The whole edifice of modern financial theory is, as described earlier, founded on a few simplifying assumptions. It presumes that homo economicus is rational and self-interested. Wrong, suggests the experience of the irrational, mob-psychology bubble and burst of the 1990s. A further assumption: that price variations follow the bell curve. Wrong, suggests the by-now widely accepted research of me and many others since the 1960s. And now the next assumption wobbles: that price variations are what statisticians call i.i.d., independently and identically distributed—like the coin game with each toss unaffected by the last. Evidence for short-term dependence has already been mounting. And now comes the increasingly accepted but still confusing evidence of long-term dependence. Some economists, when thinking about long memory, are concerned that it undercuts the Efficient Market Hypothesis that prices fully reflect all relevant information; that the random walk is the best metaphor to describe such markets; and that you cannot beat such an unpredictable market. Well, the Efficient Market Hypothesis is no more than that, a hypothesis. Many a grand theory has died under the onslaught of real data.
Under the efficient markets hypothesis, it is assumed that stock prices in the market follow a “random walk”, where prices today are independent of prices of yesterday. Mandelbrot’s research of fractal dynamics in stock market prices has indicated evidence of long-term dependence in the markets, where prices of a stock from many years back can still impact and influence its prices today.
How can we use it? I have no clue myself or I’ll be dedicating my full awake time towards gaming the markets. But what we can take away, from a broader perspective, is that the same statistical models and tools we use to calculate risk and safety (that we learned in business school) cannot be taken to be foolproof.
