Hello Ashok,

The standard deviation reported is for daily returns, because your 1 sigma range is different than the 1 sigma range I got I am not sure what numbers you used. Separately, in the piece I stated that the mean and standard deviation approach 0 and 1 (0.03% and 0.98%) - which suggests returns are normally distributed. However, I then point out that the actual distribution of returns is strongly leptokurtic (i.e. peaked) and that the tails are indeed "fat." That would argue that the distribution of returns for the S&P 500 is not normally distributed.

Separately, I am not sure I understand your point about the self-fulfilling nature of using standard deviation. Please feel free to clarify.

With smiles,

Jason