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

A firm has two divisions. Division A has expected profit of USD 40 million and a profit standard deviation of USD 30 million. Division B has expected profit of USD 60 million and a standard deviation of USD 40 million. The correlation between profits is 0.25. What is the standard deviation of combined profit, and what is the combined expected profit-to-standard-deviation ratio (approximately)?

Combined variance is 900 + 1,600 + 2(0.25)(30)(40) = 3,100, giving a standard deviation of about USD 55.7 million. With combined expected profit of USD 100 million, the ratio is about 1.80. Simply adding the standard deviations would overstate risk by ignoring diversification.

  1. AUSD 70.0 million; ratio 1.43
  2. BUSD 50.0 million; ratio 2.00
  3. CUSD 55.7 million; ratio 1.80Correct
  4. DUSD 47.9 million; ratio 2.09

Explanation

Variance = 30^2 + 40^2 + 2(0.25)(30)(40) = 900 + 1,600 + 600 = 3,100. Standard deviation = 55.68. Expected profit is 100, so ratio = 100/55.68 = 1.80. Option A ignores diversification by summing standard deviations (70). Option D wrongly subtracts the covariance term (2,500-... gives 47.9 scale error).

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