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

Using the PCA in which the eigenvalues are 8.0, 1.5 and 0.5, a risk manager wants the standard deviation of the change in a portfolio's exposure to the second component, where the portfolio's loading (exposure) on that component is 4 per unit of component score and the eigenvalue is the variance of the component score. What is the standard deviation, to two decimals, of the portfolio value change attributable to the second component?

The standard deviation is about 4.90. The second component's variance is 1.5, so its standard deviation is the square root, 1.2247. Multiplying by the portfolio exposure of 4 gives 4.899. Using variance rather than standard deviation would wrongly give 6.00.

  1. A4.90Correct
  2. B6.00
  3. C19.60
  4. D2.45

Explanation

Component standard deviation = sqrt(1.5) = 1.2247. Multiply by exposure 4 gives 4.899, about 4.90. Using the variance directly (4 x 1.5 = 6.00) is the mistake of omitting the square root; 19.60 is 4 times 4.9 incorrectly scaled, and 2.45 halves the result.

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