FRM Part II · FRM Exam Part II · Regression Hedging and Principal Component Analysis
An analyst performs PCA on a covariance matrix of five rate changes whose total variance is 50 (bp^2). The eigenvalues are 40, 6, 2.5, 1 and 0.5. What proportion of total variance is explained by the first two components together?
The eigenvalues sum to the total variance of 50. The first two components contribute 40 plus 6, which is 46, so they explain 46 divided by 50, or 92% of total variance. The first component alone would explain only 80%.
- A92%Correct
- B80%
- C86%
- D95%
Explanation
Eigenvalues sum to total variance: 40+6+2.5+1+0.5=50. The first two sum to 46, and 46/50 = 92%. 80% uses only the first component, and the others are unsupported.
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