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186****8680 · 2023年06月01日

老师，怎么知道是单尾，用1.645呢？

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2018122701000017

问题如下：

The annual mean and volatility of a portfolio are 10% and 40%, respectively. The current value of the portfolio is GBP 1,000,000. How does the 1-year 95% VaR that is calculated using a normal distribution assumption (normal VaR) compare with the 1-year 95% VaR that is calculated using the lognormal distribution assumption (lognormal VaR)?

选项：

A.

Lognormal VaR is greater than normal VaR by GBP 130,400

B.

Lognormal VaR is greater than normal VaR by GBP 175,900

C.

Lognormal VaR is less than normal VaR by GBP 130,400

D.

Lognormal VaR is less than normal VaR by GBP 175,900

解释：

C is correct.

考点 ： Parametric Estimation Approaches

解析：Normal VAR=0.1-(1.645×0.4）=0.558，

Lognormal VAR=1-exp[0.1-(1.645×0.4)]=0.4276

Hence, lognormal VaR is smaller than Normal VaR by 13.04% per year. With a portfolio of GBP 1,000,000, this translates to GBP 130,400 .

老师，怎么知道95%是单尾，用1.645呢，我用的1.96

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2 个答案

品职答疑小助手雍 · 2024年09月26日

单尾和双尾的使用主要在于使用的目的，而不是使用的数据。

比如return，在计算风险度量VAR之类的时候，只看大的损失那端，所以用单尾。

常规用中心极限定理看一个均值等不等于零，就是要看两端的，也就是双尾。

品职答疑小助手雍 · 2023年06月02日

同学你好，算Var肯定是用单尾的啊，因为var要衡量的是风险，只有最大的损失那端的情况，不用管另一端最大的收益的情况。

比夏 · 2024年09月25日

老师我希望这个问题可以有更详细的解答。 如果我们用正态分布的模型，考虑的是Return的分布，return的分布为什么不能是双尾的？ 我越做题越发现很多题目都会涉及用单尾还是双尾分布的问题。

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