A Mathematician Plays The Stock Market By John Allen Paulos

Everyone who invests their hard-earned money in the stock market should be concerned with the truth of falsity of the efficient market, random walk theory.

According to many financial academics who have studied the data, stocks and the stock market tend to move at random. All relevant information about a company or the economy as a whole is reflected in the current price. Buying the stock of just one company is akin to making a bet in a casino. You will win some, you will lose some. Eventually, the transaction costs of paying your broker will more than eat away at your profits.

Therefore, the best way to play the market is to buy a broad index fund such as the S&P 500. You will then profit as all stocks gradually go up due to the long term growth of the U.S. economy.

However, most people who risk their money in the stock market have never even heard of it. Many have heard of it but think it doesn't apply to them. Most people still pay brokers, read newsletters, and listen to investing shows on cable TV. That is, they still think they -- or somebody whose advice they listen to -- can "beat" the market.

As a mathematician, Paulos brings a trained math professional's viewpoint to the issue. But much of the value of this book comes from his experience as a stock investor who got totally sucked into losing a lot of money on one of the high tech/telecommunications giants of the late 1990s-2000 bull market, and which went bankrupt with the revelation of massive accounting fraud -- WorldCom (ticker symbol WCOM).

So Paulos illustrates a lot of common investor errors by using himself as a bad example. As WCOM's price went down, he kept buying. He bought on margin and, as the price continued to drop, met margin calls. He bought calls. He spent hours of his life in Internet discussion forums writing and reading posts about WorldCom.

So his errors inspired him to write this book examining the stock market and its behavior both from both his professional and personal experience. He makes informed speculation about the value of technical analysis and fundamental (or value) stock analysis. He gives the standard random walk theory explanations for why these techiques cannot in the long run make investors any more money than simply buying and holding index funds.

He gives the standard random walk explanation for investors such as Warren Buffett who have long records of beating the market -- they're simply coin tossers who happen to have a long record of flipping winning coins. If enough people flip coins, most will have average results but the laws of probability state that someone will flip an extremely large number of heads or tails.

This is true, but it seems awful funny that people such as Warren Buffett, Peter Lynch and others who have proven market-beating records are also people who work very hard at it.

It is a coincidence that the most famous coin-flipper of all, Warren Buffet, was a hard-working business person as a little kid? That he saved his money through his childhood, then studied investing as though his life depended on it and that he knows more about most companies than any 5 other stock analysts? That he reads more company balance sheets than most of us read emails?

My own explanation is this: the ability to pick winning stocks is part innate ability, part intelligence, part analytical ability, part the motivation to learn all you can, and so on. These abilities have a high, nonrandom correlation with the proven stock-picking records of those who possess these combinations of traits.

The traits plus motivation to pick winning stocks are randomly distributed through the population just as is intelligence. But only a few people have enough of these traits plus enough motivation plus enough opportunity (would Buffett have been quite so successful if he hadn't taken Benjamin Graham's class in college?) to beat the market. (Buffett not only took Graham's class, he was the only student Graham ever gave an A to).

Paulos explains how con artists can use Internet chat rooms to "pump and dump" and "short and distort" to defraud investors. They choose a thinly traded, penny stock company. They buy a lot of shares of it. Then they use a variety of logon names to spread rumors and talk about how great the company is and how the stock price is going to go to the moon, and so on. Once enough people have bought the stock to raise the price substantially, the con artists sell their shares at a nice profit. They can also do the same by short selling a company's stock and then talking it down in the Internet.

This book is not light reading. Sometimes he doesn't explain his math as well as I wanted. Be prepared to think a lot.

Toward the end of the book Paulos makes an interesting point regarding the possibility of buying stock that's been fraudulently misrepresented -- that doesn't change the odds. Think about this -- you've got to bet on a coin toss. You know the coin is biased, but you don't know whether it's rigged to come up heads or tails. Your odds of winning are still 50-50. Because you can pick either heads or tails and either heads or tails could be the coin's bias.

His point is that you can buy a stock or sell one short, and if there's some fraud involved, you don't know which way it's driving the stock.

That's an academic abstraction, in my opinion. In the real world, most people buy stock (or go long) rather than sell short. Plus, in the real world, if your brokerage records may be investigated it'd be a lot easier to say that you bought Microdotcom at 10 cents in hopes it would go up to 15 cents rather than have to explain why you sold Microdotcom short in hopes it would go down from 10 cents. I doubt many brokers would even allow you to sell short the type of very small company stocks that are subject to Internet frauds running down their stock prices.

Plus, since only a relatively few people in the country own shares of Microdotcom to begin with, you have to convince a sizable fraction of them to sell their shares. It'd be much easier to convince some of the vast millions who haven't yet bought that company to buy some of its shares.

So I am certain that many more investors are burned through being convinced by pump and dumpers to invest on the long side than are burned by short and distorters who convince them to sell short.

Also, the fraud associated with WorldCom, Enron, Tyco and other such companies has nothing to do with Internet cons. Executives who manipulate the stock prices of their own companies do so to make themselves wealthy with stock options. That rules out rigging the books to make the companies look less profitable.

(That form of double bookkeeping does exist, but primarily in sole proprietor and partnerships, where the owners want to reduce the taxes they must pay.)

So I feel positive that in the real world fraud burns investors on the long side much more than it does to the short. Therefore, stock price manipulation, whether done by con artists or by corporate executives, is much more likely to distort the "efficient" market price of a stock to the high side than to the low.

Paulos has a less accusatory attitude toward the fraudulent corporate executives than many writers. While he should accept responsibility for his own errors as an investor, and he made many, detecting the accounting deceit in fraudulent financial statements was impossible for him.

It's too bad Paulos doesn't consider the obvious solution: If he'd invested for income, he never would have bought WorldCom in the first place. That would have protected him from all the accounting fraud firms, because executives that are so busy ripping off the company and inflating the stock price to take advantage of stock options, don't want to pay out the company's profits as dividends to the company's mere shareholders.

Investing for income saves you from John Maynard Keynes's famous "beauty contest" analogy. Years ago, British newspapers ran beauty contests where they published pictures of many women (stocks), and readers could vote on who was most beautiful (buy those most likely to go up in price). However, the only voter to win was the one who best predicted the beauty contest winner. (You make money in the market by predicting that many other investors will buy a company's stock, thus raising the price.) Guess wrong about what other investors think about a stock, and it doesn't matter how "beautiful" the company is to you -- its price goes down and you lose money.

Boards of directors who value their shareholders enough to pay them dividends, are much less likely to be cooking the books. And even if they are, it can't be on such a grand scale, because they still have to pay out some real, hard cash. And even if the stock price does eventually go down, shareholders at least did collect dividends.

Not investing for dividends -- that was Paulos' biggest mistake as an investor, though he doesn't mention learning that lesson.