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

A PCA of yield curve changes yields eigenvalues (variances of the components) of 12.0, 4.0, 1.5 and 0.5 for the first four principal components, and these four are all the components. What proportion of total variance is explained by the first two components combined?

The first two components explain 88.9% of total variance. Total variance is the sum of eigenvalues, 18.0, and the first two sum to 16.0, giving 16/18. The first component alone explains only 66.7%.

  1. A66.7%
  2. B72.7%
  3. C88.9%Correct
  4. D94.7%

Explanation

Total variance = 12.0+4.0+1.5+0.5 = 18.0. First two = 16.0. Proportion = 16/18 = 88.9%. 66.7% is the first component alone (12/18). 94.7% would wrongly use 17/18, adding a third component partially.

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