# How to group mutual funds by volatility?

I want to group Mutual Funds by their volatility.

Ideally, I would like to end up with the mutual funds beings attached to different groups:

• High volatility
• Medium volatility
• Low Volatility

My questions is : What numbers could be consider like low , medium , high volatility ?

Maybe some intervals: 0 -5 % is low 5 - 15% is Medium and Higher is High......

I'm little bit confused on how to tackle this problem...

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I want to inform, not sell my product in this response. There is a tool called FundReveal that analyzes all of the mutual funds available in the US using exactly the approach you are investigating. Full disclosure: I am a cofounder of FundReveal. FundReveal uses standard deviation of daily returns over the time period in question. We consider funds that beat the S&P with risk (standard deviation) and higher Average Daily Returns to be those that are most likely to persist in positive performance. You can try the tool for free at www.fundreveal.com – user3238 Nov 9 '12 at 14:17
What do you call "rescued shares"? Are you trying to compute the volatility of the returns and the classify them? – SRKX♦ Nov 10 '12 at 18:40
Yes! In fact it doesn't matter what I meant by rescued shares, I just want to classify any returns by volatility. What would be a properly insight for this ? – Tomás Ayala Nov 11 '12 at 0:12
Ok I'll edit your question to make it understandable then. – SRKX♦ Nov 11 '12 at 10:19
Remainder of Anthony DuBon's comment: Since you seem to be interested in the relationship between risk and return you might look into the work of Robert Haugen. He focuses primarily on stocks. His book The New Finance challenges the nearly ubiquitous assumption that high return requires high risk securities. He and other proponents of the low risk anomaly are pursuing empirical evidence that the opposite may be true. – Tal Fishman Nov 28 '12 at 18:21
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## 1 Answer

What you are looking for is an unsupervised learning algorithm algorithm: i.e an algorithm that will by itself determine the 3 most rational groups from your dataset. This method will allow you to choose the boundaries of the groups based on the dataset you provide and not by choosing some given fixed values.

The algorithm I suggest you to use is the K-means algorithm. You provide it with the data, and the number $k$ of clusters (groups) that you want to have. The algorithm will then split the data into the $k$ groups you would like. Note that this algorithm can handle points with several features, whereas you will be using only one (volatiliy).

Here is an idea of how it works in Matlab:

````test=[0 1 2 3 100 105 98 1000 1001 997]';
[idx,C] = kmeans(test,3);
````

The value returned for `idx` is a vector where each point in `test` is attributed a cluster number (representing its group):

````idx =

 2
 2
 2
 2
 3
 3
 3
 1
 1
 1
````

You can then look at the variable `C` which contains the mean of each cluster which could be undrestood as "the perfect point for each cluster"

````c =

  999.3333
  1.5000
  101.0000
````

So it found three groups in `test` one around 999.33, one around 1.5, and one around 101.

That should do the trick.

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Thx SRKX I studied once K-means but forgot that could be useful. Thx again for your time. – Tomás Ayala Nov 11 '12 at 19:25
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