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vee · 2022年11月09日

不会

  1. CFA I
  2. Quantitative

NO.PZ2017092702000162

问题如下：

The following table shows the sample correlations between the monthly returns for four different mutual funds and the S&P 500. The correlations are based on 36 monthly observations. The funds are as follows:


Test the null hypothesis that each of these correlations, individually, is equal to zero against the alternative hypothesis that it is not equal to zero. Use a 5 percent significance level.





选项：

解释：

The critical t-value for n − 2 = 34 df, using a 5 percent significance level and a two-tailed test, is 2.032. First, take the smallest correlation in the table, the correlation between Fund 3 and Fund 4, and see if it is significantly different from zero. Accoding to the formula of correlaion t-test, its calculated t-value is t=1.903. This correlation is not significantly different from zero. If we take the next lowest correlation, between Fund 2 and Fund 3, this correlation of 0.4156 has a calculated t-value of 2.664. So this correlation is significantly different from zero at the 5 percent level of significance. All of the other correlations in the table (besides the 0.3102) are greater than 0.4156, so they too are significantly different from zero.

能不能翻译一下并解释，实在是看不懂这道题的考点。

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1 个答案

星星_品职助教 · 2022年11月09日

同学你好，

此后提问需要具体写明不懂的点在哪里，什么地方需要翻译，自己的思路是什么。

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这道题考察的是correlation的假设检验，公式如截图。

①根据表格中给出的相关系数和n=36，代公式算出检验统计量。以答案解析中选择的fund 3和fund 4的相关系数r=0.3102为例，此时t-statistic代入截图公式后计算出来为1.9026.

②根据5 percent significance level，和n=36条件下查表得到t critical value=2.032。

③由于t-statistic都小于了t critical value，所以不能拒绝原假设，即ρ=0.也就是不存在线性相关关系。

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把答案解析中涉及到Fund 2和Fund 3的r=0.4156也按照这个流程过一遍，首先代入公式得到t-statistic=2.6643，由于这个数字大于了t critical value=2.032，所以此时要拒绝原假设，即ρ≠0，这就是有线性相关关系。

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题目要求把图里的所有的相关系数都按照这个流程检验一遍。自己计算2-3个，掌握了公式和逻辑即可。


底下的这个图看的清楚一点。

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