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Tags: Malkiel | Random | Sequence | Wall Street

A Not-So-Random Walk Down Wall Street

A Not-So-Random Walk Down Wall Street
 (Mopic / Dreamstime)

Richard Grigonis By Tuesday, 05 January 2016 04:39 PM EST Current | Bio | Archive

Let’s say that Yours truly asked you to write down a series of random numbers, from 0 to 9, without relying on some randomizing device. I guarantee you that the numbers you generate would not be random.

Why? First of all, there is the psychological urge to make all of the numbers different. A sequence such as 1, 5, 3, 7, 0, 6, 2, 9, 4, 3, 0, 8, 7, 6 appears to be random, but isn’t.

A true set of random numbers would include sequences or “runs” of similar numbers or groups of numbers. A sequence such as 7, 4, 7, 2, 2, 6, 2, 8, 8, 3, 6, though it contains repetitions of “2” and “8” is actually more random than the previous sequence.

If we generate many random numbers, we will eventually produce sequences with longer stretches of identical integers such as 6, 2, 5, 5, 5, 5, 3, 0, 1, 2, 8, 8, 8.

This has implications for investors in the financial markets.

Back in the 1970s, a computer experiment simulating stock market investors took place. A thousand “investors” were created in a computer program, and each made investments in randomly-selected stocks. It was the equivalent of the proverbial group of chimpanzees throwing darts at a stocks listing page.

After running the simulation for some hours based on real time series stock market prices, some of the “investors” did very well and some did very poorly — thanks to the “runs” phenomenon mentioned earlier.

The great majority of our simulated investors, of course, achieved varying, generally mediocre results somewhere in the middle.

Now, imagine you were to show these results to a group of financial experts without detailing the experiment. Whether experienced or not, unless these people did an analysis from the standpoint of probability and statistics, they would inevitably say that the winning “investors” were the most experienced and brilliant, and the “losers” were probably novices who obviously didn’t know what they were doing.

As programmer and stock market researcher Michael Harris has written, “…we are fooled by randomness into believing there is no randomness due to limited samples…”

Professor Burton Malkiel, author of the famous book, “A Random Walk Down Wall Street,” produced a “random walk” of prices for a fake stock generated from successive coin flips, then presented it to an expert in the “technical analysis” of stocks, a so-called “chartist” who spots alleged trend patterns.

The chartist told Malkiel the “stock” was a good buy. Malkiel used this as proof to equate the stock market with a coin-flipping contest (called the “random walk” hypothesis) and advocated that his investor readers employ a passive buy-and-hold investment strategy.

Interestingly, the idea of a random walk model for stock price changes goes back to an 1863 book by French stockbroker Jules Augustin Federic Regnault (1834–1894).

The random walk model leads logically to the so-called efficient-market hypothesis, which holds that market prices reflect all available information and prices can only move in response to news, which by definition is random.

Recently, however, I came across a fascinating September 2015 online article entitled, “Hacking the Random Walk Hypothesis” by Stuart Reid. Reid notes that both computer hackers and stock market traders are alike in that they find and exploit the weaknesses of their respective systems.

He explains how random number generators are used to encrypt data and how they must therefore be as random as possible. This is difficult because arithmetic methods of generating random numbers can only be pseudo-random, never truly random. (As mathematician John von Neumann said, “Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.”)

As an aside, one wonders if so-called random events are truly random. “Random” may simply be a convenient term we humans of limited intelligence apply to events whose regularities or laws of occurrence are as yet undiscovered because they are at the moment far beyond our comprehension.

For example, in this 1974 book, “The New Nonsense,” the late polymath Charles M. Fair wrote (p. 125): “...I devised a system by which, using a random number table and a set of complicated rules as to what integers should follow any randomly drawn one, I was able to generate a graph indistinguishable from one produced by a plot of random numbers only. A computer, properly programmed, could doubtless have detected the regularities hidden in my pseudo-random graph, if it only had a big enough sample to work with. Of course, the more complicated my selection rules, the bigger the sample would have to be.”

Indeed, if you believe in the concept of “hidden variables” in physics, as I do, then we live in a deterministic universe and no events in the world are truly random; they are instead pseudo-random events governed by rules so complicated that they merely appear random.

In any case, various statistical tests exist to check well-known pseudo-random number generators for the quality of their randomness, and Reid has applied them to the financial markets to see if he could, in theory, “hack the market.”

Two of Reid’s conclusions are quite stunning:
  • Not all markets are made equally “random.” Some markets, in particular the foreign exchange rate between the USD and GBP currencies and the S&P 500 Index, exhibit much lower levels of randomness than others such as the Hang Seng Index.
  • The markets’ apparent randomness, unlike a strong pseudo-random number generator, appear to be affected by the time dimension. In other words, certain “window sizes” cause markets to appear less random. This may indicate the presence of cyclical non-random behaviors in the markets.

Reid uncovers what he believes are flaws in the random walk hypothesis; especially that randomness is relative and in the presence of new or additional information (e.g. fundamental or economic data) the market’s apparent randomness may break down.

Reid points out that all this shouldn’t be too surprising, as there are firms and individuals  — such as the incomparable Warren Buffett — who consistently beat the market over decades, an impossible feat if the markets were indeed random walks.

So rejoice all ye stock market soothsayers, “quant shop” owners and astrologers. Breathe a sigh of relief. There is hope for at least some of our prognostications to actually be correct!

Richard Grigonis is an internationally known technology editor and writer. He was executive editor of Technology Management Corporation’s IP Communications Group of magazines from 2006 to 2009. The author of five books on computers and telecom, including the highly influential Computer Telephony Encyclopedia (2000), he was the chief technical editor of Harry Newton's Computer Telephony magazine (later retitled Communications Convergence after its acquisition by Miller Freeman/CMP Media) from its first year of operation in 1994 until 2003. Read more reports from Richard Grigonis — Click Here Now.


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Write down a series of random numbers, from 0 to 9, without resorting to using some randomizing device. I guarantee you that the numbers you generate would not be random.
Malkiel, Random, Sequence, Wall Street
Tuesday, 05 January 2016 04:39 PM
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