Consider the following information: State of Probability of Rate of Return If St
ID: 2790251 • Letter: C
Question
Consider the following information: State of Probability of Rate of Return If State Occurs Economy State of Economy Stock A Stock B Stock C Boom .15 .362 .462 .342 Good .45 .132 .112 .182 Poor .35 .022 .032 .068 Bust .05 .122 .262 .102 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 and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return % What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) Variance What is the standard deviation of this portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation %
Explanation / Answer
Given Information:
State of Economy
Probability
Stock A
Stock B
Stock C
Boom
0.15
0.362
0.462
0.342
Good
0.45
0.132
0.112
0.182
Poor
0.35
0.022
0.032
-0.068
Bust
0.05
-0.122
-0.262
-0.102
Wa=0.32 (weight of asset A)
Wb=0.36 (weight of Asset B)
Wc=0.32 (weight of Asset C)
Therefore, E(R) portfolio:
E(R)=Probability of Boom×(( Wa×Ra)+ ( Wb×Rb)+ ( Wc×Rc))+
Probability of Good×(( Wa×Ra)+ ( Wb×Rb)+ ( Wc×Rc))+
Probability of Poor×(( Wa×Ra)+ ( Wb×Rb)+ ( Wc×Rc))+
Probability of Bust×(( Wa×Ra)+ ( Wb×Rb)+ ( Wc×Rc))
= 0.15×((0.32×0.362)+(0.36×0.462)+(0.32×0.342)+
0.45× ((0.32×0.132) +(0.36×0.112)+(0.32×0.182)+
0.35× ((0.32×0.022) +(0.36×0.032)+(0.32×-0.068)+
0.15× ((0.32×-0.122)+(0.36×-0.262)+(0.32×-0.102)
=0.05874+0.06336-0.00112-0.00830
=0.11268=11.268%=11.27%
Variance(2) = Probability of Boom×(( Ra-E(R)2)+ ( Rb-E(R))2+ ( Rc-E(R)2))+
Probability of Good × (( Ra-E(R)2)+ ( Rb-E(R))2+ ( Rc-E(R)2))+
Probability of Poor × (( Ra-E(R)2)+ ( Rb-E(R))2+ ( Rc-E(R)2))+
Probability of Bust× (( Ra-E(R)2)+ ( Rb-E(R))2+ ( Rc-E(R)2))+
=0.15×(( 0.362-0.11268)2+ ( 0.462-0.11268)2+ ( 0.342-0.11268)2)+
0.45×(( 0.132-0.11268)2+ ( 0.112-0.11268)2+ ( 0.182-0.11268)2)+
0.35×(( 0.022-0.11268)2+ ( 0.032-0.11268)2+ ( -0.068-0.11268)2)+
0.05 ×(( -0.122-0.11268)2+ ( -0.262-0.11268)2+ ( -0.102-0.11268)2)
=0.035516+0.002331+0.016582+0.012077=0.066506
Standard Deviation () = Variance
=0.066506
=0.257887=25.7887%=25.79%
State of Economy
Probability
Stock A
Stock B
Stock C
Boom
0.15
0.362
0.462
0.342
Good
0.45
0.132
0.112
0.182
Poor
0.35
0.022
0.032
-0.068
Bust
0.05
-0.122
-0.262
-0.102
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