Using PCA Eigenvalues to Compare Candidate Stock Portfolios

Summary

The document considers selecting five stocks from a universe of fifteen by enumerating combinations and comparing the eigenvalues of each candidate portfolio's data. It notes that a large first eigenvalue can indicate substantial variance concentrated in a dominant component, then asks whether minimizing that eigenvalue would identify the best portfolio for gains or whether other eigenvalues matter.

No solution or empirical comparison is provided, so the proposed ranking rule remains unresolved. PCA describes variance structure, not expected return or investment quality: a low first eigenvalue alone does not establish that a portfolio will earn more, nor does it summarize all portfolio risks. Results also depend on the input data, scaling, and estimation period. A useful evaluation would define the objective and examine portfolio returns, risk, and diversification with an out-of-sample process; these steps are implications of the question, not results reported in the document.

Key ideas

• The proposal compares stock combinations using eigenvalues from principal component analysis.
• A large first eigenvalue may indicate variance concentrated in the leading component.
• The document does not establish that minimizing the first eigenvalue produces higher gains.
• Eigenvalues describe variance structure rather than expected returns.
• Any portfolio comparison depends on data choices and should be assessed against a defined investment objective.

Tags

# Choose the best combination of 5 stocks from 15 stocks using PCA


# Choose the best combination of 5 stocks from 15 stocks using PCA












I am working on a project to choose the perfect combination of 5 stocks from a total of 15 stocks to get the "highest gains". Here's the approach I plan to use. Run a loop for all combinations of 5 stocks from 15 (i.e. 15C5). Once I have the eigenvalues for each combination, I have learnt that the portfolio with the largest first eigenvalues often have the highest variance/risk. Then would the right approach be to choose the portfolio with the lowest first eigenvalue?

Or is there an better indicator I should be looking at? Or perhaps I shouldn't look at only the first eigenvalue for each combination, but at the other ones as well?

Feel free to point to any resources that might help.

Thanks

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