A technique that reduces many correlated variables to a few uncorrelated factors that explain most of their variation. For yield curves, the first three are level, slope and curvature.
Where you will meet it
Principal components analysis comes up in 5 learning outcome notes across the FRM syllabus.
A few of them:
Machine-Learning Methods FRM Part I · Quantitative analysis
“Principal components analysis compresses many correlated features into a few new variables called principal components.”
Modeling Non-Parallel Term Structure Shifts and Hedging FRM Part I · Valuation and risk models
“Principal components analysis (PCA) finds them statistically.”
Regression Hedging and Principal Component Analysis FRM Part II · Market risk measurement and management
“Principal component analysis (PCA) takes the covariance matrix of changes in a set of rates and rewrites it as uncorrelated factors, the principal components, ranked by the variance each explains.”
Machine-Learning Methods FRM Part I · Quantitative analysis
“Unsupervised learning has no labels and looks for structure in the inputs alone, for example clustering with K-means or compressing features with principal components.”
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