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Shuangshuang · 2024年05月10日

麻烦写下知识点和过程

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

1 个答案
已采纳答案

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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