Question

Problem 7-13

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	%	0.03	%	-0.94	%	-1.68	%
2		7.50		6.60		6.89		0.39		-1.20
3		4.97		6.01		4.77		-1.40		2.02
4		1.13		0.29		0.71		0.37		0.13
5		-1.95		-1.63		-2.90		-3.64		4.19
6		4.25		2.34		2.76		-3.37		-1.54
7		-0.83		-2.50		-2.64		-4.60		-1.75
8		-15.48		-15.45		-16.07		-5.89		5.70
9		6.11		3.98		5.96		0.02		-3.78
10		7.61		6.80		7.01		-3.39		-2.92
11		7.86		5.54		5.87		1.27		-3.70
12		9.71		4.94		6.03		-0.33		-4.94
13		5.27		2.77		3.39		1.23		-6.15
14		-3.21		-0.50		-4.13		-5.62		1.66
15		5.46		2.51		3.27		-3.83		-3.13
16		2.49		7.24		4.43		2.97		2.73
17		-2.80		0.08		-2.31		3.37		3.04
18		6.61		3.72		4.80		3.43		-4.31
19		-3.27		-0.55		-3.51		1.96		0.70
20		-1.33		-3.97		-1.38		-1.14		-1.16
21		-1.56		0.25		-2.73		3.13		-3.19
22		6.03		5.21		5.82		-6.48		-3.21
23		2.04		2.19		3.30		7.69		-8.11
24		7.25		7.12		7.77		6.98		-9.15
25		-4.73		-2.79		-4.50		4.16		-0.07
26		1.09		-1.99		2.63		21.45		-12.04
27		9.04		5.28		5.13		-16.79		7.80
28		-4.23		-3.00		-6.18		-7.46		8.59
29		-3.33		-0.73		-4.18		-5.82		5.48
30		3.92		1.85		4.76		13.36		-8.74

1. 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	%	%	%	%	%

2. 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 -Select-higher lower return and a -Select-higher lower standard deviation than Portfolio B. Therefore, it -Select-isis not clear that one portfolio outperformed the other over this time period.

3. 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:

4. In theory, what should be the value of the correlation coefficient between the common risk factors? Explain why.

   In theory the correlations should be -Select-equal to 0equal to 1equal to -1indefinite because we want the factors to be -Select-independent of each other highly correlated.

Answer 1

a)

	Portfolio A	Portfolio B	Factor 1	Factor 2	Factor 3	Formula Used
Monthly:
Average	1.89033333	1.387	1.16	0.036	-1.291	=AVERAGE(G12:G41)
Std Dev	5.39425403	4.56119732	5.205591	6.754224	4.892908	=STDEV.P(G12:G41)
Annual:
Average	22.684	16.644	13.92	0.432	-15.492	=G45*12
Std Dev	18.6862441	15.800451	18.0327	23.39732	16.94953	=G46*SQRT(12)

b)

It is not clear whether one portfolio outperformed the other, As, Portfolio A earned a higher average return than B but at the same time its standard deviation is also high. This means that the Higher expected return of A has come at the cost of Higher Standard Deviation and hence more risk.

c)

Corr 1&2	0.22296938	=CORREL(E12:E41,F12:F41)
Corr 1&3	-0.55322189	=CORREL(E12:E41,G12:G41)
Corr 2&3	-0.75185648	=CORREL(F12:F41,G12:G41)

d)

Ideally, the correlation between the factors should be 0. i.e, we desire the factors to be uncorrelated so that they can explain as much as the variance in data as possible.