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我们 · 2022年07月14日

计算结果

  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 .

为什么我算不出来0.4276？我算出来的是0.7471



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1 个答案

李坏_品职助教 · 2022年07月15日

嗨，从没放弃的小努力你好：


lognormal var = 1-exp(mean - volatility * Z) = 1- exp(10% - 40% * 1.645)， 注意exp里面的结果是-0.558，你应该是漏掉了负号

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