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Elsa陆艳 · 2022年03月13日

还是没有很懂这个题

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2020011303000053

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. What are (a) the VaR and (b) the expected shortfall when the confidence level is 95% and the time horizon is one year?

选项：

解释：

VaR is USD 3 million. Expected shortfall (USD) is 10 × 0.6 + 3 × 0.4 = 7.2.

第一问：95%的VAR的损失为什么是3million？不是10milion？

第二步的ES也没有看懂怎么计算的，可以麻烦老师详细讲一下吗？

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李坏_品职助教 · 2022年03月13日

嗨，努力学习的PZer你好：


  1. 这道题var就是找到对应95%的损失。你从最乐观情况的概率开始累加，10milliion对应的损失概率是90% + 3% = 93%，还不够95%的阈值，所以我们需要用最差的那-10 million作为95%的var.
  2. ES是指的损失超过95% var那部分损失的数学期望（均值），由于损失超过95%的概率就是1-95% = 5%，而-10 million的概率只有3%，这个3%在5%里面占了60%，另外的40%只好用-3million损失来填补，所以ES就是10 × 0.6 + 3 × 0.4 = 7.2

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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