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除了樱花 · 2022年03月18日

confidence interval

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.

为什么第四问用portfolio return 来计算呢,不是用b1~(b1cap+- 1.96standard error)吗,不应该用β那个值作为b1cap吗?

4 个答案
已采纳答案

李坏_品职助教 · 2022年03月18日

嗨,从没放弃的小努力你好:


这个区间估计的计算还是有一定可考性的,建议记一下公式~

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努力的时光都是限量版,加油!

李坏_品职助教 · 2024年07月25日

嗨,从没放弃的小努力你好:


对,精确值是1.96,这道题 是用近似值,把1.96近似于2了,所以算出来是7.16 -16.84。


这个题目出的不是很严谨,在真实考试中,数字会用精确值。

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加油吧,让我们一起遇见更好的自己!

Circlrmo · 2024年07月25日

办什么+-2倍标准误,95%不是1.96 吗?

李坏_品职助教 · 2022年03月18日

嗨,爱思考的PZer你好:


第四问问的是portfolio return的区间估计范围,要用return的期望值(就是讲义里的point estimate)±2倍的标准误差才是对的,这道题不是问的β的估计区间,所以不能用β_cap。


给你的条件estimated return of 12%,意思就是return的期望值就是12,在此基础上±2倍的standard deviation of error就行了。



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虽然现在很辛苦,但努力过的感觉真的很好,加油!

除了樱花 · 2022年03月18日

找到了!可是上课不是说了解就行吗,这个要重点掌握吗

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