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台风来了 · 2023年08月27日

关于F统计量

  1. CFA II
  2. Quantitative

NO.PZ2023040502000009

问题如下：

You are a junior analyst at an asset management firm. Your supervisor asks you to analyze the return drivers for one of the firm’s portfolios. She asks you to construct a regression model of the portfolio’s monthly excess returns (RET) against three factors: the market excess return (MRKT), a value factor (HML), and the monthly percentage change in a volatility index (VIX). You collect the data and run the regression. After completing the first regression (Model 1), you review the ANOVA results with your supervisor.


Then, she asks you to create two more models by adding two more explanatory variables: a size factor (SMB) and a momentum factor (MOM). Your three models are as follows:

Model 1: RETi = b0 + bMRKTMRKTi + bHMLHMLi + bVIXVIXi + εi.

Model 2: RETi = b0 + bMRKTMRKTi + bHMLHMLi + bVIXVIXi + bSMBSMBi + εi.

Model 3: RETi = b0 + bMRKTMRKTi + bHMLHMLi + bVIXVIXi + bSMBSMBi + bMOMMOMi + εi.

The regression statistics and ANOVA results for the Model 1 and Model 3 are shown in Exhibit 1 and Exhibit 3



Calculate the joint F-statistic and determine whether SMB and MOM together contribute to explaining RET in Model 3 at a 1% significance level (use a critical value of 4.849).

选项：

A.

2.216, so SMB and MOM together do not contribute to explaining RET

B.

8.863, so SMB and MOM together do contribute to explaining RET

C.

9.454, so SMB and MOM together do contribute to explaining RET

解释：

B is correct. To determine whether SMB and MOM together contribute to the explanation of RET, at least one of the coefficients must be non-zero. So, H0:bSMB = bMOM = 0 and Ha: bSMB ≠ 0 and/or bMOM ≠ 0.

We use the F-statistic, where

,

with q = 2 and n – k – 1 = 90 degrees of freedom. The test is one-tailed, right side, with α = 1%, so the critical F-value is 4.849.

Model 1 does not include SMB and MOM, so it is the restricted model. Model3 includes all of the variables of Model 1 as well as SMB and MOM, so it is the unrestricted model.

Using data in Exhibit 1 and Exhibit 3, the joint F-statistic is calculated as

.

Since 8.863 > 4.849, we reject H0. Thus, SMB and MOM together do contribute to the explanation of RET in Model 3 at a 1% significance level.

老师，您好！

本题的F统计量中的n-k-1 = 95-5-1 = 89，应该是89吧？怎么是90呢？ 另外，the critical F-value is 4.849.是怎么得到的呢？谢谢！

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1 个答案

星星_品职助教 · 2023年08月28日

同学你好，

1）n=96，n-k-1=96-5-1=90.

2） the critical F-value is 4.849为已知条件


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NO.PZ2023040502000009问题如下 You are a junior analyst asset management firm. Your supervisor asks you to analyze the return ivers for one of the firm’s portfolios. She asks you to construa regression mol of the portfolio’s monthly excess returns (RET) against three factors: the market excess return (MRKT), a value factor (HML), anthe monthly percentage change in a volatility inx (VIX). You collethe ta anrun the regression. After completing the first regression (Mol 1), you review the ANOVA results with your supervisor.Then, she asks you to create two more mols aing two moreexplanatory variables: a size factor (SMana momentum factor (MOM). Yourthree mols are follows:Mol 1: RETi = + bMRKTMRKTi+ bHMLHMLi + bVIXVIXi + εi.Mol 2: RETi = + bMRKTMRKTi+ bHMLHMLi + bVIXVIXi + bSMBSMBi+ εi.Mol 3: RETi = + bMRKTMRKTi+ bHMLHMLi + bVIXVIXi + bSMBSMBi+ bMOMMOMi + εi.The regression statistianANOVA results for theMol 1 anMol 3 are shown in Exhibit 1 anExhibit 3Calculate the joint F-statistic antermine whetherSMB anMOM together contribute to explaining RET in Mol 3 a 1%significanlevel (use a criticvalue of 4.849). A.2.216, so SMB anMOM together not contribute toexplaining RETB.8.863, so SMB anMOM together contribute toexplaining RETC.9.454, so SMB anMOM together contribute toexplaining RET B is correct. To termine whether SMB anMOMtogether contribute to the explanation of RET, least one of the coefficientsmust non-zero. So, H0:bSMB = bMOM = 0 anHbSM0 anor bMOM ≠ 0.We use the F-statistiwhere,with q = 2 ann – k – 1 = 90 grees offreem. The test is one-taile right si, with α = 1%, so the criticalF-value is 4.849.Mol 1 es not inclu SMB anMOM, so it isthe restrictemol. Mol3 inclus all of the variables of Mol 1 wellSMB anMOM, so it is the unrestrictemol.Using ta in Exhibit 1 anExhibit 3, the jointF-statistic is calculateas.Sin8.863 4.849, werejeH0. Thus, SMB anMOM together contribute to theexplanation of RET in Mol 3 a 1% significanlevel. 我用F test R2那个公式算出来的不是8.863; 怎么选择使用这两个公式呢

2024-06-29 00:38 1 · 回答