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金融民工阿聪 · 2021年01月24日

怎么算的组合的标准差是19.15%的？

  1. FRM II
  2. Market Risk Measurement And Management

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。

怎么算的组合的标准差是19.15%的？

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已采纳答案

袁园_品职助教 · 2021年01月25日

直接带公式算

σP = 根号下（wA^2 * σA^2 + wB^2 * σB^2 + 2* wA * wB * σA * σB * correlation）

wA = 100/(100+50) = 2/3

wB = 50/(100+50) = 1/3

σA = 25%

σB = 20%

correlation = 0.2

你自己算一下，是19.15%

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