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stephanie_liu · 2021年04月17日

这道题完全看不懂什么意思,麻烦老师讲一下

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)

Pr(V<10)=Pr(V2017.3<102017.3)=Pr(Z<1.73)Pr(V<-10)=Pr(\frac{V-20}{17.3}<\frac{-10-20}{17.3})=Pr(Z<-1.73)

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.

这道题完全看不懂什么意思,麻烦老师讲一下

1 个答案

袁园_品职助教 · 2021年04月17日

题目告诉你 monthly return 是正态分布,期望 2%, 方差0.0003,所以标准差是1.73%.

a)问portfolio的亏损大于10million的概率(注意题目给的概率分布,是它的收益分布,所以亏损大于10million对应着收益小于-10million)

b)求一个下限,这个下限下面只有0.1%的概率,对应的分位点是均值减3.09倍的标准差,那这个线就是均值20减去3.09*17.3这个标准差,也就是 -33.46

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