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RE: Variability in a Heteroskedastic Market
You may wish to look at the arithmetic coefficient of variation of a log-normal distribution - interestingly, it is independent of the mean.
Or you can keep testing your own intuitive formula and see when it breaks down and when it appears useful.
Oh yes I see, it's basically the so called Sharpe Ratio used in finance.
However I have my problems with that, I don't use it personally, I have a better way of determining risk in a market:
I will, as I said I am not a math expert, and I didn't said this is a replacement for the variance concept, it's more like an enhancement. Certainly for measuring errors in a forecasted data it's much better since the profit/loss is always a ratio: