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和棋 · 2020年08月06日

问一道题：NO.PZ2016070202000021

  1. FRM II
  2. Market Risk Measurement And Management

问题如下：

A trading book consists of the following two assets, with correlation of 0.2.

How would the daily VAR at the 99% level change if the bank sells $50 worth of A and buys $50 worth of B? Assume a normal distribution and 250 trading days.

选项：

A.

0.2286

B.

0.4571

C.

0.7705

D.

0.7798

解释：

We compute first the variance of the current portfolio. This is (100×0.25)2+(50×0.20)2+2×0.2(100×0.25)(50×0.20)=825{(100\times0.25)}^2+{(50\times0.20)}^2+2\times0.2{(100\times0.25)}{(50\times0.20)}=825 VAR is then sqrt825×2.33250=4.226sqrt{825}\times\frac{2.33}{\sqrt{250}}=4.226 The new portfolio has positions of $50 and $100, respectively. The variance is  (50×0.25)2+(100×0.20)2+2×0.2(50×0.25)(100×0.20)=656.25{(50\times0.25)}^2+{(100\times0.20)}^2+2\times0.2{(50\times0.25)}{(100\times0.20)}=656.25 VAR is then 3.769 and the difference is -0.457. The new VAR is lower because of the greater weight on asset B, which has lower volatility. Also note that the expected return is irrelevant.

在之前的讲解中求协方差的公式一般是用权重百分比来计算的。我请问下如果这道题为什么不直接带权重进去计算呢，在未改变前权重w1是33%、w2是66%

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1 个答案

品职答疑小助手雍 · 2020年08月06日

嗨，从没放弃的小努力你好：


都可以，结果上来说是一样的，个人来说，我习惯用金额的这种，毕竟如果用权重的话可能还有近似的问题。


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0.4571 0.7705 0.7798 We compute first the varianof the current portfolio. This is (100×0.25)2+(50×0.20)2+2×0.2(100×0.25)(50×0.20)=825{(100\times0.25)}^2+{(50\times0.20)}^2+2\times0.2{(100\times0.25)}{(50\times0.20)}=825(100×0.25)2+(50×0.20)2+2×0.2(100×0.25)(50×0.20)=825 Vis then sqrt825×2.33250=4.226sqrt{825}\times\frac{2.33}{\sqrt{250}}=4.226sqrt825×250 ​2.33​=4.226 The new portfolio hpositions of $50 an$100, respectively. The varianis  (50×0.25)2+(100×0.20)2+2×0.2(50×0.25)(100×0.20)=656.25{(50\times0.25)}^2+{(100\times0.20)}^2+2\times0.2{(50\times0.25)}{(100\times0.20)}=656.25(50×0.25)2+(100×0.20)2+2×0.2(50×0.25)(100×0.20)=656.25 Vis then 3.769 anthe fferenis -0.457. The new Vis lower because of the greater weight on asset whihlower volatility. Also note ththe expectereturn is irrelevant.求variance为什么能直接代入value呢，应该带入资产比例吧？因为求var是用return去减z＊σ

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