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,
95%ES=[0.0009×20+0.042×13+(0.05-0.0009-0.0042)×9]/0.05=9.534
0.09%的概率损失会超过20,0.42%的概率损失会超过13,5%的概率损失会超过9。
加权平均的话,就是这三种损失的情况总概率是5%
那损失20的概率是0.09%,损失13的概率是0.42%-0.09%=0.33%,损失9的概率是5%-0.42%=4.58%
所以我理解应该用这个概率求平均呀,为啥答案13也是用0.42%加权的。
另外一个问题,我对于-6的prob的是0.49%应该怎么理解有一点不明白,就画了了一个图。请老师帮忙看看这样的理解是否正确。