NO.PZ2024120401000006
问题如下：
The monthly return on a hedge fund portfolio with USD 1 billion in assets is N(0.02, 0.0003). What would the line of credit need to be to ensure that the firm’s loss was less than the line of credit in 99.9% of months (or equivalently, larger than the LOC in 0.1% of months) ?
Note: Pr(Z ＜ z) = 99.9% means z= -3.09
选项：
A.
17.3 million
B.
33.46 million
C.
20 million
D.
60 million
解释：
The monthly change in portfolio value will also be normally distributed with a mean of 0.02 * USD 1 billion = USD 20 million and a variance of 0.0003 * 1 billion2 = 300 trillion. The standard deviation of the gain will be USD 17.3 million.
First, we find the quantile where Pr(Z ＜ z) = 99.9%, which gives z =-3.09. This is then scaled to the distribution of the change in the value of the portfolio by multiplying by the standard deviation and adding the mean, 17.3 *(-3.09) + 20 = -33.46. The fund would need a line of credit of USD 33.46 million to have a 99.9% chance of having loss below this level.
这题给的均值方差单位是不是不一样啊？这样算出来一个20另一个只有0.3；notes里面应该是P Z＞z=99.9 或者P Z＜z=0.1 否则z是正的3.09吧？
