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Some time ago Almgren and Chriss proposed a method for portfolio optimization based on sorting criteria such as $r_1 > r_2 >... > r_N$ instead of explicit expected returns: see portfolios from sorts and optimal portfolios from ordering information.

The 'portfolio of sorts' approach uses the centroid of the sort instead of returns, but otherwise has the same structure as a mean variance optimization, i.e. a linear program with quadratic constraints.

Is this approach used in practice, and if so, can anybody share their experience with it?

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Thanks for bringing this to our attention. The approach is very interesting. (PS - I fixed a bad link to the second paper.) – pteetor Dec 10 '13 at 19:52

A friend constructed an equal weight portfolio for a client that was constrained to a certain number of holdings. I don't mean less than 20 (less than or equal constraints are more common) but =20 holdings. He chose an ordinality based (sort) approach and he liked a paper, but I don't remember which one. Until then I hadn't thought about using the approach nor had I thought a client's policy would stipulate an equal weight portfolio.

There you have one case I know where the approach was used in practice. I don't know of any other cases, but that means almost nothing.

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This is not the Portfolio from Sorts method proposed by Almgren and Chriss, but an optimization with a cardinality constraint. – Felix Apr 9 '15 at 8:54

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