Characteristically, he did everything he could to acquaint people with Bachelier’s genius. Just as characteristically, Samuelson called Bachelier’s views “ridiculous.” Huh? Samuelson spotted a mistake in Bachelier’s work. Bachelier’s model had failed to consider that stock prices cannot fall below zero. Were stock price changes described by a conventional random walk, it would be possible for prices to wander below zero, ending up negative. That can’t happen in the real world. Investors are protected by limited liability. No matter what goes wrong with a company, the investors do not end up owing money. This spoiled Bachelier’s neat model. Samuelson found a simple fix. He suggested that each day, a stock’s price is multiplied by a random factor (like 98 or 105 percent) rather than increased or decreased by a random amount. A stock might, for instance, be just as likely to double in price as to halve in price over a certain time frame. This model, called a log-normal or geometric random walk, prevents stocks from taking on negative values.
