[ 2009 FRM Sample Exam ] Investment Management Q6

Investment, liability, expected, between, annual

6. Company XYZ's pension fund has liabilities of USD 100 million and assets of USD 120 million. The annual growth of the liabilities has an expected value of 5% with 3% volatility. The annual return of the assets has an expected value of 8% with 12% volatility. The correlation between asset return and liability growth is 0.3. What is the 95% surplus-at-risk?

USD 27.6 million

USD 22.7 million

USD 13.8 million

USD 18.1 million

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发表于 2009-6-13 11:30 | 只看该作者

Correct answer is D

A is incorrect. This solution incorrectly uses 2.33 as the 95% multiplier instead of 1.645. This answer is the 99% surplus-at-risk. fficeffice" />

B is incorrect. This solution incorrectly excludes the expected surplus growth of USD 4.6 million ( = -100 * 0.05 + 120 * 0.08).

C is incorrect. This solution incorrectly sets the 95% surplus-at-risk equal to the standard deviation of surplus growth.

D is correct. The expected surplus growth is -100 * 0.05 + 120 * 0.08 = USD 4.6 million. The variance of surplus growth is -100^2 * 0.03^2 + 120^2 * 0.12^2 + 2 * 100 * 120 * 0.3 * 0.03 * 0.12 = USD 190.44 million, and the standard deviation is USD 13.8 million. Therefore, the 95% surplus-at-risk is -1 * (4.6 - 1.645 * 13.8) = USD 18.1 million.