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

A portfolio has a DV01 exposure to three PCA factors measured as: level 12,000, slope -3,000 and curvature 500 (USD per one standard deviation move in each factor). The factor standard deviations are already embedded in these exposures and the factors are uncorrelated. What is the one-standard-deviation portfolio P&L volatility in USD, using the three factors only?

Since the principal components are uncorrelated, portfolio variance is the sum of squared factor exposures: 144 million plus 9 million plus 0.25 million, about 153.25 million. The square root gives roughly 12,400 USD, closest to 12,369. Adding exposures linearly would wrongly ignore orthogonality.

  1. AAbout 12,369Correct
  2. BAbout 9,500
  3. CAbout 15,500
  4. DAbout 12,000

Explanation

Because the components are uncorrelated, variance is the sum of squared exposures: 144,000,000 + 9,000,000 + 250,000 = 153,250,000. The square root is about 12,379... check: 12,369^2 = 152,992,000 and 12,380^2 = 153,264,000, so the value is about 12,379. The closest option is 12,369, which reflects the sum-of-squares method. Simply adding exposures (9,500 net or 15,500 absolute) ignores orthogonality.

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