提示一点答案

问题如下：

A risk manager is estimating the market risk of a portfolio using both the arithmetic returns with normal distribution assumptions and the geometric returns with lognormal distribution assumptions. The manager gathers the following data on the portfolio:

• Annualized average of arithmetic returns: 12%

• Annualized standard deviation of arithmetic returns: 30%

• Annualized average of geometric returns: 11%

• Annualized standard deviation of geometric returns: 41%

• Current portfolio value: EUR 5,200,000

• Trading days in a year: 252

Assuming both daily arithmetic returns and daily geometric returns are serially independent, which of the following statements is correct?

选项：

A.

1-day normal 95% VaR = 3.06% and 1-day lognormal 95% VaR = 4.12%

B.

1-day normal 95% VaR = 3.57% and 1-day lognormal 95% VaR = 4.41%

C.

1-day normal 95% VaR = 4.12% and 1-day lognormal 95% VaR = 3.57%

D.

1-day normal 95% VaR = 4.46% and 1-day lognormal 95% VaR = 4.49%

解释：

中文解析：

1-day normal 95% VaR = -[(0.12/252)-1.645*0.30/sqrt(252)] = 3.06%

1-day lognormal 95% VaR = 1-exp[(0.11/252)-0.41*1.645/sqrt(252)] = 4.12%