FRM Part II · FRM Exam Part II · Regression Hedging and Principal Component Analysis
PCA on a covariance matrix of three interest rate changes gives eigenvalues of 8.0, 1.5 and 0.5 (in bp² units). What proportion of total variance is explained by the first two components together, and what is the total variance?
Total variance is the sum of the eigenvalues, 10.0. The first two components together account for 9.5 of it, which is 95%. The 80% figure reflects only the first component, so it ignores the second component's contribution.
- A95% of total variance of 10.0Correct
- B80% of total variance of 10.0
- C95% of total variance of 8.0
- D85% of total variance of 10.0
Explanation
Total variance equals the sum of eigenvalues: 8.0+1.5+0.5 = 10.0. The first two explain (8.0+1.5)/10.0 = 9.5/10 = 95%. The 80% option counts only the first component; 85% is a miscalculation.
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