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 portfolio’s 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