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wuzx · 2022年03月27日

9.534怎么算出来的

  1. FRM I
  2. Valuation And Risk Models

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：

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.

The VaR is 9 and ES is

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

老师，看了前面所有回答还是不明白es的为什么这样算？麻烦老师在讲一下

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1 个答案

DD仔_品职助教 · 2022年03月28日

嗨，从没放弃的小努力你好：


同学你好，

95%的ES，及尾部5%数据取平均

loss20，占比0.09%

loss13，占比0.42%

loss9，占比超过5%，所以只占尾部5%的(0.05-0.0009-0.0042)=4.49%

尾部平均=（20*0.09%+13*0.42%+9*4.49%）/5%=9.534

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努力的时光都是限量版，加油！

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