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，这个“Normal VAR=0.1-(1.645×0.4）=0.558”计算结果应该是负的，-0.558，把-0.558代入Lognormal VAR=1-exp[0.1-(1.645×0.4)]=0.4276，结果是正的，那两个相减，应该没有答案啊？
另外，为什么有时候计算VAR是Z*σ，有时候是μ-Z*σ呢？
