FRM Part II · FRM Exam Part II · Regression Hedging and Principal Component Analysis
A risk analyst applies principal component analysis to historical changes in a government par-yield curve across maturities from 1 to 30 years. The first three components together explain nearly all of the variation. Which description of the first component's loadings is standard for such an analysis?
The first principal component of yield curve changes typically has same-signed loadings across maturities, representing a roughly parallel shift or level factor. It explains the largest portion of variance. The slope factor changes sign once, and the curvature factor has a hump or U shape.
- ALoadings of the same sign across maturities, representing a roughly parallel shift (level factor)Correct
- BLoadings that change sign once from short to long maturities, representing a steepening of the curve
- CLoadings that are positive at both ends and negative in the middle, representing a change in curvature
- DLoadings that are close to zero at all maturities, representing noise in the data
Explanation
In term structure PCA the first component typically has loadings of the same sign across maturities, so it is a level (parallel shift) factor and explains the largest share of variance. A single sign change describes the slope factor (second component). A hump or U-shaped pattern describes curvature (third component).
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