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
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
标准正态分布表是单尾？
比如置信区间是90%，
则查表应该找 1-10%/2=95%的点就是1.65？？？？？
