Capital Ideas: The Improbable Origins Of Modern Wall Street

Are Stock Prices Predictable?

It is doubtful.

Paul Samuelson, economist and Nobel laureate, once remarked that it is not easy to get rich in Las Vegas, at Churchill Downs, or at the local Merrill Lynch office. All investors, professionals as well as amateurs, acknowledge the truth of this observation. Even smart people have a hard time getting rich by predicting stock prices.

Some people never try to outguess the market: they simply hang on to the stocks they inherited, bought long ago, or acquired in some employer-sponsored savings program. Others buy and hold under the conviction that trading finances yachts only for brokers, not for customers.

Yet, in the face of admittedly high odds, enough people do try to predict stock prices to keep an entire industry humming. The demand for the wisdom produced by armies of security analysts, portfolio managers, television pundits, software peddlers, and newspaper columnists shows no sign of waning. Some of the wealthiest people on Wall Street are professionals whose bank accounts have been inflated by a constant flow of investment advisory fees. I have already pointed out that the number of investment management organizations tripled just during the 1980s. Forbes, Barron's, and The Wall Street Journal have subscribers that number in the millions. Index funds, which hold a diversified cross-section of the market and never sell one stock in order to buy another, account for less than 15 percent of all equity portfolios.

This appetite for predicting stock prices is all the more striking, because a huge volume of academic research demonstrates that it is a devilishly difficult job not likelyto get any easier. While no one goes so far as to say that it is impossible to make good predictions or that all predictions are destined to be wrong, the abundant: evidence and the robust character of the theories that explain the evidence confirm that the task of predicting stock prices is formidable by any measure.

The exploration into whether investors can successfully forecast stock prices has roots that reach all the way back to 1900, when Louis Bachelier, a young French mathematician, completed his dissertation for the degree of Doctor of Mathematical Sciences at the Sorbonne. The title of the dissertation was "The Theory of Speculation." This extraordinary piece of work, some seventy pages long, was the first effort ever to employ theory, including mathematical techniques, to explain why the stock market behaves as it does. Bachelier supported his novel theoretical analysis with a sophisticated study of the French capital markets at the turn of the century.

It is worth noting that Bachelier was an academic all the way. He employed his profound understanding of the markets for his intellectual exercise: we have no evidence that he ever speculated or invested in the markets he was analyzing. He set the style for many later theorists who, like him, refrained from putting their money where their minds were.

Bachelier was far ahead of his time. Paul Cootner, one of the leading finance scholars of the 1960s, once delivered this accolade: "So outstanding is his work that we can say that the study of speculative prices has its moment of glory at its moment of conception."

Bachelier laid the groundwork on which later mathematicians constructed a full-fledged theory of probability. He derived a formula that anticipated Einstein's research into the behavior of particles subject to random shocks in space. And he developed the now universally used concept of stochastic processes, the analysis of random movements among statistical variables. Moreover, he made the first theoretical attempt to value such financial instruments as options and futures, which had active markets even in 1900. And he did all this in an effort to explain why prices in capital markets are impossible to predict!

Bachelier's opening paragraphs contain observations about "fluctuations on the Exchange" that could have been written today. He recognizes that market movements are difficult to explain, even after the fact, and that they often generate a self-reinforcing momentum:

Past, present, and even discounted future events are reflected in market price, but often show no apparent relation to price changes....[A]rtificial causes also intervene: the Exchange reacts on itself, and the current fluctuation is a function, not only of the previous fluctuations, but also of the current state. The determination of these fluctuations depends on an infinite number of factors; it is, therefore, impossible to aspire to mathematical predictions of it....[T]he dynamics of the Exchange will never be an exact science.

Despite these demurrers, Bachelier sets himself an ambitious goal: to offer "a formula which expresses the likelihood of a market fluctuation" -- that is, a move upward or downward in stock prices. Recognizing that fluctuations over time are virtually impossible to interpret, he begins by concentrating on the market at a given instant, promising to establish "the law of probability of price changes consistent with the market at that instant. This approach leads him into more profound investigations: the theory of probability and the analysis of particles in space subject to random shocks.

In view of the originality and brilliance of Bachelier's analysis of financial markets, we might expect him to have been a man of stature in his own time. It is easy to picture him as an inspiring professor at the Sorbonne, or perhaps lured from France to Harvard or Oxford. We can note his large following of students, who, having gleaned so much wisdom, will go on to make their own mark in the study of finance, uncertainty, and random behavior. Or perhaps we can visualize him as a fabulously successful investor, a forerunner of Keynes, combining financial acumen with theoretical innovation.

The truth is far different. Bachelier was a frustrated unknown in his own time. When he presented his dissertation to the committee at the Sorbonne, they awarded it merely "mention honorable," a notch below the "mention très honorable" that was essential for anyone hoping to find a job in the academic world. It was long time before Bachelier finally won an appointment, and even then it was only at the provincial university at Besancon. Besancon is about as provincial as provincial France can get.

Some of the difficulty seems to have stemmed from a mathematical error in a paper he published in 1913 -- a slip that haunted him for many years. As late as 1929, when he applied for a position at the University at Geneva, a Professor Gevrey was still scandalized by the error, and, after consulting Paul Lévy, another expert in the field, Gevry had Bachelier blackballed from the University. Lévy later recognized the value of Bachelier's pioneering work, and the two became reconciled.

Bachelier's real problem, however, was that he had chosen an odd topic for his dissertation. He was convinced that the financial markets were a rich source of data for mathematicians and students of probability. Twenty years after writing his dissertation, he remarked that his analysis had embodied "images taken from natural phenomena...a strange and unexpected linkage and a starting point for great progress." His superiors did not agree. Although Poincaré, his teacher, wrote that "M. Bachelier has evidenced an original and precise mind," he also observed that "The topic is somewhat remote from those our candidates are in the habit of treating."

Benoit Mandelbrot, the pioneer of fractal geometry and one of Bachelier's great admirers, recently suggested that no one knew where to pigeonhole Bachelier's findings. There was no ready means to retrieve them, assuming that someone wanted to. Sixty years were to pass before anyone