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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 six par swap rates. Which statement about the resulting principal components is correct?

Principal components are uncorrelated with one another and are ordered so the first explains the largest share of total variance. Their variances sum exactly to the original total variance, so they re-express the data rather than add information.

  1. AThe components are mutually uncorrelated, and the first component explains the largest share of total varianceCorrect
  2. BThe components are mutually correlated, and the first explains the smallest share of total variance
  3. CThe components are uncorrelated, and each explains an equal share of total variance
  4. DThe components are mutually correlated, and their variances sum to more than the total variance of the original series

Explanation

PCA produces orthogonal (uncorrelated) components ordered by explained variance, so the first has the largest variance. The sum of component variances equals total variance of the original data, not more. Equal shares would only occur if the original variables were uncorrelated with equal variances.

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