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比如世界 · 2020年03月17日

问一道题：NO.PZ2020011303000068

  1. FRM I
  2. Valuation And Risk Models

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?

选项：

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.

麻烦老师具体讲解一下这道题的解题过程，谢谢

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小刘_品职助教 · 2020年03月18日

同学你好，

解答过程如下，有点尾差。

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NO.PZ2020011303000068问题如下Consir a position consisting of a US10,000 investment in asset X ana US20,000 investment in asset Y. Assume ththe ily volatilities of X anY are 1% an2% anththe coefficient of correlation between their returns is 0.3. Whis the five-y Vwith a 97% confinlevel? The stanrviation of the ily changes in the assets are (in US 100 an400. The stanrviation of the ily change in the portfolio is (100^2+400^2+2×100×400×0.3)^0.5=440.5The stanrviation of the five-y change is the square root of 5 multipliethe one-y stanrviation, whiis US984.9. The 97% Vis 1.88 times this, whiis US1852.4. 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llar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=440.55天97%的VAR=440.5*(5)^0.5*1.88=1852.4 老师好，1、黑线上半部分我哪里想的不对吗？2、答案的解析，也就是黑线下半部分，我不明白为什么V（X+Y）就直接用100和400来算了，我明白100和400是怎么来的哈，但是100和400只是资产价值啊，100^2难道就相当于V（X）？400^2相当于V（Y）？cov（X，Y）相当于0.3*100*400？不懂答案的含义是什么意思，100就是西格玛X？400就是西格玛Y？3、如果用excel计算的话，有概率计算分位点是什么函数？有分位点计算累计概率又是什么函数呢

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