Details

When the periods per year and the number of years are relatively low compared with the impact and probability of a fat tail event, the distribution of standard deviations relative to the return appears punctuated. For example, for 10 years of monthly returns with fat tails simulated by replacing moves less than 0.1 with moves of the same sign of magnitude 10, there appear about a dozen punctuated points with noise around them rather than a single seeming distribution. This is because the jumps are so large, and so infrequent, that one can essentially gather the results based on the number of jumps that have occurred. In such situations, it is better to look either at daily returns or at longer durations, or both, to get a more continuous and unified distribution. The result is that the noise from fat tails essentially offsets the gains to precision from looking at daily returns.

For more information, see P. Z. Maymin and Z. G. Maymin, "Any Regulation of Risk Increases Risk," available at ssrn.com/abstract=1587043.