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maybe a simply question, but can you describe what normalized returns and volatility is? Is it simple the percent rank of individual data sets? (independent of each other) so that within a data set of volatility, the observation with the lowest vol ranks (or has a normalized return) as 1 and the one with highest vol gets a zero? or is it more complicated than that. thanks for any insights or links to further readings or explanations.

There might be other definitions, but here is the

**Z-Score**, which for me is the most intuitive:“The standard score of a raw score x [1] is

z = {(x- μ) / σ}

where:μ is the mean of the population;

σ is the standard deviation of the population.”Which gives you a normalized range around 0. A value of 2 for example would indicate that the current value is at the 2nd standard deviation of the historical distribution. Good for detecting outliers or extremes, or for harmonizing data for example in a ranking with several factors. You can also use for volatility, then σ becomes ‘volatility of volatility’

An easier approach is using a percentile approach like you describe, but Z-Score gives you more information.

Let me know if this helps.

it does thanks. but that gives you a score around Zero. In the ranking/rotation system it uses a normalized score between 0-1. (see below) is that the percentile rank even if it is not as statistically correct as the z-score or is there a way to normalize the z-score between 0-1?

“You can use the 20 day volatility averaged over 3 month.

For the ranking I calculate the 3 month performance of all ETF’s and normalise between 0-1. The best will have 1. Then I calculate the medium 3 month 20 day volatility and also normalize from 0-1.

Then I used Ranking= 0.7*performance +0.3*volatility.

This will give me a ranking from 0-1 from which I will take the best. “Ouch, you caught me, did not get you we’re refering to the article. Frank used indeed 0-1 normalization in the strategy, to replicate use: X’ = (X – Xmin) / (Xmax – Xmin)

Personally I just like and use the Z-Score more as you see the outliers when you chart.

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