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韩潮_ · 2022年07月14日

关于计算公式的疑问

NO.PZ2016071602000003

问题如下:

The AT&T pension fund reports total assets worth $19.6 billion and liabilities of $17.4 billion. Assume the surplus has a normal distribution and volatility of 10% per annum. The 95% surplus at risk over the next year is

选项:

A.

$360 million

B.

$513 million

C.

$2,860 million

D.

$3,220 million

解释:

A is correct. The fund's surplus is the excess of assets over liabilitieswhich $19.6  $17.4 = $2.2 billion. The surplus at risk at the 95% level over one year is, assuming a normal distribution, 1.645 x 10% x $2,200 = $360 million. Answer b. is incorrect because it uses a 99% confidence level. Answers c. and d. are incorrect because they apply the risk to the liabilities and assets instead of the surplus.

为什么计算VAR,本题为Surplus at risk,公式有的时候是=μ*z*σ?有的时候是=|μ-z*σ|?

3 个答案
已采纳答案

李坏_品职助教 · 2022年07月17日

嗨,从没放弃的小努力你好:


那个不是μ,2016071602000003这道题目的μ默认是0,1.645*10%*2.2billion,算的是Z * σ * surplus,


这道题的计算如下:

surplus at risk = (μ - Z* σ) * surplus value = (0 - 1.645*10%) * 2.2billion

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

李坏_品职助教 · 2022年07月16日

嗨,爱思考的PZer你好:


2019042401000043这个题目你看下答案给的也是带负号的,带负号是准确的结果。


只是这个题选项是按照业内习惯给的绝对值,所以要把答案算出来的数字取绝对值。真实考试中根据选项来处理,不可能给你一正一负俩选项的

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

韩潮_ · 2022年07月17日

不是绝对值的问题,绝对值我是理解的。而是一个公式是μ乘以,一个公式是μ减去。

李坏_品职助教 · 2022年07月15日

嗨,努力学习的PZer你好:


surplus at risk是类似于var的概念,本身就是一种极端损失的概念,一般算出来都是负数。带上绝对值是因为有时候按照行业习惯,大家都知道surplus at risk是指的surplus在某个概率下的最小期望值(左尾数值,大概率都是负的),省掉负号只看绝对值。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

韩潮_ · 2022年07月16日

感谢老师解答,但老师可能看错我的问题了 比如本题中,surplus at risk的计算本质上和VAR计算是一样的,但本题计算公式为: μ乘以z乘以σ,即公式surplus at risk=μ*z*σ 但题目NO.PZ2019042401000043中,计算PZ的defined benefit pension的surplus at risk的解答中,计算最后结果的公式却和上面不一样,在这题中计算公式为: |μ减去z乘以σ|,即公式surplus at risk=|μ-z*σ| 上述两题求的东西是一样的,但却用了不一样的公式。 还请老师有空解答一二,谢谢。

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