Your portfolio is invested 24 percent each in A and C. and 52 percent in B. What
ID: 2751613 • Letter: Y
Question
Your portfolio is invested 24 percent each in A and C. and 52 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g.. 32.16.) What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g.. 32.16.)Explanation / Answer
Solution :
STOCK A
A
b
c
d
e
f
state of economy
Probability (p)
return (r)
P xr (i.e mean)
(c-0.128)^2
b x e
BOOM
0.15
0.38
0.057
0.063504
0.00953
GOOD
0.45
0.22
0.099
0.008464
0.00381
POOR
0.3
-0.04
-0.012
0.028224
0.00847
BUST
0.1
-0.16
-0.016
0.082944
0.00829
0.12800
0.183136
0.0301
Variance = p [(r - mean)^2]
expected rate of return = 12.80%
17.35%
Standard deviation = square root of variance = 17.35%
Variance = p [(r - mean)^2]
Standard deviation = square root of variance
STOCK B
A
b
c
d
e
f
state of economy
Probability (p)
return (r)
P xr (i.e mean)
(c-0.0965)^2
b x e
BOOM
0.15
0.48
0.072
0.14707225
0.02206
GOOD
0.45
0.19
0.0855
0.00874225
0.00393
POOR
0.3
-0.09
-0.027
0.03478225
0.01043
BUST
0.1
-0.34
-0.034
0.19053225
0.01905
0.09650
0.381129
0.05548
Variance = p [(r - mean)^2]
expected rate of return = 9.65%
23.55%
Standard deviation = square root of variance = 23.55%
STOCK C
A
b
c
d
e
f
state of economy
Probability (p)
return (r)
P xr (i.e mean)
(c-0.0805)^2
b x e
BOOM
0.15
0.28
0.042
0.03980025
0.00597
GOOD
0.45
0.15
0.0675
0.00483025
0.00217
POOR
0.3
-0.06
-0.018
0.01974025
0.00592
BUST
0.1
-0.11
-0.011
0.03629025
0.00363
0.08050
0.100661
0.01769
Variance = p [(r - mean)^2]
expected rate of return = 8.05%
13.30%
Standard deviation = square root of variance = 13.30%
Row No.
A
B
C
EXPECTED RETURN
1
0.12800
0.09650
0.08050
VARIANCE
2
0.030096
0.05548275
0.01769475
STANDARD DEVIATION
3
17.35%
23.55%
13.30%
Weight
4
0.24
0.52
0.24
1X4
5
3.07%
5.02%
1.93%
EXPECTED RETURN OF PORTFOLIO (sum of 5th row)
6
10.02%
2x4
7
0.00722304
0.02885103
0.00424674
VARIANCE OF PORTFOLIO (sum of 7th row)
8
4.03%
3x4
9
0.041635677
0.122484838
0.031925188
STANDARD DEVIATION of portfolio (sum of row 10)
10
19.60%
STOCK A
A
b
c
d
e
f
state of economy
Probability (p)
return (r)
P xr (i.e mean)
(c-0.128)^2
b x e
BOOM
0.15
0.38
0.057
0.063504
0.00953
GOOD
0.45
0.22
0.099
0.008464
0.00381
POOR
0.3
-0.04
-0.012
0.028224
0.00847
BUST
0.1
-0.16
-0.016
0.082944
0.00829
0.12800
0.183136
0.0301
Variance = p [(r - mean)^2]
expected rate of return = 12.80%
17.35%
Standard deviation = square root of variance = 17.35%
Variance = p [(r - mean)^2]
Standard deviation = square root of variance
STOCK B
A
b
c
d
e
f
state of economy
Probability (p)
return (r)
P xr (i.e mean)
(c-0.0965)^2
b x e
BOOM
0.15
0.48
0.072
0.14707225
0.02206
GOOD
0.45
0.19
0.0855
0.00874225
0.00393
POOR
0.3
-0.09
-0.027
0.03478225
0.01043
BUST
0.1
-0.34
-0.034
0.19053225
0.01905
0.09650
0.381129
0.05548
Variance = p [(r - mean)^2]
expected rate of return = 9.65%
23.55%
Standard deviation = square root of variance = 23.55%
STOCK C
A
b
c
d
e
f
state of economy
Probability (p)
return (r)
P xr (i.e mean)
(c-0.0805)^2
b x e
BOOM
0.15
0.28
0.042
0.03980025
0.00597
GOOD
0.45
0.15
0.0675
0.00483025
0.00217
POOR
0.3
-0.06
-0.018
0.01974025
0.00592
BUST
0.1
-0.11
-0.011
0.03629025
0.00363
0.08050
0.100661
0.01769
Variance = p [(r - mean)^2]
expected rate of return = 8.05%
13.30%
Standard deviation = square root of variance = 13.30%
Row No.
A
B
C
EXPECTED RETURN
1
0.12800
0.09650
0.08050
VARIANCE
2
0.030096
0.05548275
0.01769475
STANDARD DEVIATION
3
17.35%
23.55%
13.30%
Weight
4
0.24
0.52
0.24
1X4
5
3.07%
5.02%
1.93%
EXPECTED RETURN OF PORTFOLIO (sum of 5th row)
6
10.02%
2x4
7
0.00722304
0.02885103
0.00424674
VARIANCE OF PORTFOLIO (sum of 7th row)
8
4.03%
3x4
9
0.041635677
0.122484838
0.031925188
STANDARD DEVIATION of portfolio (sum of row 10)
10
19.60%
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