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PS同学 · 2024年01月30日

请问这里 portfolio 的 volatility 是如何计算的？

  1. FRM II
  2. Market Risk Measurement And Management

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。

No.PZ2018122701000018 (选择题)

来源: 品职出题

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.


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。

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1 个答案

李坏_品职助教 · 2024年01月30日

嗨，努力学习的PZer你好：


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.


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.

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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