No.PZ2020010303000012 (问答题)
来源: 原版书
The monthly return on a hedge fund portfolio with USD 1 billion in assets is N(.02, .0003). What is the distribution of the gain in a month?
b. 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)?
b. Here we work in the other direction. 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 multiply-ing 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% change of having a change above this level.
Pr(Z < z) = 99.9%，为什么z = -3.09，不是3.09？
