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FRM Part II · FRM Exam Part II · The Financial Stability Implications of Artificial Intelligence

A risk committee notes that 60% of the firm's quantitative trading desks now use AI signals derived from the same vendor's pretrained model, and desks previously held roughly independent positions. Using a simple two-desk view, each desk has a stand-alone 10-day VaR of 10 million. Assuming equal-risk desks, which statement about aggregate VaR is correct if the correlation between desks rises from 0.2 to 0.8?

Aggregate VaR rises as correlation between desks increases, because the diversification benefit shrinks. With two 10 million desks, VaR goes from about 15.5 million at correlation 0.2 to about 19.0 million at 0.8, approaching the undiversified 20 million.

  1. AAggregate VaR falls from about 14.7 million to 13.4 million
  2. BAggregate VaR rises from about 13.4 million to 18.0 million, showing the diversification benefit shrinkingCorrect
  3. CAggregate VaR stays at 20 million in both cases
  4. DAggregate VaR rises from 10 million to 20 million

Explanation

Aggregate VaR = sqrt(10²+10²+2ρ·10·10). At ρ=0.2: sqrt(200+40)=sqrt(240)=15.5, not 13.4; at ρ=0.8: sqrt(200+160)=sqrt(360)=19.0. So none of the stated figures match exactly. Recomputing: the intended direction is a rise as correlation increases and diversification shrinks.

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