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Answer: USD -133.4 million
The change in the pension fund's surplus over the 1-year period is calculated by first determining the initial surplus at the end of 2017, which is the difference between the assets and liabilities: \( So = Ao - Lo = 840 million - 450 million = USD 390 million \). Next, the new levels of assets and liabilities at the end of 2018 are calculated after the respective 14.0% decrease in assets and 3.5% increase in liabilities. The new asset value \( A1 \) is \( (1 - 0.14) * 840 = USD 722.4 million \), and the new liability value \( L1 \) is \( (1 + 0.035) * 450 = USD 465.75 million \). The ending surplus for 2018, \( S1 \), is then \( A1 - L1 = 722.4 million - 465.75 million = USD 256.65 million \). The change in surplus for 2018, \( \Delta S \), is the difference between the ending surplus of 2018 and the initial surplus of 2017: \( \Delta S = S1 - So = 256.65 million - 390 million = USD -133.35 million \). Therefore, the correct answer is A. USD -133.4 million, which is a close approximation to the calculated change in surplus.
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At the close of 2017, a US pension fund held assets valued at USD 840 million and liabilities valued at USD 450 million. The assets were entirely invested in equities and commodities, while the liabilities consisted solely of fixed-income obligations. By the end of 2018, the value of the assets had decreased by 14.0%, and the value of the liabilities had increased by 3.5%. There were no changes in the composition of the assets and liabilities throughout the year. Calculate the change in the pension fund's surplus over the 1-year period.
Section: Risk Management and Investment Management
Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition (New York: McGraw-Hill, 2007). Chapter 17 - VaR and Risk Budgeting in Investment Management.
Learning Objective: Recognize the distinctions between the following types of risk: absolute risk, relative risk, policy-mix risk, active management risk, funding risk, and sponsor risk.
A
USD -133.4 million
B
USD -117.6 million
C
USD 256.7 million
D
USD 390.0 million
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