[ 2009 FRM Sample Exam ] Investment Management Q6 Investment, liability, expected, between, annual

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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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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.