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FRM Part I · FRM Exam Part I · Modeling Non-Parallel Term Structure Shifts and Hedging

In a principal components analysis (PCA) of changes in a government par-yield curve, the first three components are typically labelled level, slope and curvature. Which description of the first component (level) is correct?

The level component is a near-parallel shift in which rates at all maturities move in the same direction by similar amounts. It is the first and most important component, explaining the largest share of yield-curve variance, unlike slope or curvature, which involve opposite-signed loadings.

  1. AShort-term and long-term rates move in opposite directions, so the curve steepens or flattens
  2. BRates of all maturities move in the same direction by roughly similar amounts, so the curve shifts in a near-parallel wayCorrect
  3. CMedium-term rates move in one direction while short- and long-term rates move in the other
  4. DIt explains the smallest share of total variance among the components

Explanation

The first principal component usually has loadings of the same sign and similar size across maturities, so it is a near-parallel shift. Opposite-sign loadings between short and long ends describe slope (second component). A hump pattern describes curvature (third). The first component explains the largest share of variance, not the smallest.

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