Skip to content

FRM Part II · FRM Exam Part II · Integrated Risk Management

A bank's ERM team assesses three business units with stand-alone economic capital of 60, 40 and 20 (USD million). The correlation between each pair of units' losses is 0.5, and capital is assumed to scale like a standard deviation. What is the firm-wide diversified economic capital, and what is the diversification benefit?

Diversified capital is 100 million and the benefit is 20 million. Combined variance is 3,600+1,600+400 plus 2×0.5×(2,400+1,200+800), which gives 10,000, so the square root is 100. The stand-alone sum is 120, leaving a 20 million diversification benefit.

  1. ADiversified capital 100.0; benefit 20.0Correct
  2. BDiversified capital 90.0; benefit 30.0
  3. CDiversified capital 120.0; benefit 0
  4. DDiversified capital 120.0 is the sum, so the benefit equals the correlation 0.5 times 120

Explanation

Variance = 60²+40²+20² + 2(0.5)(60·40+60·20+40·20) = 3600+1600+400 + (2400+1200+800) = 5600+4400 = 10000, so capital = 100. Sum of stand-alone = 120, so benefit = 20. Option 90 ignores the correlation structure and 120 assumes perfect correlation.

Did you get it right without looking?

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

Practise Integrated Risk ManagementFree diagnostic mock

More Integrated Risk Management questions