FRM Part II · FRM Exam Part II · Regression Hedging and Principal Component Analysis
A PCA on the covariance matrix of three key rate changes gives eigenvalues of 8.0, 1.5 and 0.5 (in squared basis point units). What proportion of total variance is explained by the first two components together?
The first two components explain 95% of total variance. The eigenvalues sum to 10.0, which is the total variance, and the first two add up to 9.5. Dividing 9.5 by 10.0 gives 95%.
- A80%
- B85%
- C95%Correct
- D15%
Explanation
Total variance equals the sum of eigenvalues: 8.0+1.5+0.5 = 10.0. The first two sum to 9.5, so 9.5/10 = 95%. The 80% figure is only the first component; 85% is a wrong sum (8.0+0.5).
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