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上小学 · 2023年04月05日

请问ES等于9,9534是怎么计算出来的?谢谢

NO.PZ2020011303000055

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.

Situation 1:We can calculate that the VaR is USD 3 million and the expected shortfall (USD) is 7.2 when the confidence level is 95% and the time horizon is one year.

Situation 2:Suppose that there are two independent identical investments with the properties.We can calculate:


The VaR is 9 and ES is 9.534.

Q:Check whether (a) VaR or (b) expected shortfall satisfy the subadditivity axiom for a coherent risk measure for the investments.

解释:

VaR does not satisfy the subadditivity condition because the VaR for two portfolios combined (9) is greater than the sum of the VaR for each portfolio individually(i.e.,9>3+3). Meanwhile, expected shortfall does satisfy the condition because its value for the two portfolios combined is less than the sum of each portfolios expected shortfall (i.e.,9.534 < 7.2 + 7.2).

在两个问题中,VaRES是否满足次可加性?

VaR并不满足次可加性,ES满足次可加性。

ES计算不清楚 不同的例子计算方法不同,完全不明白了。

1 个答案
已采纳答案

pzqa27 · 2023年04月06日

嗨,爱思考的PZer你好:


ES就是VaR的平均了,那就算平均好了,已知95%的VaR是9,在这5%种0.0009的概率是20,0.0042的概率是13,那么只有0.898的概率是9,然后随机变量求期望就是0.0009*20+13*0.0042+0.898*9=9.534.

这个题并不需要我们自己算,已经给出来了

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虽然现在很辛苦,但努力过的感觉真的很好,加油!