But the EMH isn't the only thing Fama has worked on, and he deserves great credit for a half-century of detailed empirical studies of financial markets. Way back in 1963, in fact, it was Fama who took pains in his very first published paper to bring attention to the work of Benoit Mandelbrot on what we now call "fat tails" in the distribution of financial returns. I may have known this before, but I had forgotten and only relearned it when watching this interview of Fama by Richard Roll on the Journal of Finance web site. The paper was entitled "Mandelbrot and the Stable Paretian Hypothesis." Fama gives a crystal clear description of Mandelbrot's empirical studies on price movements in commodities markets, showing a preponderance of large, abrupt movements -- far more than would be expected by the Gaussian or normal statistics assumed at the time. He explored Mandelbrot's hypothesis that the true empirical distributions might be fit by "Stable Paretian" distributions, which we today call "Stable Levy" distributions, for which statistical measures of fluctuations, such as the mean square variance, may be formally infinite. All of this 48 years ago.
How did Fama know about Mandelbrot so early on, when the rest of the economics profession took so long to take notice (and in many cases still haven't)? It turns out that Mandebrot visited Chicago for several months in 1963 and he and Fama spent much time discussing the former's empirical work. As Fama says in the interview, he's always been convinced that a lot of research depends on serendipity. Good example.
Given much better data, we now know (and have for more than a decade) that the Stable Levy distributions aren't in fact adequate for describing the empirical distribution of market returns. If we define the return R(t) over some time interval t as the logarithm of the ratio of prices, s(t)/s(0) -- this makes the return be centered roughly about zero -- then the distribution of R has been found in all markets studied to have power law tails with P(R) inversely proportional to R raised to a power α = 4, at least approximately. See this early paper, for example, as one of many finding the same pattern. Stable Levy distributions can't cope with this as they only yield tail exponents α between 1 and 3.
Given that power laws of this sort arise quite naturally in systems driven out of equilibrium (in physics, geology, biology, engineering etc), these observations don't sit comfortably with the equilibrium fixation of theoretical economics -- or with the EMH in particular. But that's another matter. Fama clearly saw the deep importance of the power law deviation from Gaussian regularity, noting that it implies a market with much more unruly fluctuations than one would expect in a Gaussian world. As he put it,
"...such a market is inherently more risky for the speculator or investor than a Gaussian market."