When PCA Eigenvectors Represent Eigenportfolios

Summary

The document asks whether each eigenvector from a principal component analysis of an asset covariance matrix can be interpreted as an eigenportfolio. With no components discarded, it proposes that a portfolio of n assets yields n such portfolios, ordered by their marginal explanatory power.

It presents the terminology question but provides no answer, derivation, or empirical evidence. The key distinction for readers is that an eigenvector gives portfolio weights associated with a principal component; calling the resulting weighted portfolio an eigenportfolio is common in some contexts, though usage can vary. The document does not discuss normalization, constraints on weights, or how the components might be used in portfolio construction, so it offers little guidance beyond identifying the concept and asking for clarification.

Key ideas

• A covariance matrix PCA produces eigenvectors that can be interpreted as directions in asset return space.
• Each eigenvector can define a portfolio through its asset weights, often called an eigenportfolio.
• The document asks about terminology but gives no answer or practical analysis.
• Principal components are ordered by explained variance, not necessarily by investment quality.

Tags

# Terminology - are each of the eigenvectors of a PCA themselves called an "eigen portfolio"


# Terminology - are each of the eigenvectors of a PCA themselves called an "eigen portfolio"












Sorry, I suspect this is rather trivial but just want to confirm that, given a portfolio constructed of `n` assets, each of the `n` eigenvectors (assuming no cutoff / variance threshold etc. has been applied) produced as the result of a PCA of those asset's covariance are each themselves called "eigen portfolios"? i.e. one portfolio of n assets has become n eigen portfolios (of decreasing marginal explanatory power)? Thanks

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