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jzhuangst · 2024年02月02日

单位问题

  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.

文中说 (Expressed in Decimal Form, i.e., 1% = 0.01)，在计算t-statistic的时候，为什么不是 (0.4350-0.005 / 0.0202) 呢？

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2 个答案

品职助教_七七 · 2024年03月28日

嗨，爱思考的PZer你好：


@Caroline123456

是的

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

品职助教_七七 · 2024年02月02日

嗨，从没放弃的小努力你好：


case中给出的关系“for each 1 percent increase in pre-offer price adjustment, the initial return will increase by less than 0.5 percent”和用小数还是用百分数表示都没有关系，因为都会约掉。

如用小数，就是X增加0.01，Y增加不到0.005。进而转化为X增加1，Y增加不到0.5。所以系数依然是检验0.5。不受数字计量的方式影响。

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加油吧，让我们一起遇见更好的自己！

Caroline123456 · 2024年03月28日

那是否所有的t检验，都要调整成X变动1个单位，Y的变动量？

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