; such as two of the assumptions which form the basis of current wisdom: markets are normal/Gaussian and price changes are statistically independent.

Mandelbrot, the father of fractals, was also the thesis advisor of Eugene Fama (not just one of the best known portfolio and market theorists but also practitioners; he is still research director at Dimensional Funds) and of more recent fame Nassim Taleb (author of Black Swan).

Mandelbrot states that while this book won’t make you rich, it will certainly make you look at the world in a new way (Certainly true!). He also leaves his readers with research recommendations. His recommendations for portfolio building include “stress testing”, performing “what-if scenarios” and use Monte Carlo simulation using fat-tail distributions. He argues the inappropriateness of using risk/volatility measures based on variance (or standard deviation). He also suggests more research on valuing options, since Black-Scholes option pricing is based on bell-curve, constant volatility assumption and the assumption that prices don’t jump. And finally, on managing risk, he states that Value-at-Risk measures are flawed and give us false security (as banks found out recently) and “there is no limit how bad it could get for the bank”; he recommends approaches based on “extreme value theory”.

Mandelbrot starts his book with a very readable history of finance/market theory and people who played a role its development. Some concepts discussed are Capital Asset Pricing Model (Sharpe), Modern Portfolio Theory (Markowitz), Option pricing (Black-Scholes), efficient market hypothesis (Fama), efficient portfolio (Sharpe) and riding the market with passive investing (Samuelson). But all is built on shaky/absurd assumptions like: people are rational and aim to get rich…all investors are alike…price changes are practically continuous…and that standard deviation is a good proxy for risk/volatility’. He (doesn’t pull punches and) suggests that current techniques are used not because they work but because “the math is easy”!

He suggests a new fractal and multi-fractal geometry” based approach to finance theory. I won’t try to explain how/why he thinks that fractals (which have “a special kind of invariance or symmetry that relates the whole to its parts”) are the path to improving finance theory and practice, as I won’t be able to do justice to it (this part of the book is less easy reading.). For analyzing investments he proposes the use of the H- exponent (“measuring the dependence of price changes upon past changes”) and alpha parameter (“exponent that measures how wildly prices vary”). Using fractals, adjusting the few key parameters in simple equations describing power-law behavior, Mandelbrot suggests that one can model (past) market behavior (cotton/stocks/natural phenomena). Unlike the bell-curve which is egalitarian (e.g. applicable to height of people), market behavior is not (e.g. more like a blind archer who could be off-mark by a great deal.)

Some other Mandelbrot observations:

-what matters is not the size of the variations but their precise sequence; future price is shaped by the past and it’s not always easy to determine how long the dependence lasts

-inflation is “persistent” …”once it starts, it is difficult to stop”

-this “persistence” applies to the memories of market participants; once those who lived through the 1929 market crash left the scene, the frequency of crashes increased dramatically (1987, 1997, 1998, 2001, 2008)

-if aliens arrived they may conclude that earth can be described using Bible analogies like Noah-effects (abrupt, rather than continuous, changes) and Joseph-effects (almost trends, like 7 fat years followed by 7 lean years); certainly not Gaussian/normal

-the prime mover in financial markets is not value or price, but price differences; “not averaging, but arbitraging” (between places and/or times)

-Mandelbrot also lists his ten heresies of finance:  (1) markets are turbulent, (2) markets are very, very risky, (3) market timing matters greatly (doesn’t mean one can do it well), (4) prices often leap, not glide, (5) in markets time is flexible, (6) markets in all ages and places work alike, (7) markets are inherently uncertain and bubbles are inevitable, (8) markets are deceptive, (9) forecasting prices may be perilous, but you can estimate the odds of future volatility, and (10) in financial markets the idea of “value” has limited value.

WOW, that sure puts a dent in the level of confidence that we can assign to our financial forecasting. As long as you keep in mind that his admonition that while this book won’t make you rich, it will certainly make you look at the world in a new way, then it can be an interesting read and a much needed reminder about the limitations of our current financial models.