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Cooljas · 2022年06月05日

第四问可以再具体解释一下吗?另外,置信区间求解公式里的均值,为啥是用Y值的12%,而不要用到 alpha、beta啊?

NO.PZ2016062402000023

问题如下:

Which of the following statements about the linear regression of the return of a portfolio over the return of its benchmark presented below are correct?

I. The correlation is 0.71.

II. About 34% of the variation in the portfolio return is explained by variation in the benchmark return.

III. The portfolio is the dependent variable.

IV. For an estimated portfolio return of 12%, the confidence interval at 95% is (7.16%-16.84%).

选项:

A.

II and IV

B.

Ill and IV

C.

I, II, and III

D.

II,IIIand IV

解释:

The correlation is given by 0.66=0.81\sqrt{0.66}=0.81 so answer I is incorrect. Next,66% of the variation in Y is explained by the benchmark, so answer II. is incorrect. The portfolio return is indeed the dependent variable Y, so answer III. is correct. Finally, to find the 95 % two-tailed confidence interval, we use a from a normal distribution, which covers 95% within plus or minus 1.96, close to 2.00. The interval is theny2SD(e),  y+2SD(e)y-2SD{(e)},\;y+2SD{(e)} or (7.16 -16.84). So answers III. and IV. are correct.



2 个答案

DD仔_品职助教 · 2022年06月06日

嗨,努力学习的PZer你好:


题目说的是对于一个估计是12%的return来说,95%的置信区间下这个return的范围是多少。

虽然没有说是均值,但是通过翻译就可以很清楚我们是以12%作为标准向左右开出1.96倍的标准差,就是公式里均值的含义。

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DD仔_品职助教 · 2022年06月05日

嗨,从没放弃的小努力你好:


第四问是个假设,说的是如果均值是12%,那么在95%的概率下,这个return的波动是左右开出12%的1.96倍的标准误2.42%,那么就是(7.16%-16.84%)。

12%不是通过regression计算出来的,而是题目给出来的条件~

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加油吧,让我们一起遇见更好的自己!

Cooljas · 2022年06月05日

请问为什么题目给出的estimated portfolio return 是指的均值啊?

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