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13581943293 · 2021年08月30日

请问,老师在课堂上讲99%confident interval,对应的是2.33, 怎么这个图中99%的值是2.58.请帮我梳理一下。谢谢

* 问题详情,请 查看题干

NO.PZ201512181000007204

问题如下:

Based on Exhibit 1, the daily 5% VaR estimate is closest to:

选项:

A.

1.61%

B.

2.42%.

C.

2.69%.

解释:

C is correct. Measuring VaR at a 5% threshold produces an estimated value at risk of 2.69%.
From Exhibit 1, the annual portfolio return is 14.1% and the standard deviation is 26.3%. Annual values need to be adjusted to get their daily counterparts.
Assuming 250 trading days in a year, the expected annual return is adjusted by dividing by 250 and the standard deviation is adjusted by dividing by the square root of 250.
Thus, the daily expected return is 0.141/250 = 0.000564 and volatility is
0 263/ the square root of 250. = 0.016634.
5% daily VaR = E(
Rp) – 1.65σp = 0.000564 – 1.65(0.016634) = –0.026882. The portfolio is expected to experience a potential minimum loss in percentage terms of 2.69% on 5% of trading days.




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已采纳答案

星星_品职助教 · 2021年08月30日

同学你好,

图中并没有找到“这个图中99%的值是2.58”的信息。

但关键值的区别在于单尾的面积

对于VaR而言,只考虑左侧单尾,所以此时99%置信区间对应就是左侧尾部面积为1%。关键值也就是-2.33.

但对于数量中的置信区间而言,全部考虑的都是双尾的情况,所以此时99%的置信区间对应的单尾面积就是两边各为0.5%,此时关键值为±2.58.

同理,

95%的VaR关键值(单尾面积5%)为-1.65。但数量中95%的置信区间(单尾面积2.5%)的关键值为±1.96;90%的置信区间(单尾面积5%)关键值为±1.65