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Borina · 2022年06月10日

为什么最后求VAR的时候要乘以数量150

  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。

是不是可以理解为t=0时，VAR= −μ+2.33×σ  求出来的是一个单位的组合即（2/3A+1/3B）的VAR，要求150个单位的组合的VAR就要*150？也就是VAR符合homogeneity即齐次性

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1 个答案

品职答疑小助手雍 · 2022年06月11日

同学你好， 这个扯到homogeneity勉强也算是吧。

其实是一个是百分比的var，一个是$var。百分比的var乘以资产总数就可以获得dollar var。

当然能这么乘也和homogeneity算是有关系。

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