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wilsonxu · 2021年08月21日

老师这个一阶导和二阶导不能混用还可以在详细说明一下吗？

  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。

不能，有μ的时候不能这么算。 先求俩var，再算组合是建立在假设了μ等于0的基础上的，有了μ的话两个var求组合var的那个公式就不成立了，因为一阶导和二阶导不能混用。
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AliciaLi · 2022年01月18日

σP =19.15%,这里怎么算出来的， 能详细列一下计算吗， 我用了Varp^2=(W1^2 * Var1^2)+(W2^2 * Var2^2)+0.2*W1*W2*Var1*Var2 但是得不到正确的数字

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李坏_品职助教 · 2021年08月21日

嗨，努力学习的PZer你好：


当μ不为0的时候，我们就必须先求资产组合的σ，再求组合的var。因为这个时候μ会影响资产组合的μ，如果直接把两个资产的var组合起来会不准确。


这里应该和导数没有什么关系。



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李坏_品职助教 · 2022年01月18日

嗨，爱思考的PZer你好：


表格里的volatility指的是标准差。σa = 0.25, σb = 0.2. 因为题目设定A是100，B是50，所以Wa = 100/150 = 2/3,Wb = 1/3


σp^2 = (（2/3）^2 * 0.25^2 ) + (（1/3）^2 * 0.2^2) + 2*（2/3）* （1/3） * correlation * 0.25 * 0.2 =  0.03667. 所以σp = 0.1915

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