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Archie · 2022年05月09日

次可加性

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).

老师您好,我想知道var在什么情况下满足次可加性

1 个答案

品职答疑小助手雍 · 2022年05月09日

同学你好, 一般情况下,比如你用参数法算的var都是满足次可加性的,上课时候和本题用了一个比较极端的例子说明了非参数法下不满足次可加性的情况。