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Lisa Zhang · 2022年09月01日

ES计算

  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

ES的计算不是应该是算数平均吗？为什么要去成各自的概率

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2 个答案

DD仔_品职助教 · 2022年10月17日

嗨，从没放弃的小努力你好：


中括号里的加权是认为尾部数据是100%，但是尾部数据5%，所以还要除上5%。

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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 · 2022年09月01日

嗨，爱思考的PZer你好：


同学你说的平均数是算术平均值，也就是各个数据相加除个数，这个前提假设是每个数据的权重相同，当每个数据权重不同的时候就要用加权平均，也就是每个数据*发生的概率之后再相加。

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努力的时光都是限量版，加油！

Miracle_ · 2022年10月16日

请问中括号里的不已经是加权平均了吗？为啥还要除以0.05？

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