Using Joint PCA to Measure Risk Across Multiple Yield Curves or Assets

Summary

The document raises a portfolio risk question: how to use principal component analysis when positions depend on more than one correlated time series, such as UK and euro yield curves or several commodities. PCA on a single curve can summarize its major movements, including a parallel shift, but separate analyses may omit relationships between the curves or assets.

The author asks whether combining the series in one PCA would capture those correlations and remain statistically sound, and how to calculate total portfolio risk and each asset’s contribution. The text gives no answer, worked method, or empirical evidence, so it is best read as a problem statement rather than a complete risk framework. In particular, it does not specify how to align or scale inputs, estimate covariance, map principal components back to positions, or allocate risk contributions. Those choices would be needed before applying a joint PCA result to a portfolio.

Key ideas

• Separate PCAs may miss correlations between distinct yield curves or other asset series.
• A joint PCA is proposed as a way to capture cross-series relationships in portfolio risk analysis.
• The question asks how to translate principal components into total portfolio risk and asset-level contributions.
• The document does not provide a solution, calculation procedure, or empirical results.

Tags

# PCA on portfolio depending on multiple time series


# PCA on portfolio depending on multiple time series












There is extensive documentation about PCA on specific time series (for example the UK yield curve). When you have a portfolio which only depends on the change of the UK yield curve then a PCA on the UK Yield Curve will be enough the calculate the risk of such a portfolio.

Now I wonder how one can calculate the risk of a portfolio which depends on multiple time series (for example the UK and the EUR Yield Curve) or a portfolio consisting of multiple different commodities. When running a PCA on the time series separately we will miss the correlation between these time series. A solution would be to run a single PCA on a combination of these time series but I wonder if this will work and if this will be statistically correct.

My main question: How can one calculate the risk of the portfolio based on PCA. Also how can I calculate the risk contribution per asset. Because normally PC1 corresponds with a parallel shift in the yield curve while you also want to know to which yield curve/time series.

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