Reprint: One of My Favorite Nonfiction Titles

Mandelbrot is one of my great heroes--not for the book that I treat below, but for his amazing contribution to the understanding of fractals.  But the book reviewed below is worth a read for anyone interested in understanding chaotic dynamics and one view of the stock market.
When I was doing my graduate work, I hated most statistics. Most particularly I hated "random walk" models and "monte-carlo simulations." Whenever there was an anomalous blip that could not be readily explained, someone trotted out these hoary old creatures and set them to dancing.
How delightful then to chance upon this:
from The (Mis)Behavior of Markets
Benoit Mandlebrot and Richard L. Hudson

With such theories [Bachelier's Analysis, Gaussian Curves (Bell-Curves), and Random Walks] , economists developed a very elaborate toolkit to analyzing markets, measuring the "variance" and "betas" of different securities and classifying investment portfolios by their probability of risk. According to the theory, a fund manager can build an "efficient" portfolio to target a specific return, with a desired level of risk. It is the financial equivalent of alchemy. Want to earn more without risking too much more? Use the modern finance toolkit to alter the mix of volatile and stable stocks, or to change the ratio of stocks, bonds, and cash. Want to reward employees more without paying more? Use the tollkit to devise an employee stock-option program,with a tunable probability that the option grants will be "in the money." Indeed, the Internet bubble, fueled in part by lavish executive stock options, may not have happened without Bachelier and his heirs.
Alas, the theory is elegant but flawed, as anyone who lived through the booms and busts of the 1990s can now see. The old financial orthodoxy was founded on two critical assuptions in Bachelier's key model: Price changes are statistically independent, and they are normally distributed. The facts, as I vehemently argued in the 1960s and many economists now acknowledge, show otherwise.
The financial equivalent of Alchemy! Now there's a delight. I'll be the first to admit that I understand almost nothing of the stock market and its workings. What's more, life is too short, I don't plan to spend a lot of time learning more--I have far more essential things to be spending time with. However, my general theory of statistics and most statistical approaches was shaped, in part by my advisor, who quoting some source, now lost to memory, used to say, "A scientist uses statistics as a drunk uses a lamppost--for support, not illumination."

Yeah. Well, he had a higher opinion of most statistical work than I do. Once I discovered that you could manipulate your statistics by running non-parametrics, I realized that you could indeed make black into white. Didn't like the graphing in eigenspace try canonical cross-correlation, or better yet, run a rank variable analysis and then use a nonparametric correlation technique. I could run the information from my fossil sites through the number cruncher and come up with any environmental model you wanted. Want to prove that there was a gigantic four-hundred mile-an-hour hurricane that lasted most of the Permian Period? Just dump that paleocurrent data you derived from bryozoan analysis into the magic black box and turn the crank. You'd be amazed at what could spill out.

So, I will long cherish the trenchant analysis--"The financial equivalent of alchemy." Oh well, perhaps it's one of those things that you have to have been there.

Following on the previous post (my enthusiasm for this book bubbles over) this bit of analysis:
from The (Mis)Behavior of Markets
Benoit Mandelbrot and Richard L. Hudson

Second, contrary to orthodoxy, price changes are very far from following the bell curve. If they did, you should be able to run any market's price records through a computer, analyze the changes and watch them fall into the approximate "normality" assumed by Bachelier's random walk. They should cluster about the mean, or average, of no change. In fact, the bell curve fits reality very poorly. From 1916 to 2003, the daily index movements of the Dow Jones Industrial Average do not spread out on graph paper like a simple bell curve. The far edges flare too high: too many big changes. Theory suggests that over time there should be fifty-eight days when the Dow moved more than 3.4 percent; in fact, there were 1,001. Theory predicts six days of index swings beyond 4.5 percent; in fact, there were 366. And index swings of more than 7 percent should come once every 300,000 years; in fact, the twentieth century saw forty-eight such days. Truly a calamitous era that insists on flaunting all predictions. Or, perhaps, our assumptions are wrong.
The (Mis)Behavior of Markets
You have seen sufficient excerpts of this book on and off at this blog, so that I need say little more about it except to emphasize how very accessible and interesting this whole study is. Mandelbrot is attempting to define a new science of economics and the stock market and admits that he is far from being there; however, the problems he unearths are significant and should give pause to those who argue loudly (and at length) about the privatization of Social Security. The risks involved in even the most conservative stock/bond/cash portfolio far outweigh the perceived advantages until there is a better way of managing risk.

That is largely what the book is about--how does the market really run and how can you best assemble investments to minimize risk and maximize profits. In the process of this discuss Mandelbrot touches on invariant and scalable phenomena in markets, in language, and in the annual flooding of the Nile. That so many disparate phenomena can be looked at through multifractals and brownian motion is interesting in itself. That the common practice of Monte Carlo simulation based on Gaussian rather than Cauchy distributions is a dangerous misstep is made evident throughout.

The main difference between the simple bell curve (Gaussian) and the Cauchy curve is that in a bell-curve an additional bundle of data will not particularly disturb a heavily weighted center. That is, if enough data has been collected, then additional data will not appreciably affect the "center of gravity" of the curve. Large outliers will not affect averages.

With the Cauchy curve it is these large outliers that define the essence of the curve. It is a better measure of rapidly fluctuating environments with inherent turbulence (at least so Mandelbrot implies, and I certainly am not one with the least ability to naysay). As a result, additional data added to the Cauchy distribution will result in significant differences in the measures of central tendency.

Another interesting idea uncovered by Mandelbrot is that it is not only the fluctuations in prices that are important, but also the order in which they occur. And this extends to the study of floods on rivers as well. He pointed out that if the data is entered randomly and stirred together, you end up with a nice well-behaved bell curve distribution. But if the data are analyzed in order, what you find instead are a series of parallel curves that reveal a scalability in the phenomenon that is otherwise invisible.

Mandelbrot argues that as long as outdated means are used to evaluate the market, events like October 1987, and the entire year of 2001, but particularly 9/11 (we're speaking here only of market effects) are inevitable. Bubbles will arise and burst based on old means of buying, holding, and selling stocks. Portfolios will continue to experience rapid fluctuations, even based on very conservative, very deliberate buying and selling. Anyone who went through 2001 realizes what this can mean in a very, very short time.

Mandelbrot's book is required reading for all of those who will propose a means whereby social security will be partially privatized. It is recommended reading for everyone else. Despite Mandelbrot's annoying, but slight, tendency toward focusing the spotlight on himself, the book is quite good. It is one of those eye-opening works where many phenomena of the natural world are brought together and part of the pattern underlying them revealed.



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