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FRM Part II · FRM Exam Part II · Regression Hedging and Principal Component Analysis

A risk analyst applies principal component analysis to daily changes in a set of government par yields from 2 years to 30 years. The first three components are labeled level, slope and curvature. Which description of the typical loadings on the first component is most consistent with the level factor?

The level factor has loadings of the same sign across maturities, so a one-standard-deviation shock moves yields in roughly parallel fashion. Slope has one sign change and curvature has two, which is why those descriptions fit the second and third components instead.

  1. ALoadings of the same sign across maturities, so a shock moves all yields in roughly the same directionCorrect
  2. BLoadings that change sign once between short and long maturities, so short and long yields move in opposite directions
  3. CLoadings that change sign twice, with the belly moving opposite to the wings
  4. DLoadings that are near zero for all maturities except the shortest

Explanation

The level factor is a roughly parallel shift, so its loadings have the same sign across the curve. A single sign change describes the slope factor, and two sign changes describe curvature. Loadings concentrated at one maturity would not describe a curve-wide factor.

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