Question #94
Reading: Reading 1 Multiple Regression
PDF File: Reading 1 Multiple Regression.pdf
Page: 45
Status: Unattempted
Correct Answer: A
Question
A fund has changed managers twice during the past 10 years. An analyst wishes to measure whether either of the changes in managers has had an impact on performance. R is the return on the fund, and M is the return on a market index. Which of the following regression equations can appropriately measure the desired impacts?
Answer Choices:
A. The desired impact cannot be measured
B. R = a + bM + c1D1 + c2D2 + c3D3 + ε, where D1 = 1 if the return is from the first manager, and D2 = 1 if the return is from the second manager, and D3 = 1 is the return is from the third manager
C. R = a + bM + c1D1 + c2D2 + ε, where D1 = 1 if the return is from the first manager, and D2 = 1 if the return is from the third manager. Raul Gloucester, CFA, is analyzing the returns of a fund that his company offers. He tests the fund's sensitivity to a small capitalization index and a large capitalization index, as well as to whether the January effect plays a role in the fund's performance. He uses two years of monthly returns data, and runs a regression of the fund's return on the indexes and a January-effect qualitative variable. The "January" variable is 1 for the month of January and zero for all other months. The results of the regression are shown in the tables below. Regression Statistics Multiple R 0.817088 R2 0.667632
Explanation
The effect needs to be measured by two distinct dummy variables. The use of three
variables will cause collinearity, and the use of one dummy variable will not appropriately
specify the manager impact.
(Module 1.4, LOS 1.l)
Raul Gloucester, CFA, is analyzing the returns of a fund that his company offers. He tests the
fund's sensitivity to a small capitalization index and a large capitalization index, as well as to
whether the January effect plays a role in the fund's performance. He uses two years of
monthly returns data, and runs a regression of the fund's return on the indexes and a
January-effect qualitative variable. The "January" variable is 1 for the month of January and
zero for all other months. The results of the regression are shown in the tables below.
Regression Statistics
Multiple R
0.817088
R2
0.667632
Adjusted R2
0.617777
Standard Error
1.655891
Observations
24
ANOVA
df
SS
MS
Regression
3
110.1568
36.71895
Residual
20
54.8395
2.741975
Total
23
164.9963
Coefficients
Standard Error
t-Statistic
Intercept
-0.23821
0.388717
-0.61282
January
2.560552
1.232634
2.077301
Small Cap Index
0.231349
0.123007
1.880778
Large Cap Index
0.951515
0.254528
3.738359
Exhibit 1: Partial F-Table (5% Level of Significance)
Degree of Freedom Denominator
Degree of Freedom Numerator
1
2
3
18
4.41
3.55
3.16
19
4.38
3.52
3.13
20
4.35
3.49
3.10
21
4.32
3.47
3.07
22
4.30
3.44
3.05
23
4.28
3.42
3.03
Gloucester plans to test for serial correlation and conditional and unconditional
heteroskedasticity.