"With such theories, economists developed a very elaborate toolkit for analyzing markets, measuring the "variance" and "betas" of different securitie… - Benoit Mandelbrot

When the weather changes and hurricanes hit, nobody believes that the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed. It's the same stock market with the same mechanisms and the same people.

"He focuses then, then, only on the odds for a crash-sharp, catastrophic price drops. After all, it is not small declines that wipe an investor out, it is the crashes. So their scaling formula minimizes the odds of too many of the assets in a portfolio crashing at the same time. They used that to draw a "generalized efficiency frontier"-analogous to Markowitz's original portfolio technique-to help pick a portfolio that maximizes returns for a given amount of crash-protection. As the paper put it, "the frequency of very large, unpleasant losses is minimized for a certain level of return."

Thus, it is not just the stock-picking that is important, but also the risk-protection. For the latter, Bouchaud says, multifractal thinking is most useful."

Just the opposite appears to happen in the medium term, three to eight years. A stock that was rising over one multi-year stretch has slightly greater odds of falling in the next. A 1988 study by Fama and another economist, Kenneth R. French, documented this. They looked back over the price records of hundreds of stocks and grouped them into portfolios based on their size. They found that about 10 percent of a stock's performance in one eight-year period-that is, there was a small but measurable tendency for a stock doing well in one decade to do poorly in the next. The effect was weaker, but still statistically significant, at shorter time-scales of three to five years. Others have corroborated such findings.