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梦梦 · 2024年03月03日

有两个问题

  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


老师您好，这是您之前对某个学生的解答，但有两个问题，第一个您帮我看看我的公式有问题吗，我算了很多遍都是2.16%，并不是1.47%。

第二个问题是方法二为什么不计算X资产和Y资产的权重呢？

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2 个答案

pzqa27 · 2024年03月06日

嗨，努力学习的PZer你好：


X占1/3是因为组合中有10000是X，20000是Y。X和Y的占比是根据value的比例来确定的。在第二种计算方法中，X的波动率是10000*1%得到的100，因此在计算过程中实际上是考虑了X的value，因此不用把权重纳入其中。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

pzqa27 · 2024年03月04日

嗨，爱思考的PZer你好：


第一个问题：你没开根号。

第二个问题：权重是按value为权重，因此第二种算法中已经考虑了各个资产对应的value，它算的是美金形式的波动率，所以不用再额外计算权重了。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

梦梦 · 2024年03月06日

“权重是按value为权重，因此第二种算法中已经考虑了各个资产对应的value，它算的是美金形式的波动率，所以不用再额外计算权重了。”这句话还是不太明白，不需要考虑X资产占1/3，Y占2/3了？

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