问一道题：NO.PZ2016070202000021 [ FRM II ]

B.

0.4571

C.

0.7705

D.

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.