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FRM Part II · FRM Exam Part II · Range of Practices and Issues in Economic Capital Frameworks

A bank computes stand-alone economic capital of USD 600 million for credit risk, USD 300 million for market risk and USD 200 million for operational risk. It aggregates with a variance-covariance approach using a correlation of 0.50 between credit and market, 0.25 between credit and operational, and 0.25 between market and operational. Which total is closest to the aggregated economic capital?

The aggregated figure is about USD 872 million, found by summing the squared stand-alone amounts and the correlation cross terms to get 760,000 and taking the square root. Of the listed options, USD 855 million is the closest, while simple summation gives USD 1,100 million.

  1. AUSD 1,100 million
  2. BUSD 780 million
  3. CUSD 855 millionCorrect
  4. DUSD 1,006 million

Explanation

Variance = 600^2 + 300^2 + 200^2 + 2(0.5)(600)(300) + 2(0.25)(600)(200) + 2(0.25)(300)(200) = 360,000 + 90,000 + 40,000 + 180,000 + 60,000 + 30,000 = 760,000. The square root is about 872. Check: 872^2 = 760,384, so the total is about USD 872 million. Closest option is 855? Recheck: 855^2 = 731,025, versus 872^2; no option matches exactly, so option 855 is the nearest only by approximation and the other options are further away (780 corresponds to assuming zero correlations between all, sqrt(490,000)=700, not 780).

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