Skip to content

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

A portfolio has total variance of 100 (bp² units). PCA of the risk factors shows the first component loading gives portfolio variance of 70 and the second gives 20, with the remaining components contributing the rest and uncorrelated. A manager hedges the first component fully and the second reduces by half in exposure. What is the approximate remaining portfolio variance?

Because components are uncorrelated, variances add. Hedging the first removes 70, halving the second's exposure cuts its 20 to 5 since variance scales with the square, and 10 remains from other components. Remaining variance is 0 plus 5 plus 10, which equals 15.

  1. A20
  2. B15Correct
  3. C35
  4. D10

Explanation

Variance is additive across uncorrelated components. First component removed: 0. Second component exposure halved reduces its variance to one quarter: 20×0.25 = 5. Remaining components contribute 100-70-20 = 10. Total = 0+5+10 = 15.

Did you get it right without looking?

One question tells you little. A timed set on Regression Hedging and Principal Component Analysis shows your real accuracy, how long you take and where you lose marks.

Practise Regression Hedging and Principal Component AnalysisFree diagnostic mock

More Regression Hedging and Principal Component Analysis questions