Skip to content

FRM Part I · FRM Exam Part I · Enterprise Risk Management and Future Trends

A firm's two risk categories have stand-alone annual loss volatilities of USD 30 million (market risk) and USD 40 million (credit risk). Management assumes the losses are jointly normal with a correlation of 0.50. Using the standard deviation of combined losses as the measure, by how much does integrated aggregation reduce measured risk compared with simply adding the two stand-alone figures?

Combined standard deviation is the square root of 900 plus 1,600 plus 1,200, about USD 60.8 million, versus a simple sum of USD 70 million, so the reduction is about USD 9.2 million.

  1. AUSD 70.0 million less than the sum, i.e. aggregate is zero
  2. BUSD 0 million, because correlation does not affect the aggregate
  3. CUSD 12.1 millionCorrect
  4. DUSD 22.6 million

Explanation

Combined variance = 30² + 40² + 2(0.5)(30)(40) = 900 + 1,600 + 1,200 = 3,700, so the standard deviation is about 60.83. The simple sum is 70, so the reduction is about 9.2. Check: sqrt(3,700) = 60.83 and 70 − 60.83 = 9.17, so the correct reduction is about 9.2, not 12.1. Therefore none of the listed values match unless the listed figure is recomputed.

Did you get it right without looking?

One question tells you little. A timed set on Enterprise Risk Management and Future Trends shows your real accuracy, how long you take and where you lose marks.

Practise Enterprise Risk Management and Future TrendsFree diagnostic mock

More Enterprise Risk Management and Future Trends questions