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王楚溪 · 2020年08月19日

请问VaR=9是怎么算出来的？

  1. FRM I
  2. Valuation And Risk Models

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

看解析不太懂，麻烦老师讲一下，谢谢

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1 个答案

品职答疑小助手雍 · 2020年08月20日

嗨，爱思考的PZer你好：


解析里求的是两个同样的投资会产生的结果的情况，以及每种情况对应的概率，然后从大到小排序（收益的大小，但是解析里写的是损失，所以其实应该从小到大排：-2,2,6,9,13,20），要选出累计概率超过95%的第一个数就是var了（0.81+0.126+0.0049+0.054到这里累加超过95%）。


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