Using Ranked Signals in Portfolio Optimization

Summary

The document asks how to incorporate cross-sectional scores, such as recent momentum or price-to-book ratios, into a minimum-variance portfolio. The proposed idea is to balance portfolio variance against a reward for holding assets with stronger scores. It highlights a practical difficulty: the relative scaling of the risk and signal terms depends on coefficients that may be hard to choose.

The only answer points to the “portfolios from sorts” approach associated with Chris and Almgren. This offers a reference for translating ranked characteristics into portfolios, but the document does not explain the method, compare it with direct score-based objectives, or provide implementation steps. It also gives no empirical results or guidance on scaling, constraints, turnover, transaction costs, or out-of-sample validation. The note is therefore useful as a pointer to a relevant portfolio construction idea, rather than a complete recipe for combining signals and risk.

Key ideas

• The question concerns combining a minimum-variance objective with ranked asset characteristics.
• A direct risk-minus-score objective requires a choice of scale for the risk and signal terms.
• The cited “portfolios from sorts” work is offered as a relevant approach to investigate.
• The document does not explain implementation or provide empirical comparisons.

Tags

# Including a score or a rank in portfolio-optimization


# Including a score or a rank in portfolio-optimization












I have gathered a lot of experience using min-var optimization of the form $$ w' \Sigma w \rightarrow Min, $$ where $w$ are the weights of the assets and $\Sigma$ is the covariance matrix. Of course we have to take care to use a meaningful $\Sigma$ and we need a lot of constraints in real life.

Now, assume we have calculated a set of scores (e.g. momentum over the last 2 months) or P/B ratio which can be ranked (the higher the better, transform if necessary). What are practical approaches to add this to the objective in the above problem?

Something like

$$ a (w' \Sigma w) - b(scores) \rightarrow Min $$ with some constants $a,b>0$. But wouldn't it be really difficult to choose $a$ and $b$?

How would you approach this? Are there reference on the web?

## Answer by alex castaldo (score -2)

https://quant.stackexchange.com/a/28001

See Chris and Almgren "portfolios from sorts"

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.