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蜗牛也是牛Megan · 2024年02月29日

疑问

  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.

The correct test statistic is: t = (0.435-0.50)/0.0202 = -3.22

为什么是减去0.5，另外这个题目的t分布的值是怎么查找出来的，为什么是负数

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已采纳答案

品职助教_七七 · 2024年02月29日

嗨，从没放弃的小努力你好：


1）根据“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....”，得到关系为X增加1，Y增加不到0.5。由于这是研究人员相信“believe”的，所以放备择假设，由此得到备择假设为Ha：bj＜0.5；

2）由于是单尾检验，单尾面积即为significance level=0.05。可直接对应出表格中的1.645。又因为拒绝域由备择假设决定，本题拒绝域在左尾，所以关键值为-1.645。这里的正负实际无所谓，因为最终比较的是test statistic和critical value的绝对值。

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