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		1.08	%	0.00	%	0.03	%	-1.03	%	-1.75	%
2		7.58		6.64		6.89		0.28		-1.31
3		4.98		6.00		4.76		-1.47		1.93
4		1.18		0.36		0.56		0.40		0.20
5		-1.88		-1.50		-2.87		-3.59		4.37
6		4.31		2.38		2.91		-3.42		-1.46
7		-0.75		-2.39		-2.78		-4.52		-1.78
8		-15.41		-15.37		-16.14		-5.87		5.77
9		5.97		4.09		5.97		0.03		-3.71
10		7.69		6.67		7.21		-3.40		-2.93
11		7.70		5.57		5.87		1.43		-3.71
12		9.67		4.98		5.95		-0.39		-4.95
13		5.18		2.74		3.45		1.05		-6.21
14		-3.22		-0.64		-4.25		-5.69		1.75
15		5.41		2.56		3.23		-3.90		-3.00
16		2.41		7.30		4.39		2.79		2.80
17		-2.87		0.08		-2.38		3.50		3.16
18		6.54		3.59		4.75		3.45		-4.24
19		-3.34		-0.54		-3.38		1.91		0.70
20		-1.21		-3.99		-1.35		-1.26		-1.36
21		-1.40		0.16		-2.72		3.26		-3.11
22		5.99		5.39		5.84		-6.60		-3.10
23		1.97		2.35		3.26		7.69		-8.13
24		7.17		7.17		7.77		7.08		-9.02
25		-4.79		-2.86		-4.39		4.03		-0.26
26		0.98		-2.03		2.54		21.52		-12.10
27		8.99		5.21		5.03		-16.65		7.75
28		-4.28		-2.93		-6.25		-7.54		8.61
29		-3.35		-0.66		-4.34		-5.91		5.41
30		3.83		1.83		4.76		13.30		-8.75

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

2. 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-well bad as the -Select-adjusted R2multiple RinterceptItem 26 values in both regressions are -Select-high enough not high enough low enoughnot low enough.

3. 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 3 is the most likely candidate for the market factor, because it has a -Select-large, significant, and positive large, significant, and negative small, not significant, and negative small, not significant, and positive effect on both portfolios.

4. 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 A or Portfolio B is the more likely candidate for the value-oriented portfolio as it has a -Select-positive or negative loading on this factor.

   -Select-Portfolio A or Portfolio B is the more likely candidate for the growth-oriented portfolio as it has a -Select-positive or negative loading on this factor.