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pinzhixiaoguo · 2022年09月13日

请问求组合的标准差，带入的数据具体是什么？

  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。

题目给的产品A的volatility是25%，也就是说A的方差是25%，则A的标准差应该是25%的平方根也就是0.5，才对吧？我怎么就算不出正确答案啊？麻烦助教老师给算一下吧。

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DD仔_品职助教 · 2022年09月14日

嗨，爱思考的PZer你好：


同学你好，你的概念理解错了，在FRM考试中我们认为volatility是标准差不是方差。

同学可以看下下面的计算过程，会更清晰一些。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

kanjani · 2023年02月23日

我记得在CFA考试中volatility是方差啊，两个是反着的？

DD仔_品职助教 · 2023年02月23日

嗨，努力学习的PZer你好：


金融里一般的定义都是：volatility=risk=σ=标准差

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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