In the report you describe a methodology for computing volatility (displayed here):
But in the math courses I have taken with regard to finance (and the textbooks I check for reference) volatility is typically expressed as the standard deviation of the set of price points and would be
In the alternative formula used here the number of items in the data set (N) has been replaced with the average price. Why?
It makes - some - reasonable sense that because the average of price data here will always be positive we can replace the number of items in the data set with the average price, but I wasn’t able to come up with a stronger, intuitive reason for such a change.
The other change made, which is much more confusing to me personally, is you entirely replaced the “sum of the square of the difference of the items and the population mean” with the much simpler “difference of highest and lowest price.”
I have a degree in mathematics and have some experience in accounting. I am certainly not a high level financial data analyst.
My guess is that the alternative formulas you have used are industry standard for something and during my formal education for math I never ran into that kind of thing.
Since the volatility formula is used as the basis for the observed volatility and the adaptation factor I was hoping you would provide insight into why you chose these specific formulas instead of the more widely known formulas.
Thank you so much for this report by the way. I really tried to approach it as a total skeptic and by the end you guys made me a total fanboy. I was really trying to come up with some useful criticism for the paper - for the sake of academics - and this was the only thing I could come up with.
So if it seems like a bit of a contrived nitpick… it kinda is.