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Danlei · 2021年10月30日

第四问的计算有些疑问

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.

为什么用12+/-1.96*2.42,不用0.12+/-1.96*2.42?


1 个答案

DD仔_品职助教 · 2021年10月30日

嗨,从没放弃的小努力你好:


他这里没有标百分号,但是standard deviation的error在这里,是回报率的标准误,是一个百分数的概念。

那么组合的回报率是12%,所以在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%。

如果按你写的来计算,回报率是0.12+/-4.74,算下来是4.86~-4.62,回报率竟然是正负400%多,这个估计的回报率数字也太夸张了吧。。。

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努力的时光都是限量版,加油!

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