Last time I had a look at the Vix's returns plotted against each other with a quarter lag.
Now I am doing the same with the S&P 500.
Whereas the Vix's returns were mostly found in the bottom left corner and reflected positive skew, I promised equities would be in the top right and imply negative skew.
The S&P 500 however is fairly centred, the largest drop of ~-40% not that much greater than the largest jump at ~30%.
The bottom left quadrant is a lot less well populated than the other three quadrants however.
The Vanguard small cap growth is a better contrast. I haven't checked, but I dare say it has more negative skew than the S&P 500 - almost all the data is found in the top right quadrant.
The small cap growth ETF returns are monthly (only 10 year's history).
Interestingly the ellipses are very 'circular' i.e. mean reversion and momentum more or less balance each other out - i.e. the process is 'time-invariant' which is nice.
Invariance means that each return doesn't depend on the last, so we can mix, match and make statistical inferences about them.
We have covered positive and negative skew plus mean reversion, which means momentum is next up.