Given the following information, which investment is better, based upon the risk
ID: 2720070 • Letter: G
Question
Given the following information, which investment is better, based upon the risk (as measured by the standard deviation) and return of each?
STOCK A1
Return Probability Expected Rate of Return Standard Deviation
11% 0.30 ?
15% 0.40 ?
19% 0.30 ? ?
STOCK B1
Return Probability Expected Rate of Return Standard Deviation
-05% 0.20 ?
06% 0.30 ?
14% 0.30 ?
22% 0.20 ? ?
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PART 2
The following are end of the month prices for both the Standard & Poors 500 Index and Nike's Common stock. Using the data here calculate the holding-period returns, the average monthly return and the standard deviation for both the S&P 500 and Nike. Use Microsoft Excel to construct your submission.
2011 NIKE S&P 500 INDEX
June $89.98 $1,320.64
July $90.15 $1,292.28
August $86.65 $1,218.89
September $85.51 $1,131.42
October $96.35 $1,253.30
November $96.18 $1,246.96
December $96.37 $1,257.60
2012 NIKE S&P 500 INDEX
January $103.99 $1,312.41
February $107.92 $1,365.68
March $108.44 $1,408.47
April $111.87 $1,397.91
May $108.18 $1,310.33
June $98.45 $1,335.69
Thanks.
Explanation / Answer
Calculation of Expected Return and Standard Deviation:
STOCK A1
Return
Probability
Expected Return
Deviation
Deviation ^2
A
B
A*B
C
D=A-C
E=D*D
11%
0.30
3.30%
15.00%
-4.00%
0.1600%
15%
0.40
6.00%
15.00%
0.00%
0.0000%
19%
0.30
5.70%
15.00%
4.00%
0.1600%
Expected Return
15.00%
Sum of Deviation ^2
0.3200%
Standard Deviation = (Sum of Deviation ^2 / (3-1))^(1/2)
5.66%
STOCK B1
Return
Probability
Expected Return
Deviation
Deviation ^2
A
B
A*B
C
D=A-C
E=D*D
-5%
0.20
-1.00%
5.80%
-10.80%
1.1664%
-6%
0.30
-1.80%
5.80%
-11.80%
1.3924%
14%
0.30
4.20%
5.80%
8.20%
0.6724%
22%
0.20
4.40%
5.80%
16.20%
2.6244%
Expected Return
5.80%
Sum of Deviation ^2
5.8556%
Standard Deviation = (Sum of Deviation ^2 / (3-1))^(1/2)
24.20%
Standard Deviation of Stock A1 is lower and Expected Return of Stock A1 is higher, hence based upon the risk (as measured by the standard deviation) and return, Stock A1 is better for investment.
Calculation of Expected Return and Standard Deviation:
STOCK A1
Return
Probability
Expected Return
Deviation
Deviation ^2
A
B
A*B
C
D=A-C
E=D*D
11%
0.30
3.30%
15.00%
-4.00%
0.1600%
15%
0.40
6.00%
15.00%
0.00%
0.0000%
19%
0.30
5.70%
15.00%
4.00%
0.1600%
Expected Return
15.00%
Sum of Deviation ^2
0.3200%
Standard Deviation = (Sum of Deviation ^2 / (3-1))^(1/2)
5.66%
STOCK B1
Return
Probability
Expected Return
Deviation
Deviation ^2
A
B
A*B
C
D=A-C
E=D*D
-5%
0.20
-1.00%
5.80%
-10.80%
1.1664%
-6%
0.30
-1.80%
5.80%
-11.80%
1.3924%
14%
0.30
4.20%
5.80%
8.20%
0.6724%
22%
0.20
4.40%
5.80%
16.20%
2.6244%
Expected Return
5.80%
Sum of Deviation ^2
5.8556%
Standard Deviation = (Sum of Deviation ^2 / (3-1))^(1/2)
24.20%
Standard Deviation of Stock A1 is lower and Expected Return of Stock A1 is higher, hence based upon the risk (as measured by the standard deviation) and return, Stock A1 is better for investment.
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