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朵朵0927 · 2020年02月02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.

请老师能指教下,什么时候用权重计算什么时候直接计算求?有什么方法辨别并且快捷计算吗?

1 个答案

品职答疑小助手雍 · 2020年02月04日

同学你好,不考虑收益的情况,这两种算法我觉得看个人习惯,结果一样而且计算量都差不多。我个人喜欢直接计算,感觉比较直观一些。