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

In a decentralized risk budgeting structure, a chief investment officer assigns each asset manager a VaR limit, and managers run their portfolios within those limits. Which is the main reason the sum of the managers' standalone VaRs typically exceeds the total fund VaR?

The sum of standalone VaRs exceeds total fund VaR because of diversification: managers' positions are not perfectly correlated, so combined risk is lower than the sum of individual risks. This is why sponsors use diversified or component measures when setting overall budgets.

  1. AManagers use different confidence levels from the fund
  2. BDiversification across managers' positions, as correlations among them are below oneCorrect
  3. CVaR is not subadditive for normal distributions
  4. DBenchmark risk is added at the fund level but not the manager level

Explanation

When correlations are below one, combined risk is less than the sum of the parts, so standalone VaRs add to more than total VaR. For normally distributed returns VaR is subadditive. The other choices are not the cause.

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