# What is the relation between return volatility and return rank volatility, and how can I control the latter?

I have no experience in finance, but I've been playing around with a virtual portfolio.

I'm trying to control the "rank volatility" distribution - that is, the volatility of a stock's daily rank in returns instead of of the volatility of the returns themselves. I'm particularly interested symmetric distributions on rank, more concentrated in high and low ranks than uniform distribution.

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Hi Elliot, welcome to quant.SE. Ranking stocks and analyzing rank directly is one of the most underappreciated tools of quant finance, IMO. I am a bit confused by your question, though. How can you "control" the volatility of a stock? Also, what are you looking for in terms of the relation between rank and the actual characteristic? – Tal Fishman Dec 29 '11 at 22:28
Example: suppose I have a portfolio that I invest in a single stock each day. I can make the distribution of the "rank" of my stock uniform trivially (choose a random stock). If I could hypothetically have a 50-50 chance of choosing the best stock or the worst stock, my portfolio will perform extremely well (I tested this out). When I say I want a high-volatility distribution on rank, what I mean is that I want the standard deviation of rank (or the mean absolute deviation, or whatever other measure you care for) to be large. E.g. I want a "smile" distribution instead of a uniform or normal. – Elliot Jans Dec 29 '11 at 22:39
You can get a variance matrix for the assets by estimating it on ranks rather than returns. Then if you want your portfolio to have large volatility in that sense (I'm not convinced you really do), then you could use an optimizer to get that. (You may have a hard time with many optimizers, I know one where it would be easy.) – Patrick Burns Dec 30 '11 at 10:33
What is that optimizer, if I may ask (or the method it uses - I should be able to implement most reasonable optimization methods). Is there a way other than a covariance approach to focus on extreme movements? Maybe incorporating stuff like knowing there's an upcoming announcement? – Elliot Jans Dec 30 '11 at 19:26
Portfolio Probe is the one I had in mind. I see two possibilities to get where you want easily: 1) maximize portfolio variance, for which (I think) you need an optimizer that doesn't mind negative eigenvalues in the variance matrix. 2) a minimum constraint on portfolio variance. Though there may be other ways to trick something into giving you what you want. – Patrick Burns Dec 31 '11 at 10:24