NO.PZ2020010303000012
问题如下:
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?
a. The fund has access to a USD 10 million line of credit that does not count as part of its portfolio. What is the chance that the firm’s loss in a month exceeds this line of credit?
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)?
选项:
解释:
a. The monthly return is 2%, and the monthly standard deviation is 1.73%. In USD, the monthly change in portfolio value has a mean of 2% * USD 1 billion = USD 20 million and a standard deviation of 1.73% * USD 1 billion = USD 17.3 million. The probability that the portfolio loses more than USD 10 million is than (working in millions)
Using the normal table, Pr(Z<-1.73)=4.18%
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.
The probability that the portfolio loses more than USD 10 million is than (working in millions),为什么要统一单位为million?做题思路是什么?
第二题看不懂,能翻译一下以及解释下考点吗?