The (Mis)Behavior of Markets

by Benoît B. Mandelbrot

Thus, Markowitz and others transformed investing from a game of stock tips and hunches to an engineering of means, variances, and “risk aversion” indices. In fact, the term “financial engineering” has been popular on Wall Street ever since. There were problems, of course. First, as Markowitz himself pointed out, it is not certain that using the bell curve is the best way to measure stock-market risk; it is easy, but not necessarily right. Second, to build efficient portfolios you need good forecasts of earnings, share prices, and volatility for thousands of stocks. Otherwise, garbage in, garbage out. Finally, for each stock, you must laboriously calculate its “covariance” with, or how it fluctuates against, every other stock. For a thirty-stock portfolio, about the minimum needed to make the numbers work well, that means 495 different calculations of mean, variance, and covariance.