The stock market is a highly tempting place these days. Fund managers and financial advisers report a growing number of calls from investors nervously wondering if it is time to start buying again. But before blowing the dust off your cheque book, it is worth listening to the cautionary tale of John Allen Paulos.
At the end of it, he said this week: "I learned the talking heads you see on television and read in the papers often don't know much of anything. How people with impressive credentials and extensive backgrounds could come to such diametrically opposed opinions on stocks or the market in general and not be fazed by the differences is beyond me."
Professor Paulos is professor of mathematics at Temple University, Philadelphia, and adjunct professor of journalism at Columbia University, New York. A frequent guest on TV chat shows, he has written several books and scholarly papers on probability, logic, and the philosophy of science and articles in The New York Times, Wall Street Journal, Forbes, The Nation and the London Review of Books.
But he fell into the trap of thinking his formidable intellectual armoury would be more than enough to conquer the vagaries of the stock market.
How wrong he was. He has published a breathtakingly honest account of how he got suckered into one of the biggest scandals of the past decade: WorldCom, the US phone company that went so spectacularly bust and filed for bank-ruptcy last year. It lost $180bn (£110bn), leaving its shares worthless. It is now called MCI.
A Mathematician Plays the Market (Penguin £12.99) is, says Professor Paulos, "The story of my disastrous love affair with WorldCom, how I lost my shirt (or at least had my sleeves shortened)." Early in 2000, when the dot.com mania was at its height, Professor Paulos came into a windfall. So he thought he could consign it to a basket which was, he admits, "more vulnerable to whim".
Perhaps that made him less rigorous than he might have been about how he invested. As he says: "The psychological ease with which such funds tend to be spent was no doubt a factor in my using the expected money to buy shares of WorldCom". They claimed to be the pre-eminent global communications company for the digital generation. He paid $47 a share: In 1999, they were $64.
The flamboyant Bernie Ebbers, a former milkman, founded WorldCom. He shunned Wall Street to stride around his ranch in cowboy boots and Stetson, and turned WorldCom into one of the world's biggest long-distance telecoms carriers through more than 75 takeovers. He persuaded most buyers to accept WorldCom shares. These deals left WorldCom saddled with $30bn of debt, a crippling burden as the dot.com boom imploded. Mr Ebbers resigned in April last year amid investigations into his personal finances.
A report by US lawyers for the new management says dozens of employees helped WorldCom inflate reported revenue improperly to prevent it missing financial targets, which would have hurt its share price. The US authorities have spent 12 months trying to establish where the blame lies. Professor Paulos says: "Today, WorldCom is synonymous with fraud, but in the halcyon late 1990s it seemed an irrepressibly successful devourer of hi-tech telecommunications companies. Bernie Ebbers is now viewed by many as a pirate, but then he was a swashbuckler."
Wall Street's analysts were singing WorldCom's praises; it owned the giant MCI long-distance phone company, and the then dominant internet player, UUNet. It had 25 million customers and annual revenues of $25bn. Professor Paulos was hooked. Having bought a few WorldCom shares, his mathematical logic told him it would be even better to buy more, chasing the price up. All shareholders will recognise the feeling. "I was falling disastrously in love," Professor Paulos says. His mania extended to finding out everything he could about the stock market. Business television talk-shows became his daily diet. Trying to predict the market became an obsession.
But Professor Paulos found that to his mathematical concepts of portfolio theory, efficient market hypotheses, bell curves and other paraphernalia, he had to add the great intangible: market psychology. Because he discovered a terrible truth: it does not matter whether you have made a right or wrong judgement. All that matters is whether other investors think you are right or wrong by buying or selling after you bought.
By late summer 2000, WorldCom shares were $30. Just as Professor Paulos had bought more when the price rose, now he used reverse psychology. The shares were cheaper, so it made sense to buy more. He says: "My purchases were not rational. By this I don't mean there wasn't a rational basis for investing in WorldCom stock. my reasons owed less to an assessment of trends in telecommunications or an analysis of company fundamentals than to an unsuspected gambling instinct and a need to be right. I searched for the good news, angles and analyses about the stock, while avoiding the less sanguine indications."
By April last year, when the WorldCom price fell below $5, Professor Paulos persuaded himself it was worth buying to bring down his average price. Then, just as in human love affairs, his faith snapped. He says: "I did firmly and definitively resolve to sell. By Friday, 19 April, [the price] had risen to over $7, which would have allowed me to recoup at least a small portion of my losses."
But a business trip delayed Professor Paulos putting through the sell order. He had to wait until Monday, when it fell by a third. He got out just before the final collapse. "After selling, I felt as if I were gradually and groggily coming out of a self-induced trance," he says. "I'd long known about one of the earliest 'stock' hysterias, the 17th-century tulip-bulb craze in Holland. I smiled ruefully at my smug dismissal of people like the tulip-bulb 'investors'. I was as vulnerable to transient delirium as the dimmest bulb-buying bulbs."
Professor Paulos dismisses share-price charts and fundamental analysis of a company's trading figures and annual accounts. He knows now that narratives and numbers coexist uneasily on Wall Street and other stock markets. He says: "Markets, like people, are largely rational beasts occasionally provoked and disturbed by their underlying animal spirits. The basis for the application of mathematical tools is the sometimes shifty and always shifting attitudes of investors. Since these psychological states are to a large extent imponderable, anything that depends on them is less exact than it appears. But, despite rancid beasts like WorldCom, I'm still rather fond of the pageant that is the market."
THE WISDOM OF JOHN ALLEN PAULOS
* There is a huge element of chance in the stock market.
* Compound interest is the root of all money.
* Don't put all your eggs in one basket.
* Work out what is hype and what is fact, and don't succumb to the hype.
* Insure against sudden price falls with put options.
* Don't buy on margin (by borrowing).
* Work out a strategy and stick to it. Don't change your mind as you go along, or you will just keep buying or - even worse - buying and selling the same share.
* With care, you can minimise the risk of a portfolio without hurting its expected rate of return.
* Diversification is something we do naturally in dealing with the inevitable trade-offs in our daily lives. But there are situations where bulleting one's efforts is preferable to bland diversification.
* There is no guarantee stocks will continue to outperform bonds.
* Viewed as less risky, stocks become more risky because their price rises; viewed as risky, they become less risky because their price falls.
* We tend to gravitate towards people whose view of a share is the same as our own, to confirm our opinion;
* Don't believe all you are told: your source may have a hidden agenda.
* An attempt to cover up a scandal often results in a much worse scandal.
* Many cases of insider trading and stock manipulation result in the miscreant guessing wrong about how the market will respond to his illegal actions.
* Even when the market is "wrong", it is always right: don't fight it.