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苏·Xu · 2022年11月09日

NO.PZ2015120604000108

问题如下:

If a Portfolio's SFR is 1.4 and  threshold level's return is  supposed to be 2%, what is the probability of return less than 2%?

选项:

A.

8.08%.

B.

30.20%.

C.

9.68%.

解释:

A is correct.

Using the table, we get F( -1.4) is 1 - 0.9192 = 8.08%.

为什么是Z<-1.4 的概率?

1 个答案

星星_品职助教 · 2022年11月09日

同学你好,

根据题干问的“ what is the probability of return less than 2%?”,可知要计算的是P(X<2%),

由于普通正态分布不能查表,所以需要先做标准化,转化为标准正态分布后查z表,即P[ z<(2%-μ)/ σ] 。

由于μ和σ都未知,所以z<(2%-μ)/ σ求不出来,但目前已知SFR=1.4,所以代入SFR的公式,就可以知道 SFR=(μ-2%)/σ=1.4,正好是上面标准化公式的负值。


由此得到要计算的就是z<-1.4的概率

此后查表即可得到答案。

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