NO.PZ202208220100000205
问题如下:
You are a junior analyst at an asset management firm. Your supervisor asks you toanalyze the return drivers for one of the firm’s portfolios. She asks you to constructa regression model of the portfolio’s monthly excess returns (RET) againstthree factors: the market excess return (MRKT), a value factor (HML), and themonthly percentage change in a volatility index (VIX). You collect the data andrun the regression. After completing the first regression (Model 1), you reviewthe ANOVA results with your supervisor.
Then, she asks you to create two more models by adding two more explanatoryvariables: a size factor (SMB) and a momentum factor (MOM). Your three modelsare as follows:
The regression statistics and ANOVA results for the three models are shown in
Exhibit 1, Exhibit 2, and Exhibit 3.
Your supervisor asks for your assessment of the model that provides the best fit
as well as the model that is best for predicting values of the monthly portfolio
return. So, you calculate Akaike’s information criterion (AIC) and Schwarz’s
Bayesian information criterion (BIC) for all three models, as shown in Exhibit 4.
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 theexplanation 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.
freedom. The test is one-tailed, right side, with a = 1%, so the critical F-value is 4.849.