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上小学 · 2023年03月11日

尾部平均是简单平均法何时又变成加权平均了?

NO.PZ2020011303000054

问题如下:

A one-year project has a 3% chance of losing USD 10million, a 7% chance of losing USD 3 million, and a 90% chance of gaining USD 1 million.

Suppose that there are two independent identical investments with the properties.

What are (a) the VaR and (b) the expected shortfall for a portfolio consisting of the two investments when the confidence level is 95% and the time horizon is one year?

解释:

有一个项目,3%的概率会损失10m7%损失3m90%概率会获得1m假设这俩投资都是独立相同的,求95%置信区间下1年的VaRES

Losses (USD) of 20, 13, 9, 6, 2, and 2 have probabilities of 0.0009, 0.0042, 0.054, 0.0049, 0.126, and 0.81, respectively.

95%VaR=9

95%ES=[0.0009×20+0.042×13+(0.05-0.0009-0.0042)×9]/0.05=9.534

根据讲义为简单平均法。为何此题目又采用加权平均?那么尾部损失平均到底用简单平均还是加权平均?还是有何例外?谢谢

2 个答案

DD仔_品职助教 · 2023年03月14日

嗨,努力学习的PZer你好:


尾部数据取平均是将尾部数据作为100%来取平均的,

尾部5%损失有:

20,占比0.0009/0.05=0.018;

13,占比0.0042/0.05=0.084

9,占比1-0.018-0.084=0.898,或者可以用答案的方法(0.05-0.0009-0.0042)/0.05=0.898

尾部数据去加权平均=20*0.018+13*0.084+9*0.898=9.534

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

DD仔_品职助教 · 2023年03月11日

嗨,从没放弃的小努力你好:


同学你好,

讲义里描述的ES是尾部损失取期望值,期望的计算指的就是加权平均,简单的平均法可以认为是权重都相同的加权平均,所以说的更准确点:ES的计算是尾部损失取加权平均。

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努力的时光都是限量版,加油!

上小学 · 2023年03月14日

您好,我明白是加权平均了。不过我又听了基础客,在ES这块确实讲的按照简单算术平均。不过现在我纠正为加权平均。另一个问题产生了,上述解题公式看不懂,9的概率为啥不是0.54?(0.05-0.0009-0.0042)×9 这个是啥意思? 为什么又除以一个0.05?95%ES=[0.0009×20+0.042×13+(0.05-0.0009-0.0042)×9]/0.05 加权平均是数字乘以概率,为什么还需要除以0.05?这个是什么意思?期望公式为具体数字乘以概率就OK了

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