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152****9033 · 2024年10月09日

能不能直接计算(50A-50B)组合

NO.PZ2018122701000018

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:

B is correct.

考点 Parametric Estimation Approaches

解析 The trade will decrease the VaR by 0.4776。

易错点:求daily VaR,但题干给的是annual return。

t=0,组合由$100A+$50B构成,μP =13.33%, 由年转化为天,13.33%/250=0.0533%.

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%.

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。

能不能直接计算(50A-50B)组合的均值和标准差,然后再算VAR

1 个答案

pzqa39 · 2024年10月10日

嗨,努力学习的PZer你好:


不可以的,算不出来答案。题目要求的是考虑组合中的资产比例调整,而不是纯粹的两者相减,直接把两者相减当成一个组合,其中的均值和波动性不能反映整体组合的变化。

 

VaR 计算通常是基于整个投资组合的价值变化来衡量的。在题目中,资产 A 和 B 的权重从最初的 $100A + $50B 改变为 $50A + $100B,组合的均值和波动性都随着权重的变化而发生变化。直接使用50A−50B 组合会忽略权重变化对整个组合波动性的影响,从而得出的 VaR 结果不正确。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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