Hello Ashok,

In general, I feel that you are correct. I would add that just because the mean and standard deviation approximate normal does not necessarily mean that the entire curve approximates normal. After all, essentially mean and standard deviation are two point estimates of a two-dimensional curve. I can think of many geometrical shapes that would have similar points, but radically different shapes. In fact, that is what we have with the S&P 500's returns. I feel the most surprising thing of the above data is the extreme leptokurtic quality of the returns. Typically we only hear about the "fat tails" of market returns, but what about the giraffe head? This is strongly non-normal.

I would also point out that I feel differing the time scale will change the results, just as changing your sieve changes the texture of your refined spice. Yet, the spice will taste the same even if it does not look the same.

Ashok, you point out the importance of adjusting for dispersion (n) is making comparisons. Yet, this adjustment for Brownian motion is essentially a normal distribution/stochastic/random transform. But applying this transform to a curve that is certainly non-normal is probably tough to justify. Take a look at this other The Enterprising Investor piece about this topic: http://blogs.stage.cfainstitute.org/investor/2012/05/29/holes-in-some-o…

As always, thanks for your invaluable contribution!

Jason