When Genius Failed: The Rise and Fall of Long-Term Capital Management

by Roger Lowenstein

Eugene Fama, Scholes’s thesis adviser, wondered what his old student was up to as well. Fama had all the admiration in the world for the option formula as a model. But trusting people’s money to such models was different. In the early 1960s, Fama had written his thesis on the price movements of the thirty Dow Jones Industrial Average stocks and discovered a remarkable pattern: for every stock, there were many more days of extreme price movements than would occur in a normal distribution. Fama’s stocks were like a world in which most people were average height but every twentieth person was either a giant or a dwarf. There were too many extreme readings, or “outliers,” that random distribution could not explain. As Fama put it: If the population of price changes is strictly normal, on the average for any stock . . . an observation more than five standard deviations from the mean should be observed about once every 7,000 years. In fact such observations seem to occur about once every three to four years.9 Graphically, Fama’s stocks depicted a bell curve with the ends swollen, representing too many incidents at the extremes (known as the “tails”).