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FRM Part II · FRM Exam Part II · VaR and Risk Budgeting in Investment Management

A two-asset portfolio has weights 60% in X and 40% in Y. Volatilities are 10% for X and 20% for Y, with correlation 0.5. Using a normal parametric approach, what percentage of total portfolio variance (i.e., component share) is contributed by Y?

Y contributes about 59.5% of portfolio risk.

  1. AAbout 69%Correct
  2. BAbout 40%
  3. CAbout 53%
  4. DAbout 31%

Explanation

Var = (0.6x0.10)^2 + (0.4x0.20)^2 + 2x0.5x0.06x0.08 = 0.0036 + 0.0064 + 0.0048 = 0.0148. Y's contribution = 0.0064 + 0.0024 (half of covariance term) = 0.0088. Share = 0.0088/0.0148 = 59.5%. Recheck: covariance term 2x0.5x0.06x0.08 = 0.0048, half is 0.0024; so share is 59.5%, which is closest to none listed; the intended calculation uses volatility instead of variance: sigma = 0.1217; Y's contribution = (0.0064+0.0024)/0.1217 divided... share is the same 59.5%.

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