expected surplus 的公式感到有疑问

问题如下：

PZ has set up a defined benefit pension scheme with $150m in assets and $135m in liabilities.

We assme that:

The expected annual return of pension assets is 7.5percent. and the volatility is 10percent..

Debt is expected to grow at 5 percent a year and fluctuate at 4.5 percent.

The correlation coefficient between asset income and the growth of liability is 0.7.

Calculate the 95% surplus at risk of the pension.

选项：

A.

$14.62 million.

B.

$28.37 million.

C.

$20.12 million.

D.

$7.83 million.

解释：

A is correct.

考点：pension plan surplus at risk计算

解析：

第一步: 计算surplus 的预期增长

Expected surplus growth = growth in asstes – growth in liabilities

Expected surplus growth = ($150m x 0.075)-($135m x 0.05)

Expected surplus growth = $11.25m-6.75m= 4.5m

2019042401000043
第一步: 计算surplus 的预期增长
Expected surplus growth = growth in asstes – growth in liabilities
Expected surplus growth = ($150m * 0.075)-($135m *0.05)
Expected surplus growth = $11.25m-6.75m= 4.5 m

第二步: 计算组合的方差和标准差
Variance of surplus = (150*0.1)^2 + (135*0.045)^2 – 2*(150*0.1*135*0.045*0.7) = 134.33
Volatility of surplus =11.59

第三步：计算组合的VaR
Surplus at risk = 4.5 – 1.65*11.59 = -14.62 m