# Ranking volatilty measures

I am creating a SQL query for a model I am developing that uses historical volatility. I am using the below methods to determine historical volatility:

1. close to close zero mean
2. close to close standard calculation for sample
3. parkinson
4. garman klass
5. rogers satchell
6. yang zhang

Generally speaking, how would these be ranked in terms of size? Which measure produces the largest value, second largest value, ..., smallest?

Thank you

• What is the reason you want to rank them in terms of size?
– Pleb
Nov 30, 2021 at 17:38
• Some of these measures include the overnight (i.e. close to open) move, some do not (they measure the intraday vol only). This can cause the latter to be smaller, but it is not always true. There is no complete ranking of them AFAIK. Nov 30, 2021 at 17:54
• i want to see if the answers i am getting are reasonable. by reasonable, i mean relatively speaking. i know there is no hard and fast rule but just curious in general what is the order Dec 1, 2021 at 0:55
• I know one comparison - the mean zero close-close will always be larger (almost by definition) than the close-close standard calculation (with the empirical mean subtracted). Dec 1, 2021 at 15:08

## 1 Answer

Your question is ill-posed.

This type of question appears quite a bit in the field of statistics and is intrinsically problematic.

Consider the two most common standard estimators of variance for a normally distributed variable. $$\hat{\sigma}^2_F=\frac{\sum_{i=1}^n(x_i-\bar{x})^2}{n-1}$$ and $$\hat{\sigma}^2_L=\frac{\sum_{i=1}^n(x_i-\bar{x})^2}{n}.$$

Although both estimates are built on the same foundational axioms, they are constructed under different assumptions. It will always be true that $$\hat{\sigma}^2_F>\hat{\sigma}^2_L$$ but that is completely unimportant.

Now it seems like a simple ranking is possible, but that is because they differ by a constant.

Each of the varying formulas that you have chosen does not differ by constants. There would never be a stable ranking, except possibly in some local dataset. All methods are optimal if and only if their assumptions are met.

There is no way to assess reasonableness by looking at their values because you do not know the ground truth. If you have fictional data with a defined volatility and ran thousands of Monte Carlo simulations, then you could assess their properties. The issue is a bit problematic because the formulas contain assumptions that require you to add nuisance parameters and may vary strongly with those nuisance parameters.

They have official properties but you can look at others such as robustness or breakdown point that are not part of the official derivations or assumptions.

The proper solution is to work backward and ignore the observed answers.

What properties do you want to have in an estimator?