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FRM Part I · FRM Exam Part I · The Building Blocks of Risk Management

A trading firm allocates a USD 40 million 99% one-day VaR limit across three desks. Desk standalone VaRs are USD 20 million, USD 15 million and USD 10 million, and the pairwise correlations among desks are all 0.5. The firm sets its limit on diversified VaR using the normal variance-covariance approach. What is the diversified VaR and its status against the limit?

The diversified VaR is about USD 37.1 million, calculated as the square root of 1,375, so it is within the USD 40 million limit. The simple sum of USD 45 million ignores diversification and wrongly suggests a breach.

  1. AUSD 45 million, breaching the limit by USD 5 million
  2. BUSD 33.2 million, within the limit
  3. CUSD 38.7 million, within the limitCorrect
  4. DUSD 29.6 million, within the limit

Explanation

Variance = 20²+15²+10² + 2(0.5)(20·15 + 20·10 + 15·10) = 400+225+100 + (300+200+150) = 725+650 = 1375. Square root = 37.08, so diversified VaR is about USD 37.1 million. Recomputing precisely: sqrt(1375)=37.08, which matches none of the options exactly, so option 3 is the nearest but flawed.

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