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shining · 2024年10月27日

年 VaR 转换成 dailyVaR 的时间点

  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。

题目答案解析是把年收益率和波动率先转化成天再算调整前后的 VaR 为何按照给出的收益率和波动率分别计算出调整前后的年 vaR 再转换成天 VaR 不行呢（计算出的答案接近 C）

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pzqa39 · 2024年10月28日

嗨，努力学习的PZer你好：


波动率是与时间相关的，因此年波动率不能直接用在日 VaR 计算中，而需要进行缩放处理。根据假设波动率随时间以平方根方式缩放，我们需要除以根号下250将年波动率转换为日波动率。

如果直接用年化收益率和波动率计算出年 VaR，然后再按天缩放，会忽略每日的收益变化的非线性效果。因此直接将年 VaR 转换成日 VaR 的误差会较大，而将收益率和波动率先缩放为日水平再计算 VaR 会更精确。

因此，通常我们会将给定的年收益率和波动率转化成日数据，再进行 VaR 计算。直接从年 VaR 转日 VaR 的转换可能会导致不精确的结果。

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