The Motley Fool Discussion Boards

Previous Page

Investing/Strategies / Retirement Investing


Subject:  Re: RFO (Request for Opinions) Date:  11/28/2004  2:37 PM
Author:  rkmacdonald Number:  43326 of 75335

joelxwil wrote:
Bernstien and Malkiel have written books based on a very faulty perception of the market, and bad mathematics.

This is NOT true.

Stocks do not vary according to a random walk, nor do they behave according to a normal distribution.

This IS true. However the difference is very very minimal, and simply not big enough to base any type of successful trading strategy.

For some sound mathematics, see Mandelbrot's "The (Mis)Behavior of the Markets". Unfortunately, this book will not tell you how to trade, but it does completely debunk the other stuff.

As a former electrical engineer focusing on communications theory, I have read many of Mandelbrot's works on fractal geometry. Nothing in his book about the market should surprise anyone who has been around the market for an extended period of time. Nothing he says 'debunks' any of the investing principles put forth by Bernstein or Malkiel.

The fact is that the disturbances to traditional statistical methods that Mendelbrot has described, are so minimal that they do not contribute statistical significance to any of the movements in a properly diversified portfolio.

In fact, the effects noted by Mendelbrot have been descibed in a different way by Malkiel and others by what is called the Weak Form of the Efficient Maret Hypothesis. In this hypothesis, it states that for short periods of time, the market is NOT efficient, and therefore does not conform to standard statistical methods. However, this period is so short that there is no way to capitalize on it in any kind of trading system.

This effect that Mendelgrot has described in terms of fractal geometries has been studied by statisticians for decades. Please read my post from 12/16/00 on the Foolish Four Board, at

Here is part of it (for those of you who are not mathemeticians, skip down to the last sentence where I summarize the implications):

"OK. I will get into a little of it, but the limitations of a regular keyboard make mathmematical discussions painful and hard to understand.

You are partially correct about my personal experience with probabilitic issues. However, almost all the stochastic processes we use in control and communication engineering are constructed to have some sort of stationarity. For others who may be reading this, stationarity can be pictured intuitively as the absence of any drift in the ensemble of member functions as a whole. More to the point, the past history of a stationary stochastic process can be used to predict the future of the process in a probabilitic sense. This speaks to the very heart of this stock market discussion.

There are actually three main flavors of stationarity. Assume a stochasatic process

[X(.,t);t member set gamma]

It is called first order stationary if:

Fx(z,t1)=Fx(z,t2) for all (t1,t2) and all real numbers z.

Similarly, wide sense or second order stationarity (also sometimes called covariance stationary) is described:


for all (z1,z2) and all allowable (t1,t2,tau)

Lastly, the one that I believe is most germaine to us in analyzing the stock market is strictly stationary as follows:


for all sets of real numbers (z1,z2,...,zn)

(this is very difficult to do, and I don't think this is a very good place to be discussing details of probability theory, so I think I stop here)

It is my contention that unless the market can be shown to be stochastic and strictly stationary, many tools used by the statistician are of questionable value.

However, it may be that the market is close enough in many situations that these tools would give a reasonable result."

This whole discussion is just another way of saying that the market doesn't exactly conform to normal statistical methods, just as Mendelbrot points out in his book, but it is close enough to allow the modern portfolio theory to work just fine.

Copyright 1996-2014 trademark and the "Fool" logo is a trademark of The Motley Fool, Inc. Contact Us