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HUANGy · 2019年12月18日

问一道题：NO.PZ2015120204000015

  1. CFA II
  2. Quantitative

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.

这里面的t-value是指什么？课上好像没有讲t-value吧？

这道题看不懂，老师能否给我解答一下？

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1 个答案

星星_品职助教 · 2019年12月18日

同学你好，

t-value指的是t分布表中的critical value，就是查t分布表查出的临界值。其实看第一行数，例如单尾的5%对应1.645，也可以联想下一级的时候要求背的那一组值（1.645,1.96,2.58等等）。

这道题说的是原假设应该怎么设和是否拒绝原假设。由于题干中给出了the initial return will increase by less than 0.5 percent, 所以bj=0.5的原假设是不正确的，排除A。而B,C选项建立的假设都可以，由此计算出 的pre-offer price adjustment对应t统计量为t = (0.435-0.50)/0.0202 = -3.22 ，大于临界值-1.645，所以要拒绝原假设。

这道题主要还是复习一级的内容。但是这个逻辑和解题思路在二级还会应用到，所以需要掌握，加油。

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