Part 1 .
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 % -1.04 % -1.59 %
2 7.59 6.60 6.84 0.31 -1.14
3 5.11 6.06 4.73 -1.39 1.83
4 1.23 0.32 0.76 0.32 0.16
5 -1.92 -1.68 -2.96 -3.58 4.39
6 4.24 2.45 2.86 -3.44 -1.52
7 -0.70 -2.51 -2.68 -4.55 -1.69
8 -15.52 -15.41 -16.17 -5.88 5.60
9 6.02 4.07 5.89 0.03 -3.77
10 7.68 6.74 7.04 -3.38 -2.91
11 7.76 5.44 5.83 1.33 -3.78
12 9.71 4.80 5.89 -0.23 -4.86
13 5.30 2.69 3.40 1.08 -6.19
14 -3.29 -0.58 -4.22 -5.50 1.67
15 5.30 2.63 3.35 -3.85 -3.04
16 2.32 7.34 4.51 2.91 2.82
17 -2.96 0.07 -2.36 3.45 3.06
18 6.43 3.68 4.79 3.47 -4.23
19 -3.47 -0.55 -3.48 1.99 0.71
20 -1.21 -4.13 -1.38 -1.18 -1.36
21 -1.46 0.09 -2.62 3.21 -3.20
22 5.91 5.36 5.71 -6.53 -3.24
23 2.09 2.23 3.25 7.75 -8.13
24 7.14 6.99 7.80 6.88 -9.14
25 -4.86 -2.69 -4.36 4.08 -0.21
26 1.02 -1.97 2.60 21.51 -11.97
27 9.03 5.25 5.10 -16.67 7.71
28 -4.41 -2.92 -6.19 -7.59 8.61
29 -3.39 -0.56 -4.22 -5.78 5.48
30 3.82 1.90 4.72 13.30 -8.81
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
Сonstant
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Factor 1
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Factor 2
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Factor 3
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Regression for Portfolio B
Сonstant
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Factor 1
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Factor 2
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Factor 3
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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
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as the
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values in both regressions are
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.
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.
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is the most likely candidate for the market factor, because it has a
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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.
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is the more likely candidate for the value-oriented portfolio as it has a
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loading on this factor.
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is the more likely candidate for the growth-oriented portfolio as it has a
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loading on this factor.
part 2
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 1.13 % 0.00 % 0.01 % -1.04 % -1.67 %
2 7.50 6.54 6.83 0.34 -1.16
3 5.07 5.98 4.77 -1.53 1.98
4 1.26 0.27 0.62 0.47 0.12
5 -1.97 -1.55 -2.90 -3.67 4.35
6 4.20 2.35 2.91 -3.46 -1.58
7 -0.66 -2.56 -2.64 -4.56 -1.82
8 -15.54 -15.38 -16.19 -5.94 5.63
9 6.09 3.96 5.93 0.01 -3.83
10 7.75 6.71 7.09 -3.45 -2.77
11 7.78 5.47 5.91 1.46 -3.69
12 9.55 4.92 5.96 -0.23 -4.95
13 5.27 2.80 3.57 1.07 -6.16
14 -3.14 -0.47 -4.20 -5.67 1.58
15 5.39 2.61 3.39 -3.87 -3.02
16 2.38 7.26 4.38 2.98 2.84
17 -2.83 0.11 -2.36 3.36 3.11
18 6.54 3.68 4.67 3.44 -4.33
19 -3.45 -0.53 -3.52 2.00 0.76
20 -1.16 -4.15 -1.36 -1.17 -1.30
21 -1.43 0.10 -2.59 3.29 -3.14
22 6.05 5.34 5.74 -6.44 -3.20
23 1.99 2.19 3.19 7.63 -8.10
24 7.28 7.14 7.83 7.06 -8.95
25 -4.71 -2.81 -4.52 4.02 -0.26
26 0.99 -2.02 2.57 21.58 -12.11
27 9.07 5.19 5.07 -16.65 7.84
28 -4.21 -3.03 -6.24 -7.52 8.50
29 -3.45 -0.56 -4.35 -5.76 5.39
30 3.85 1.71 4.76 13.28 -8.87
Compute the average monthly return and monthly standard return deviation for each portfolio and all three risk factors. Also state these values on an annualized basis. (Hint: Monthly returns can be annualized by multiplying them by 12, while monthly standard deviations can be annualized by multiplying them by the square root of 12.) Use a minus sign to enter negative values, if any. Do not round intermediate calculations. Round your answers to three decimal places.
Portfolio A Portfolio B Factor 1 Factor 2 Factor 3
Monthly:
Average
%
%
%
%
%
Std Dev
%
%
%
%
%
Annual:
Average
%
%
%
%
%
Std Dev
%
%
%
%
%
Based on the return and standard deviation calculations for the two portfolios from Part a, is it clear whether one portfolio outperformed the other over this time period? Do not make any additional calculations to answer this question.
Portfolio A earned a
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return and a
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standard deviation than Portfolio B. Therefore, it
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clear that one portfolio outperformed the other over this time period.
Calculate the correlation coefficients between each pair of the common risk factors (i.e., 1 & 2, 1 & 3, and 2 & 3). Use a minus sign to enter negative values, if any. Do not round intermediate calculations. Round your answers to four decimal places.
Correlation between 1 & 2:
Correlation between 1 & 3:
Correlation between 2 & 3:
In theory, what should be the value of the correlation coefficient between the common risk factors? Explain why.
In theory the correlations should be
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