问一道题：NO.PZ2016070202000021

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：

0.2286

0.4571

0.7705

0.7798

解释：

We compute first the variance of the current portfolio. This is ${(100\times0.25)}^2+{(50\times0.20)}^2+2\times0.2{(100\times0.25)}{(50\times0.20)}=825$ VAR is then $sqrt{825}\times\frac{2.33}{\sqrt{250}}=4.226$ The new portfolio has positions of $50 and $100, respectively. The variance is ${(50\times0.25)}^2+{(100\times0.20)}^2+2\times0.2{(50\times0.25)}{(100\times0.20)}=656.25$ 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.

为什么不考虑return，retur在两个portfolio 中都有变化啦

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小刘_品职助教 · 2020年10月15日

同学你好，

你说的是对的，严格意义上来说，是要加上return的，加进去之后因为计算的是daily VAR所以影响会十分有限。

针对考试而言，daily的题，先算variance的变化基本都可以快一些找到答案，找不到答案的话再考虑上return的影响。

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为什么不考虑均值呢？资产比例发生变化，均值也变化了呀

2020-10-02 22:10 1 · 回答

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

2020-09-20 15:06 1 · 回答

可以用后面讲的组合的VAR公式来算这一道题吗？

2020-09-17 15:37 1 · 回答

老师好，这道题如果考虑均值，计算过程是否是以下截图步骤？

2020-08-29 18:07 2 · 回答

问一道题：NO.PZ2016070202000021

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