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徐威廉 · 2024年04月21日

完全不懂

  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?

选项：

解释：

有一个项目，3%的概率会损失10m，7%损失3m，90%概率会获得1m，假设这俩投资都是独立相同的，求95%置信区间下1年的VaR和ES？

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.

95%VaR=9

95%ES=[0.0009×20+0.042×13+(0.05-0.0009-0.0042)×9]/0.05=9.534

看了解释也不知道再算什么？

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品职答疑小助手雍 · 2024年04月21日

同学你好，95%的置信度水平，意味着我们需要去找尾部5%对应的最大亏损。前两个prob加起来也不到5%，算到第三个Loss恰好能大于5%，所以var就是这个阈值：9。

然后根据尾部5%的概率分别对应的损失值就ES即可。

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