Consider the following information: Rate of Return If State Occurs State of Prob
ID: 2717076 • Letter: C
Question
Consider the following information: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C Boom .17 .352 .452 .332 Good .43 .122 .102 .172 Poor .33 .012 .022 .052 Bust .07 .112 .252 .092 Requirement 1: Your portfolio is invested 32 percent each in A and C and 36 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Expected return of the portfolio % Requirement 2: (a) What is the variance of this portfolio? (Do not round intermediate calculations. Round your answer to 5 decimal places (e.g., 32.16161).) Variance of the portfolio (b) What is the standard deviation of this portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Standard deviation %
Explanation / Answer
Solution :
STOCK A
a
b
c
d
e
f
state of economy
Probability (p)
return (r)
P xr (i.e mean)
(c-0.10842)^2
b x e
BOOM
0.17
0.352
0.05984
0.059331
0.0101
GOOD
0.43
0.122
0.05246
0.000184
8E-05
POOR
0.33
0.012
0.00396
0.009297
0.0031
BUST
0.07
-0.112
-0.00784
0.048585
0.0034
0.10842
0.117397
0.0166
Variance = p [(r - mean)^2]
expected rate of return = 10.842%
12.90%
Standard deviation = square root of variance = 12.90%
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-0.11)^2
b x e
BOOM
0.17
0.452
0.07684
0.116745
0.0198
GOOD
0.43
0.102
0.04386
6.92E-05
3E-05
POOR
0.33
0.022
0.00726
0.0078
0.0026
BUST
0.07
-0.252
-0.01764
0.131276
0.0092
0.11032
0.255891
0.0316
Variance = p [(r - mean)^2]
expected rate of return = 11.032%
17.79%
Standard deviation = square root of variance = 17.79%
STOCK C
a
b
c
d
e
f
state of economy
Probability (p)
return (r)
P xr (i.e mean)
(c-0.11)^2
b x e
BOOM
0.17
0.332
0.05644
0.050715
0.0086
GOOD
0.43
0.172
0.07396
0.004251
0.0018
POOR
0.33
-0.052
-0.01716
0.025217
0.0083
BUST
0.07
-0.092
-0.00644
0.039521
0.0028
0.10680
0.119705
0.0215
Variance = p [(r - mean)^2]
expected rate of return = 10.680%
14.68%
Standard deviation = square root of variance = 14.68%
Row No.
A
B
C
EXPECTED RETURN
1
0.10842
0.11032
0.10680
VARIANCE
2
0.016634504
0.03164
0.02153776
STANDARD DEVIATION
3
12.90%
17.79%
14.68%
Weight
4
0.32
0.36
0.32
1X4
5
3.47%
3.97%
3.42%
EXPECTED RETURN OF PORTFOLIO (sum of 5th row)
6
10.86%
2x4
7
0.005323041
0.01139
0.006892083
VARIANCE OF PORTFOLIO (sum of 7th row)
8
2.36055%
3x4
9
0.041271942
0.064035
0.046962396
STANDARD DEVIATION of portfolio (sum of row 10)
10
15.23%
STOCK A
a
b
c
d
e
f
state of economy
Probability (p)
return (r)
P xr (i.e mean)
(c-0.10842)^2
b x e
BOOM
0.17
0.352
0.05984
0.059331
0.0101
GOOD
0.43
0.122
0.05246
0.000184
8E-05
POOR
0.33
0.012
0.00396
0.009297
0.0031
BUST
0.07
-0.112
-0.00784
0.048585
0.0034
0.10842
0.117397
0.0166
Variance = p [(r - mean)^2]
expected rate of return = 10.842%
12.90%
Standard deviation = square root of variance = 12.90%
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-0.11)^2
b x e
BOOM
0.17
0.452
0.07684
0.116745
0.0198
GOOD
0.43
0.102
0.04386
6.92E-05
3E-05
POOR
0.33
0.022
0.00726
0.0078
0.0026
BUST
0.07
-0.252
-0.01764
0.131276
0.0092
0.11032
0.255891
0.0316
Variance = p [(r - mean)^2]
expected rate of return = 11.032%
17.79%
Standard deviation = square root of variance = 17.79%
STOCK C
a
b
c
d
e
f
state of economy
Probability (p)
return (r)
P xr (i.e mean)
(c-0.11)^2
b x e
BOOM
0.17
0.332
0.05644
0.050715
0.0086
GOOD
0.43
0.172
0.07396
0.004251
0.0018
POOR
0.33
-0.052
-0.01716
0.025217
0.0083
BUST
0.07
-0.092
-0.00644
0.039521
0.0028
0.10680
0.119705
0.0215
Variance = p [(r - mean)^2]
expected rate of return = 10.680%
14.68%
Standard deviation = square root of variance = 14.68%
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