surplus的方差从哪来的？

问题如下：

SkyLine Airways has a defined benefit pension scheme with assets of $165 million and liability of $150 million. The annual growth of the liabilities is expected to be 4.5% with 2.4% volatility. The annual return on the pension assets has an expected value of 7.8% with 12% volatility. The correlation between asset return and liability growth is 0.35. What is the 95% surplus at risk for SkyLine?

选项：

A.$24.97million B.$54.81million C.$18.84million D.$6.12million

解释：

Expected surplus growth = ($165m × 0.078) - ($150m × 0.045) Expected surplus growth = $12.87m - $6.75m = $6.12m Variance of surplus = 355.104，Standard Deviation = 18.84m Surplus at risk = expected growth in surplus – 1.65 × Standard Deviation of Surplus Surplus at risk = $6.12m - $31.086m = -$24.97m Note: Although it is a negative, it is usually expressed as a positive figure as it is assumed that it is a shortfall.