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

A trading desk has a 1-day 99% VaR limit of USD 10 million, derived from a firm-level appetite of USD 25 million across three desks. Desk standalone VaRs are USD 10 million, USD 12 million and USD 15 million, and the firm-level VaR is USD 25 million after diversification. Desk A's VaR is USD 10 million. Which conclusion is correct?

The firm sits exactly at its USD 25 million appetite on a diversified basis. The USD 37 million sum of standalone VaRs is not the relevant measure; the USD 12 million difference is the diversification benefit, not headroom, because VaR is not additive.

  1. AThe firm is within its aggregate appetite, but the sum of standalone VaRs of USD 37 million exceeds it only because VaR is not additive; diversification explains the gapCorrect
  2. BThe firm breaches appetite because standalone VaRs sum to USD 37 million
  3. CThe firm has USD 12 million of headroom, the difference between 37 and 25
  4. DDiversification benefit is USD 25 million

Explanation

Sum of standalone VaRs = 10+12+15 = 37. Firm VaR is 25, equal to the limit, so it is within appetite (at the limit). Diversification benefit = 37 − 25 = 12 million, not headroom. Appetite is measured against the diversified firm VaR, so summing standalones is wrong.

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