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ralph318 · 2021年10月22日

为什么最后要除以0.05？不是每种损失的算术平均吗？

  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

为什么最后要除以0.05？不是每种损失的算术平均吗？

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1 个答案

李坏_品职助教 · 2021年10月22日

嗨，努力学习的PZer你好：


这里的0.0009, 0.0042概率，是损失占所有收益率分布的情况。


我们需要求的ES是在超过了VaR的那些损失里，所有损失的平均数。 除以0.05是为了把5%的显著性水平剥离出去。


这个原理类似于贝叶斯公式：P（A|B） = P(AB) / P (B)， B可以看成是VaR的阈值5%


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