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

PCA on a yield curve gives eigenvalues of the covariance matrix of 8.0, 1.5, 0.3 and 0.2 (units of bp squared) for the four principal components of a simplified four-rate system. What proportion of total variance do the first two components explain together?

The first two components explain 95% of total variance. Total variance is the sum of eigenvalues, 10.0, and the first two eigenvalues sum to 9.5, so the ratio is 0.95. Using only the first component would give 80%.

  1. A80%
  2. B95%Correct
  3. C75%
  4. D90%

Explanation

Total variance equals the sum of eigenvalues: 8.0+1.5+0.3+0.2 = 10.0. The first two explain 9.5/10.0 = 95%. The 80% answer counts only the first component.

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