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努力的KK · 2025年04月01日

讲解一下这道题

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.

讲一下怎么做

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NO.PZ2024120401000006问题如下 The monthly return on a hee funportfolio with US 1 billion in assets is N(0.02, 0.0003). Whwoulthe line of cret neeto to ensure ththe firm’s loss wless ththe line of cret in 99.9% of months (or equivalently, larger ththe LOC in 0.1% of months) ?Note: Pr(Z < z) = 99.9% means z= -3.09 A.17.3 millionB.33.46 millionC.20 million60 million The monthly change in portfolio value will also normally stributewith a meof 0.02 * US1 billion = US20 million ana varianof 0.0003 * 1 billion2 = 300 trillion. The stanr viation of the gain will US17.3 million.First, we finthe quantile where Pr(Z < z) = 99.9%, whigives z =-3.09. This is then scaleto the stribution of the change in the value of the portfolio multiplying the stanrviation anaing the mean, 17.3 *(-3.09) + 20 = -33.46. The funwoulneea line of cret of US33.46 million to have a 99.9% chanof 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?

2025-02-26 12:19 1 · 回答

NO.PZ2024120401000006 问题如下 The monthly return on a hee funportfolio with US 1 billion in assets is N(0.02, 0.0003). Whwoulthe line of cret neeto to ensure ththe firm’s loss wless ththe line of cret in 99.9% of months (or equivalently, larger ththe LOC in 0.1% of months) ?Note: Pr(Z < z) = 99.9% means z= -3.09 A.17.3 million B.33.46 million C.20 million 60 million The monthly change in portfolio value will also normally stributewith a meof 0.02 * US1 billion = US20 million ana varianof 0.0003 * 1 billion2 = 300 trillion. The stanr viation of the gain will US17.3 million.First, we finthe quantile where Pr(Z < z) = 99.9%, whigives z =-3.09. This is then scaleto the stribution of the change in the value of the portfolio multiplying the stanrviation anaing the mean, 17.3 *(-3.09) + 20 = -33.46. The funwoulneea line of cret of US33.46 million to have a 99.9% chanof having loss below this level. 老师你好,这题我就没太明白啥意思,能给讲讲不,谢谢

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