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Jin WANG · 2020年06月03日

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:

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.

两个组合均值不同啊,一个是20 一个是25. 这道题是直接假设均值为0了么?

1 个答案

袁园_品职助教 · 2020年06月04日

同学你好!

这道题答案不是很严谨,应该还要把均值代进去计算的(不过这道题算出来结果最接近应该还是选B)

考试的时候如果考到,建议先把均值值算进去,看一下有没有答案匹配,没有的话再按这种方法计算。