Using Sort-Based Portfolios When Expected Returns Are Unavailable

Summary

The document describes a portfolio construction approach that uses ordinal rankings instead of explicit expected return estimates. In a portfolio of sorts, the centroid of each ranked group supplies the inputs, while the optimization retains a mean-variance-like structure with quadratic constraints. The question asks whether this method is used in practice, particularly when a portfolio must hold an exact number of assets.

The only practical example is a report of a client portfolio constrained to exactly 20 holdings. Its manager used an ordering-based approach to create an equal-weight portfolio and found a relevant paper, though the respondent could not identify it. This anecdote shows one possible application when holdings requirements make conventional portfolio construction awkward. It does not provide implementation details, performance evidence, or a comparison with alternative methods. The answerer knows of no other examples but cautions that this limited personal knowledge should not be taken as evidence that usage is rare.

Key ideas

• Sort-based portfolios use ranking information in place of explicit expected return estimates.
• The described optimization resembles mean-variance optimization and uses quadratic constraints.
• A practitioner reportedly applied an ordinal approach to an equal-weight portfolio with exactly 20 holdings.
• The account is anecdotal and gives no performance results or detailed implementation guidance.

Tags

# Portfolios from Sorts


# Portfolios from Sorts












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?

## Answer by Nathan S. (score 1)

https://quant.stackexchange.com/a/16893

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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