Shuangshuang · 2024年05月10日
NO.PZ2023100703000021
问题如下：
The bank’s trading book consists of the following two assets:
Correlation (A, B) = 0.2
How would the daily VaR at 99% level change if the bank sells 50 worth of asset A and buys 50 worth of asset B?
Assume there are 250 trading days in a year.
选项：
A.0.2286
B.0.4776
C.0.7705
D.0.7798
解释：
The trade will decrease the VaR by 0.4776麻烦写下知识点和过程
pzqa39 · 2024年05月11日
嗨，从没放弃的小努力你好：
t=0，组合由$100A+$50B构成，μP =13.33%, 由年转化为天，13.33%/250=0.0533%.
t=0的时候，A的权重是2/3 （100/150），B的权重是1/3 （50/150），所以σp^2 = (2/3)^2 × 0.25^2 + (1/3)^2 × 0.2^2 + 2×(2/3)×(1/3)×0.2×0.25×0.2 = 0.0367, 所以σP = 0.1915.
σP =19.15%, 由年转化为天, 19.15%/SQRT(250)=1.2111%
daily 99%VaR=（2.33*1.2111%-0.0533%）*$150=$4.1528
t=1，组合由$50A+$100B构成，μP =16.66%, 由年转化为天，16.66%/250=0.0667%.
t=1的时候，A的权重变成了1/3，B的权重变成2/3，所以σp^2 = (1/3)^2 × 0.25^2 + (2/3)^2 × 0.2^2 + 2×(1/3)×(2/3)×0.2×0.25×0.2 = 0.0292, 所以σP = 0.1708.
σP =17.08%, 由年转化为天, 17.08%/SQRT(250)=1.0801%
daily 99%VaR=（2.33*1.0801%-0.0667%）*$150=$3.6749
所以$4.1528-$3.6749=0.4779，最接近的是B选项。
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