【風險管理與投資管理】FRM">FRM二級每日一題
At the end of 2007, Chad & Co.’s pension had USD 350 million worth of assets that were fully invested in equities and USD 180 million in fixed-income liabilities with a modified duration of 14. In 2008, the wide spread effects of the subprime crisis hit the pension fund, causing its investment in equities to loss 50% of their market value. In addition, the immediate response from the government – cutting interest rates – to salvage the situation, caused bond yields to decline by 2%. What was the change in the pension fund’s surplus in 2008?
- USD -55.4 million
- USD -124.6 million
- USD -225.4 million
- USD -230.4 million
Answer: C
The change in the pension fund’s surplus for the year 2008 is equal to the initial surplus S0 at the end of 2007 less the ending surplus S1 at the end of 2008.
The initial surplus is calculated as S0 = 350 – 180 = 170.
Next we have to calculate the surplus at the end of 2008. Given the 50% decline in the equity market, the new level of assets A1 at the end of 2008 is equal to:
(1 – 0.5)×350 = 175
The new level of liabilities L1 can be calculated as:
L1 = (1 – 14×(-0.02))×180 = 230.4
Therefore the 2008 surplus S1 is equal to A1 – L1 = 175 – 230.4 = -55.4 (which implies the pension fund is actually in a deficit situation at the end of 2008). The change in surplus for 2008 is hence S1 – S0 = -55.4 – 170 = -225.4 million.
