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壹贰三番 · 2023年04月22日

A为什么是at least 不是at most

NO.PZ2021101401000017

问题如下:

Galic, who is 62 years old, decides to allocate C$2 million (representing 10% of his net worth) to an account with GWP and stipulates that portfolio assets be restricted exclusively to domestic securities. Although GWP has not backtested its strategies with such a restriction, it has backtested its strategies using a global index that includes domestic securities. Rom shows the following risk measures to Galic for three factor portfolios.


Which of the following conclusions of Exhibit 1 is least likely to be true?

选项:

A.

5% of the time, losses from Factor 1 would be at least 6.49%.

B.

When the VaR is exceeded in Factor 1, we should expect an average loss of 15.73%.

C.

5% of the time, losses from Factor 2 are likely to be worse than losses from Factor 1.

解释:

C is correct. The VaR metrics in Exhibit 1 show that 5% of the time, losses will be at least 6.49% and 0.77%, respectively, for Factor 1 and Factor 2. The CVaR metrics in Exhibit 1 show that the weighted average of all loss outcomes that exceed the VaR loss are 15.73% and 4.21% for Factor 1 and Factor 2, respectively. Thus, A is true because it correctly defines VaR, and B is true because it correctly defines CVaR, whereas C is untrue because both VaR and CVaR are lower for Factor 2 than Factor 1.

A为什么是at least 不是at most

1 个答案

星星_品职助教 · 2023年04月23日

同学你好,

如果从5%的角度出发,VaR就是最小损失,因为VaR左侧尾部的其他损失都比它大;

如果从95%的角度出发,VaR就是最大损失,因为所有VaR右侧的损失都比它小,从0开始右侧都已经是盈利了。

本题A选项是从5%的角度考察的,所以VaR=最小损失,也就是至少(at least)损失VaR=6.49%这么多,其余损失都比6.49%大。所以描述是正确的。

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