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Fair · 2022年01月24日

不明白解题思路和t分别为0和1的意思。

  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。

这一题的思路不太明白，是先求组合的u和σ对吧，组合的u就是各自的权重乘以对应的u相加，但是组合的σ是怎么求出来的呢？然后t分别=0和1，这个又是什么意思？

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1 个答案

DD仔_品职助教 · 2022年01月24日

嗨，爱思考的PZer你好：


同学你好，


t=0时刻是变化前的头寸，A=100，B=50.

A的权重是2/3， B是1/3.


t=1是变化后的头寸，银行卖了50的A，买了50的B，A=50，B=100.

A的权重是1/3， B是2/3.


根据权重的变化，可以求出变化前与变化后的组合σ：

组合的σ=A的权重^2*σA^2+B的权重^2*σB^2+2*A的权重*B的权重*σA*σB*相关系数。

题目给的σ是年的，我们求出来的组合σ也是年华的，但是题目让我们求的是daily的，σ根据平方根法则计算，dailyσ=年的σ/根号下250天，因为一年250个交易日。


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