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FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

A two-factor model has factor volatilities of 10% (Factor 1) and 5% (Factor 2) and the factors are uncorrelated. A portfolio has exposures of 0.8 to Factor 1 and 1.6 to Factor 2. Residual risk is zero. What is the percentage of portfolio variance contributed by Factor 2?

Factor 2 contributes 50% of variance. Factor 1 contributes (0.8 x 10%)^2 = 64 and Factor 2 contributes (1.6 x 5%)^2 = 64, with no covariance because the factors are uncorrelated, so each accounts for half of the total of 128.

  1. A50%Correct
  2. B67%
  3. C33%
  4. D80%

Explanation

Factor 1 variance contribution = (0.8 x 10)^2 = 64. Factor 2 contribution = (1.6 x 5)^2 = 64. The factors are uncorrelated so there is no covariance term; total = 128. Factor 2 share = 64/128 = 50%. Option D ignores the factor volatility scaling and compares exposures only (1.6 vs 0.8 would not give 80% either), so it is wrong.

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