Individual US stock performance is not normally distributed.
James Owen Weatherall’s The Physics of Wall Street: A Brief History of Predicting the Unpredictable (Houghton Mifflin Harcourt, 2013) is an engrossing book. Even though I was familiar with many of the stories the author recounts, at no point was I tempted to skip a page. Coming from me, that’s high praise indeed.
In the first chapter Weatherall takes the reader on a journey from sixteenth- and seventeenth-century attempts at a systematic theory of probability (Cardano, de Méré, Pascal, and Fermat) through Bachelier’s 1900 dissertation, A Theory of Speculation. Bachelier is credited with having come up with the random walk model/efficient market hypothesis. Like many quants, he was ahead of his time. “In a just world, Bachelier would be to finance what Newton is to physics. But Bachelier’s life was a shambles, in large part because academia couldn’t countenance so original a thinker.” (p. 27)
It wasn’t until Maury Osborne’s 1959 paper entitled “Brownian Motion in the Stock Market,” similar in both topic (predicting stock prices) and solution to Bachelier’s thesis, that people began to understand that physics could make a substantial contribution to finance. By then, as Osborne said, “Physicists essentially could do no wrong.” (p. 28) Scientists were in demand in industry, research facilities, and government. Pre-The Graduate, think nylon and the Manhattan Project.
Osborne found that stock prices don’t follow a normal distribution as Bachelier had suggested; rather, the rate of return on a stock (the “average percentage by which the price changes each instant”) is normally distributed. “Since price and rate of return are related by a logarithm, Osborne’s model implies that prices should be log-normally distributed.” (more…)