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Cooljas · 2024年05月02日

红框里的第二问和第三问可以详细解释下吗？

  1. FRM I
  2. Quantitative

NO.PZ2023091601000122

问题如下：

A regression of a stock’s return (in percent) on an industry index’s return (in percent) provides the following results:

Coefficient Standard Error

Intercept 2.1 2.01

Industry index 1.9 0.31

Degrees of Freedom SS

Explained 1 92.648

Residual 3 24.512

Total 4 117.160

Which of the following statements regarding the regression is correct?

I.The correlation coefficient between the X and Y variables is 0.889.

II.The industry index coefficient is significant at the 99% confidence interval.

III.If the return on the industry index is 4%, the stock’s expected return is 10.3%.

IV.The variability of industry returns explains 21% of the variation of company returns

选项：

A.

III only

B.

I and II only

C.

II and IV only

D.

I, II, and IV

解释：

The R2 of the regression is calculated as ESS/TSS = (92.648/117.160) = 0.79, which means that the variation in industry returns explains 79% of the variation in the stock return. By taking the square root of R2, we can calculate that the correlation coefficient (r) = 0.889. The t-statistic for the industry return coefficient is 1.91/0.31 = 6.13, which is sufficiently large enough for the coefficient to be significant at the 99% confidence interval. Since we have the regression coefficient and intercept, we know that the regression equation is Rstock = l.9X + 2.1. Plugging in a value of 4% for the industry return, we get a stock return of 1.9 (4) + 2.1 = 9.7%.



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1 个答案

李坏_品职助教 · 2024年05月02日

嗨，努力学习的PZer你好：


第一个红框：这个求的是industry coefficient的t统计量（就是求industry这个自变量系数的t统计量）。

题目告诉我们Industry index系数是1.9，standard errors是0.31，所以t统计量 = 系数 / standard error = 1.9/0.31 = 6.13



第二个圆形红框里面的99%的意思是，由于前面算出来t统计量是6.13，是一个很大的数字（大于3就可以），所以在99%的置信度下是显著的，意思就是这个industry的系数显著不为0.


第三个红框的意思是，由于industry这个自变量的系数是1.9，而intercept（截距项）是2.1，所以可以写出回归方程：y = 1.9*x + 2.1.

y就是stock’s return（股票的收益率），而x是industry return。当industry return = 4时(题目开头说是in percent，所以计算时要去掉百分号%)，

stock return = 1.9 * 4 + 2.1 = 9.7，也就是stock return是9.7%

----------------------------------------------
努力的时光都是限量版，加油！

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