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FRM Part II · FRM Exam Part II · Stress Testing Banks

A bank aggregates stress results for two business lines. Standalone stressed losses are USD 300 million for credit and USD 400 million for market risk. Management assumes the two losses are correlated at 0.5 and aggregates them like standard deviations. What is the aggregated stress loss, and how does it compare with simple addition?

The aggregated loss is about USD 608 million, the square root of 90,000 plus 160,000 plus 120,000. It is below the USD 700 million simple sum because correlation of 0.5 gives diversification. Using zero correlation would wrongly give USD 500 million.

  1. AUSD 700 million, same as simple addition
  2. BUSD 500 million, below simple addition
  3. CUSD 608 million, below simple additionCorrect
  4. DUSD 790 million, above simple addition

Explanation

Aggregate = sqrt(300^2 + 400^2 + 2*0.5*300*400) = sqrt(90,000 + 160,000 + 120,000) = sqrt(370,000) = 608.3. This is below 700 because the correlation is below 1. USD 500 million assumes zero correlation (sqrt(250,000)).

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