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Danlei · 2021年10月27日

损失9对应的权重是怎么理解呢？

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2020011303000054

问题如下：

previous question：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 specified in the previous question. 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?

选项：

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

9对应的权重是否可以为（0.9949-0.95）/（0.9949-0.9409）呢？

最终计算得出的ES=20*0.0009+13*0.0042+9*（0.9949-0.95）/（0.9949-0.9409）=7.556


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2 个答案

李坏_品职助教 · 2021年10月28日

嗨，努力学习的PZer你好：


9是正好是一个亏了10m，一个赚了1m。5%是所有极端loss的概率，用5%减去更高的loss的概率就是9的权重，但是也要除以0.05，原因如下。


ES要算的是在超出VaR阈值的损失里面，所有极端损失的均值。这是一个条件概率，不是P（AB），而是P（A|B）= P(AB) / P(B)，P（B）就是var的0.05的概率。要分别用每一个Loss的发生概率去除以0.05从而求得条件概率。



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李坏_品职助教 · 2021年10月28日

嗨，爱思考的PZer你好：


损失9的意思是有一个项目损失了10m，另一个赚了1m。有两种可能：第一个项目赚，第二个项目亏，或者反过来。


所以概率就是2* 0.03 * 0.9 = 0.054

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Danlei · 2021年10月28日

损失9对应的概率我理解，但是在计算ES时，对应的权重怎么理解呢？麻烦老师看下我之前问题中写的计算方式，这种思路问题出在哪里呢？

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