Consider the following information: Your portfolio is invested 26 percent each i
ID: 2770047 • Letter: C
Question
Consider the following information: Your portfolio is invested 26 percent each in A and C, and 48 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
Answer a.
Expected return = (0.1295*0.26)+(0.1125*0.48)+(0.0805*0.26)
= 10.86%
State
Probability
Stock A(ROR)
Prob*ROR
Boom
0.15
0.33
0.0495
Good
0.55
0.18
0.099
Poor
0.25
-0.05
-0.0125
Bust
0.05
-0.13
-0.0065
Total
0.1295
State
Probability
Stock B(ROR)
Prob*ROR
Boom
0.15
0.43
0.0645
Good
0.55
0.14
0.077
Poor
0.25
-0.08
-0.02
Bust
0.05
-0.18
-0.009
Total
0.1125
State
Probability
Stock B(ROR)
Prob*ROR
Boom
0.15
0.23
0.0345
Good
0.55
0.12
0.066
Poor
0.25
-0.06
-0.015
Bust
0.05
-0.1
-0.005
Total
0.0805
Answer B
Portfolio variance =(0.02*0.26)+(0.03*0.48)+(0.01*0.26)
= 0.0222
Answer C
Portfolio standard deviation =(0.14*0.26)+(0.17*0.48)+(0.10*0.26)
=0.144
State
Probability
Stock A(ROR)
Prob*ROR
ROR-0.1295
(ROR-0.1295)^2
(ROR-0.1295)^2)*Prob
Boom
0.15
0.33
0.0495
0.2005
0.040
0.01
Good
0.55
0.18
0.099
0.0505
0.003
0.00
Poor
0.25
-0.05
-0.0125
-0.1795
0.032
0.01
Bust
0.05
-0.13
-0.0065
-0.2595
0.067
0.00
Total
0.1295
-0.188
0.142311
0.02
Variance
0.02
Std deviation sqrt(0.02)
0.14
State
Probability
Stock B(ROR)
Prob*ROR
ROR-0.1125
(ROR-0.1125)^2
((ROR-0.1125)^2) *prob
Boom
0.15
0.43
0.0645
0.3175
0.101
0.02
Good
0.55
0.14
0.077
0.0275
0.001
0.00
Poor
0.25
-0.08
-0.02
-0.1925
0.037
0.01
Bust
0.05
-0.18
-0.009
-0.2925
0.086
0.00
Total
0.1125
-0.14
0.224175
0.03
Variance
0.03
Std deviation sqrt(0.03)
0.17
State
Probability
Stock C(ROR)
Prob*ROR
ROR-0.0805
(ROR-0.0805)^2
(ROR-0.0805)^2)*prob
Boom
0.15
0.23
0.0345
0.1495
0.022
0.00
Good
0.55
0.12
0.066
0.0395
0.002
0.00
Poor
0.25
-0.06
-0.015
-0.1405
0.020
0.00
Bust
0.05
-0.1
-0.005
-0.1805
0.033
0.00
Total
0.0805
-0.132
0.076231
0.01
Variance
0.01
Std deviation sqrt(0.01)
0.10
State
Probability
Stock A(ROR)
Prob*ROR
Boom
0.15
0.33
0.0495
Good
0.55
0.18
0.099
Poor
0.25
-0.05
-0.0125
Bust
0.05
-0.13
-0.0065
Total
0.1295
State
Probability
Stock B(ROR)
Prob*ROR
Boom
0.15
0.43
0.0645
Good
0.55
0.14
0.077
Poor
0.25
-0.08
-0.02
Bust
0.05
-0.18
-0.009
Total
0.1125
State
Probability
Stock B(ROR)
Prob*ROR
Boom
0.15
0.23
0.0345
Good
0.55
0.12
0.066
Poor
0.25
-0.06
-0.015
Bust
0.05
-0.1
-0.005
Total
0.0805
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