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Problem 7-14

Consider the data contained in the table below, which lists 30 monthly excess returns to two different actively managed stock portfolios (A and B) and three different common risk factors (1, 2, and 3). (Note: You may find it useful to use a computer spreadsheet program such as Microsoft Excel to calculate your answers.)

Period	Portfolio A	Portfolio B	Factor 1	Factor 2	Factor 3
1		1.09	%	0.00	%	0.01	%	-0.96	%	-1.74	%
2		7.54		6.54		6.80		0.26		-1.20
3		4.95		6.01		4.75		-1.41		1.97
4		1.07		0.28		0.70		0.33		0.18
5		-1.91		-1.67		-2.86		-3.56		4.30
6		4.27		2.31		2.92		-3.47		-1.62
7		-0.82		-2.45		-2.74		-4.52		-1.88
8		-15.56		-15.40		-16.07		-5.85		5.63
9		5.97		4.15		6.05		0.01		-3.67
10		7.72		6.76		7.11		-3.27		-2.94
11		7.81		5.49		5.93		1.44		-3.76
12		9.58		4.82		6.02		-0.23		-4.87
13		5.34		2.68		3.40		1.12		-6.09
14		-3.18		-0.62		-4.13		-5.64		1.58
15		5.38		2.49		3.22		-3.82		-3.12
16		2.36		7.31		4.50		2.97		2.86
17		-2.78		0.09		-2.32		3.54		3.06
18		6.61		3.68		4.68		3.37		-4.32
19		-3.35		-0.64		-3.46		2.08		0.80
20		-1.15		-4.16		-1.32		-1.23		-1.25
21		-1.46		0.13		-2.62		3.17		-3.10
22		6.06		5.30		5.86		-6.54		-3.17
23		2.12		2.24		3.15		7.65		-8.17
24		7.25		7.11		7.82		7.03		-8.95
25		-4.87		-2.76		-4.52		4.02		-0.10
26		0.98		-2.12		2.47		21.57		-11.93
27		9.02		5.25		5.07		-16.67		7.76
28		-4.37		-2.98		-6.31		-7.44		8.57
29		-3.46		-0.57		-4.17		-5.79		5.46
30		3.86		1.72		4.75		13.29		-8.74

1. Using regression analysis, calculate the factor betas of each stock associated with each of the common risk factors. Which of these coefficients are statistically significant at 5% level of significance? Fill in the table below. Use a minus sign to enter negative values, if any. Do not round intermediate calculations. Round your answers for factor betas to three decimal places and answers for t-statistics to two decimal places.

	bi	t-statistic	Significance
Regression for Portfolio A
onstant			-Select-significantnot significantItem 3
Factor 1			-Select-significantnot significantItem 6
Factor 2			-Select-significantnot significantItem 9
Factor 3			-Select-significantnot significantItem 12
Regression for Portfolio B
onstant			-Select-significantnot significantItem 15
Factor 1			-Select-significantnot significantItem 18
Factor 2			-Select-significantnot significantItem 21
Factor 3			-Select-significantnot significantItem 24

How well does the factor model explain the variation in portfolio returns? On what basis can you make an evaluation of this nature?

The factor models explain -Select-wellbadItem 25 as the -Select-adjusted R2multiple RinterceptItem 26 values in both regressions are -Select-high enoughnot high enoughlow enoughnot low enoughItem 27 .

Suppose you are now told that the three factors used in the models represent the risk exposures in the Fama-French characteristic-based model (i.e., excess market, SMB, and HML). Based on your regression results, which one of these factors is the most likely to be the market factor? Explain why.

-Select-Factor 1Factor 2Factor 3Item 28 is the most likely candidate for the market factor, because it has a -Select-large, significant, and positivelarge, significant, and negativesmall, not significant, and negativesmall, not significant, and positiveItem 29 effect on both portfolios.

Suppose it is further revealed that Factor 3 is the HML factor. Which of the two portfolios is most likely to be a growth-oriented fund and which is a value-oriented fund? Explain why.

-Select-Portfolio APortfolio BItem 30 is the more likely candidate for the value-oriented portfolio as it has a -Select-positivenegativeItem 31 loading on this factor.

-Select-Portfolio APortfolio BItem 32 is the more likely candidate for the growth-oriented portfolio as it has a -Select-positivenegativeItem 33 loading on this factor.