请问既然是标准差，不是应该乘以根号4么？

问题如下：

John Flag, the manager of a $150 million distressed bond portfolio, conducts stress tests on the portfolio. The portfolio’s annualized return is 12%,with an annualized return volatility of 25%. In the past two years, the portfolio encountered several days when the daily value change of the portfolio was more than 3 standard deviations. If the portfolio would suffer a 4-sigma daily event, estimate the change in the value of this portfolio.

选项：

A.

  $9.48 million

B.

  $23.70 million

C.

  $37.50 million

D.

  $150 million

解释：

ANSWER: A

First, we transform the volatility into a daily measure, which is $\frac{25\%}{\sqrt{252}}=1.57\%$. $150\times1.57\%\times4=\$9.45.$

解析：有一个基金经理管理着150m美元不良债券投资组合，他对投资组合进行压力测试。 该投资组合的年化收益率为 12%，年化收益率波动率为 25%。 在过去的两年中，投资组合遇到了几天投资组合的每日价值变化超过 3 个标准差的情况。 如果投资组合每天价值变化超过4个标准差，请估计该投资组合的价值变化。

daily σ=25%*（252^0.5）=1.57%

组合价值在一天内变化达到4个标准差，变动值就是组合价值*4*标准差=150m*4*1.57%=9.48m

选A。