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上小学 · 2023年03月11日

每日波动计算正确，但是为何不使用 Z乘 每日波动呢？这个公式不适用吗？为啥不能用？

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2020011303000068

问题如下：

Consider a position consisting of a USD 10,000 investment in asset X and a USD 20,000 investment in asset Y. Assume that the daily volatilities of X and Y are 1% and 2% and that the coefficient of correlation between their returns is 0.3. What is the five-day VaR with a 97% confidence level?

解释：

The standard deviation of the daily changes in the assets are (in USD) 100 and 400. The standard deviation of the daily change in the portfolio is (100^2+400^2+2×100×400×0.3)^0.5=440.5

The standard deviation of the five-day change is the square root of 5 multiplied by the one-day standard deviation, which is USD 984.9. The 97% VaR is 1.88 times this, which is USD 1852.4.

题目问：有一个头寸包含10,000$的资产X，20,000$的资产Y，假设每日波动是1%和2%，相关系数是0.3，求5天97%的VaR?

每日波动的dollar值：X=10,000*1%=100，Y=20,000*2%=400

组合每日的波动=(100^2+400^2+2×100×400×0.3)^0.5=440.5

5天97%的VAR=440.5*(5)^0.5*1.88=1852.4

U 减去Z 乘波动公式不能适用吗？和例题一样啊。反而解题公式没看到过。请详细说说。为啥不能用讲义上的公式，十分困惑。多谢

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DD仔_品职助教 · 2023年03月11日

嗨，从没放弃的小努力你好：


同学你好，

这题没写均值是多少，这种情况下我们金认为均值μ(ps.均值的符号是μ不是U)为0。

这道题是组合求VaR，给出了组合中两个资产的σ情况，这种题可以先求组合sigma，然后再dollar化求VaR。或者先求组合%形式的VaR再求组合的VaR都行。具体喜欢哪种方法看自己，下面是这两种解法的具体步骤：

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加油吧，让我们一起遇见更好的自己！

上小学 · 2023年03月14日

这个题目解释的非常清楚，多谢了

DD仔_品职助教 · 2023年03月14日

嗨，努力学习的PZer你好：


加油呢！!

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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