Choosing PCA Inputs: Price Levels, Returns, and Standardization

Summary

The document raises a methodological question about applying principal component analysis to financial asset series. It compares using price levels with using returns, and asks whether the selected series should be standardized before calculating covariance. The motivation for standardization is to put assets on a common scale so that high-variance assets do not dominate the components.

It also notes a competing consideration: PCA is often applied to stationary data, which points toward returns rather than raw price levels. The document does not provide an answer, empirical comparison, or recommended procedure. It is therefore a useful framing of two separate choices—whether to transform levels into returns and whether to scale those returns—but offers no evidence about how the choices affect loadings or downstream analysis. A researcher would need to choose based on the question being studied and assess the resulting components.

Key ideas

• The choice between price levels and returns changes the data analyzed by PCA.
• Raw asset series may have different scales and variances, affecting covariance-based components.
• Standardizing returns gives assets comparable scale but changes the covariance structure used by PCA.
• The document poses the methodological tradeoff without offering a recommendation or empirical evidence.

Tags

# PCA on levels or returns, and standardized or not?


# PCA on levels or returns, and standardized or not?












When you run PCA on some financial assets, let’s say stocks, do you calculate covariance on levels, standardized levels, returns or standardized returns?

I’ve seen several papers and posts that suggest to calculate covariance on the series that has been standardized (removed mean and divided by standard deviation) with the main idea being to put assets on the same scale. Otherwise, PCA can load heavily on the asset with the highest variance.

However, there are many authors that claim that in PCA, covariance should be calculated on the stationary series. Therefore, would you skip standardization and just calculate covariance on returns or would you calculate returns and then standardize these returns before calculating covariance?

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