5.) Consider the following information: Rate of Return if State Occurs State of
ID: 2741966 • Letter: 5
Question
5.) Consider the following information: Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A Stock B Stock C Boom .15 .35 .45 .27 Good .55 .16 .10 .08 Poor .25 –.01 –.06 –.04 Bust .05 –.12 –.20 –.09 Requirement 1: Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected return of the portfolio? (Do not round your intermediate calculations.) Requirement 2: (a) What is the variance of this portfolio? (Do not round your intermediate calculations.) (b) What is the standard deviation? (Do not round your intermediate calculations.)
Explanation / Answer
1.
State of Economy
Probability of State of Economy
Stock A
Stock B
Stock C
Rate of Return
Rate of return * Probability
Rate of Return
Rate of return * Probability
Rate of Return
Rate of return * Probability
Boom
0.15
0.3500
0.0525
0.4500
0.0675
0.2700
0.0405
Good
0.55
0.1600
0.0880
0.1000
0.0550
0.0800
0.0440
Poor
0.25
-0.0100
-0.0025
-0.0600
-0.0150
-0.0400
-0.0100
Bust
0.05
-0.1200
-0.0060
-0.2000
-0.0100
-0.0900
-0.0045
0.1320
0.0975
0.0700
Stock
Expected return
Weight
Weighted return
Stock A
0.1320
30%
0.0396
Stock B
0.0975
40%
0.0390
Stock C
0.0700
30%
0.0210
0.0996
Expected return of the portfolio = 9.96%
2.
Stock
Expected return
Weight
Weighted return
(Expected return - expected return of portfolio)^2
Stock A
0.1320
30%
0.0396
0.00105
Stock B
0.0975
40%
0.0390
0.00000
Stock C
0.0700
30%
0.0210
0.00088
0.0996
0.00193
a. Variance of the portfolio = 0.00193
b. Standard deviation of the portfolio = Square root of 0.00193 = 0.0440 = 4.40%
State of Economy
Probability of State of Economy
Stock A
Stock B
Stock C
Rate of Return
Rate of return * Probability
Rate of Return
Rate of return * Probability
Rate of Return
Rate of return * Probability
Boom
0.15
0.3500
0.0525
0.4500
0.0675
0.2700
0.0405
Good
0.55
0.1600
0.0880
0.1000
0.0550
0.0800
0.0440
Poor
0.25
-0.0100
-0.0025
-0.0600
-0.0150
-0.0400
-0.0100
Bust
0.05
-0.1200
-0.0060
-0.2000
-0.0100
-0.0900
-0.0045
0.1320
0.0975
0.0700
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.