A Random Walk through Mandelbrot

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 dellightful 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 classifiying investment portfolios by their probability of risk. According to the theory, a fund manager can build an "efficient" porfolio 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.