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

A risk analyst applies principal component analysis (PCA) to the covariance matrix of daily changes in eight key-rate points on a government yield curve. Which statement about the resulting principal components is correct?

Principal components are uncorrelated with each other and each is a linear combination of the original rate changes. They are ranked by explained variance, with the first being largest. They do not map to single rates, and covariance eigenvalues are non-negative.

  1. AThe components are mutually uncorrelated, and each is a linear combination of the original rate changesCorrect
  2. BThe components are mutually correlated, with the first component having the smallest variance
  3. CEach component corresponds to exactly one of the original key-rate points
  4. DThe components are ordered by the sign of their eigenvalues, with negative eigenvalues indicating the most important factors

Explanation

PCA produces orthogonal (uncorrelated) factors, each a linear combination of the original variables, ordered by the variance they explain. The first component has the largest variance, not the smallest. Components do not map to single rates, and eigenvalues of a covariance matrix are non-negative.

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