Volatility:

- Physically, “volatility” is the wiggling of stock prices or index values, as illustrated by Shiller.
- A statistical definition for volatility is here: investopedia.com/terms/v/volatility.asp. A majority of financial experts seem to believe that variance/volatility is connected to “risk.”

- What if a trader could ride the wiggles, each way, and profit each way, on stock XYZ? What basis would one use to represent “risk” for such trading?

People want a measure of return potential. Instead they get something like this: “Past performance is no guarantee of future results.”

The Reniassance fund is often regarded as a benchmark example for better hedge fund performance.

People look at the returns, the growth. They talk about it, they write about it.

Whatever the “volatility” of the fund might be, it does not seem to matter much.

Some organizations are exploring new scientific frameworks, such as the Flatiron Institute.

Some entities specifically mention “robust methods” and “collaboration,” such as The Voleon Group.

In price data, one must distinguish between Gaussian white noise, Brownian motion (aka 1/f, Red, or Random Walk noise), and The Information.

Some statistical procedures seem to welcome havoc. Sample thoughts.

Differencing price data removes lower frequency spectral content and keeps high frequency content.

Differencing amplifies noise enormously, by definition (R W Hamming, 1989).

With differenced data, “spurious correlations” should be expected (G Udny Yule, 1926).

The S&P index, when viewed over a long time period, does not exhibit ergodic behavior around some fixed mean value.