# How to classify stocks by their volatility?

I would like to hear other possible ways of classifying Stocks by the Volatility of their returns. Assuming that I want to characterize each stock as Low, Medium or High Volatility Stock and assuming that I know the Annualized Volatility for each of the stocks in my sample, what ways are there to do such classification? I can think of two:

• Below, say, 30th percentile (of the Annualized Volatilities) -> Low Volatility; Between 30th and 70th Percentile -> Medium Volatility; Top 30th percentile -> High Volatility
• (-2)*Std.Dev (of the distribution of the Annualized Volatilities) -> Low Volatility; Between (+-2)*Std.Dev -> Medium Volatility; (+2)*Std.Dev -> High Volatility

Feel free to point out papers where I can find my answer.

There are a lot of ways of doing this and what a good way of doing this will be driven by your needs as well. Criteria such as whether the method needs to be (in)sensitive to outliers and whether or not your groups need to be of the same size will influence this.

One way to do this would be sorting the volatilities and group them:

• in groups of equal size
• such that the mean differences between the two groups are equally large
• as a nearest neighbor algorithm with 3 groups dictates
• such that the sum of variance with groups is minimized (I think that's almost the same as nearest neighbors)
• ...

As long as you pick something and apply it consistently, it might not even matter that much which you pick.

It really depends what you're trying to achieve! What is the ultimate goal? What are your constraints? Which stocks are you looking at?

Without the answers to the above, any partition is just arbitrary: why choose 30th and 70 percentile, vs 10th and 90th? Why choose (-2)*Std.Dev and (+2)*Std.Dev vs just -1 and +1?

The selected (and perhaps only correct) way to classify volatilities is the one that satisfies (or at least optimizes) your ultimate goal.

• Hallo Shahar, and thank you for your reply. I want to classify the stocks in my sample in order to study whether certain properties are shared by the stocks in each volatility group. I'm not asking for the optimal/best way of doing it but simply for suggestions of how it can be done. The constraint is that I want only to use the annualized volatility to classify them. The choice of the cut of values in the methods I suggested would be clearly determined by my ultimate goal (whether I want to focus on outliers or not, etc...) but I was simply giving them as an example. Any ideas/suggestions? Aug 27, 2014 at 21:57
• My suggestion is to consider forgoing these arbitrary groups altogether, at least for now. Calculate the properties you're interested in for each stocks, and then perform more meaningful ensemble analysis. For example, you can then correlate annualized volatility to property1, property2, etc. Then you may be able to make statements such as, "for volatilities<v1, property1 hold; >v2, property2 holds..." - but again, unless you have a compelling reason to do otherwise, just forget about this classification for now. It is the volatility itself that counts, not its high/medium/low label. Aug 28, 2014 at 14:24
• Let me be more clear about what I'm trying to do. I'm selecting 100 tickers out of the several thousands of stocks that were traded in 2010 and 2011 on the NASDAQ and NYSE. I want to pick them according to several criteria, including their annualized volatility. I cannot look at their properties now since those properties will be the result of my research. Once, or if, I find any interesting properties, i will look at whether they are shared among stocks that belong to the same group (for example, same volatility group.) The volatility per se doesn't count but it's used to classify the stocks. Aug 28, 2014 at 14:33