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杨小洋洋 · 2020年10月19日

问一道题:NO.PZ201512181000007204

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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.

为什么5%对应的是1.65而不是1.96呢?

1 个答案
已采纳答案

星星_品职助教 · 2020年10月19日

同学你好,

1.65是正态分布下,90%的置信区间对应的关键值。也就是说1.65对应的significance level是10%,这10%是两侧尾巴的面积的加总,即单尾面积是5%。

同理,1.96是正态分布下,95%置信区间对应的关键值,即单侧面积是2.5%。

所以对于本题而言,5% VaR意思是左尾单尾面积为5%,这种情况对应的是1.65,而不是1.96、