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

A large asset owner lets each manager run its own portfolio and report VaR, then the central risk team aggregates the numbers. What is the main reason the central team should compute total VaR from the combined positions rather than just add manager-level VaRs?

The central team should compute VaR on combined positions because summing manager VaRs ignores diversification, overstating risk, and obscures offsetting or concentrated exposures across managers. Combined positions reveal the true overall risk and enable proper allocation of the risk budget.

  1. AAdding VaRs understates risk because managers always take offsetting positions
  2. BAdding VaRs ignores diversification and can overstate risk, and also hides offsetting or concentrated positions across managersCorrect
  3. CCombined VaR is always larger than the sum of manager VaRs
  4. DManager VaR is not measured in currency units

Explanation

Summing stand-alone VaRs assumes perfect correlation, so it overstates total risk when diversification exists, and it can miss netting or concentration across managers. Aggregating positions captures these effects. Combined VaR is typically no greater than the sum for normal-type distributions, and VaR is expressed in currency.

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