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ZAA · 2021年02月22日

表格中T statistic是什么

  1. CFA II
  2. Quantitative

NO.PZ2015120204000015

问题如下：

Based on past research, Hansen selects the following independent variables to predict IPO initial returns:

Underwriter rank = 1–10, where 10 is highest rank

Pre-offer price adjustment (Expressed as a decimal) = (Offer price – Initial filing price)/Initial filing price

Offer size ($ millions) = Shares sold × Offer price

Fraction retained (Expressed as a decimal) = Fraction of total company shares retained by insiders

He also believes that for each 1 percent increase in pre-offer price adjustment, the initial return will increase by less than 0.5 percent, holding other variables constant. Hansen wishes to test this hypothesis at the 0.05 level of significance.

Hansen collects a sample of 1,725 recent IPOs for his regression model.

\Hansen’s Regression Results Dependent Variable: IPO Initial Return (Expressed in Decimal Form, i.e., 1% = 0.01)

Selected Values for the t-Distribution (df = ∞)

The most appropriate null hypothesis and the most appropriate conclusion regarding Hansen’s belief about the magnitude of the initial return relative to that of the pre-offer price adjustment (reflected by the coefficient bj) are:

选项：

Null Hypothesis
Conclusion about bj(0.05 Level of Significance)
A.
H0: bj=0.5
Reject H0
B.
H0: bj≥0.5
Fail to reject H0
C.
H0: bj≥0.5
Reject H0

解释：

C is correct.

C To test Hansen’s belief about the direction and magnitude of the initial return, the test should be a one-tailed test. The alternative hypothesis is H1: bj<0.5b_j<0.5, and the null hypothesis is H0:bj≥0.5b_j\geq0.5 . The correct test statistic is: t = (0.435-0.50)/0.0202 = -3.22, and the critical value of the t-statistic for a one-tailed test at the 0.05 level is -1.645. The test statistic is significant, and the null hypothesis can be rejected at the 0.05 level of significance.

这个为什么求出来是-3.2

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星星_品职助教 · 2021年02月22日

同学你好，

t-statistics（t检验统计量）是计算得到的。

多元回归中，回归系数的假设检验为H0： bj=The hypothesized value。t-statistics的公式为（bj cap- hypothesized value）/bj cap的标准误。

本题中，要检验的是自变量“pre-offer price adjustment”的系数。根据题干表格得知，系数估计量为0.4350，对应的标准误为0.0202.

根据题干描述，假设检验里的“hypothesized value”=0.5.

所以t-statistics=（0.4350-0.5）/0.0202=-3.22

随后和题干最后一个表格中给出的t critical value对比（绝对值）即可。

-----------------

绝大部分题目中，这个“ hypothesized value”都是0。也就是H0：bj=0，此时t-statistics的公式即可简化为bj cap/bj cap的标准误.

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