Consider the following information: Rate of Return If State Occurs State of Prob
ID: 2721626 • 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 .58 .07 .15 .33 Bust .42 .16 .06 .06 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return % b. What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 32.161616.) VarianceExplanation / Answer
The portfolio return of equally weighted portfolio would be:
Rp = (RA + RB + RC)/3
Expected return of the portfolio:
ER = sum of P x Rp
State
P
R A
R B
RC
Rp
P x Rp
Boom
0.58
0.07
0.15
0.33
0.183333
0.106333
Burst
0.42
0.16
0.06
-0.06
0.053333
0.0224
12.87%
Variance
Rp = 0.20 RA + 0.60 RB + 0.20 RC
State
P
R A
R B
RC
Rp
P x Rp
Boom
0.58
0.07
0.15
0.33
0.22
0.1276
Burst
0.42
0.16
0.06
-0.06
0.152
0.06384
19.14%
Expected return ER = 19.14%
Variance = sum of P x(Rp -ER)^2
State
P
Rp -ER
P x(Rp -ER)^2
Boom
0.58
2.86%
0.000473091
Burst
0.42
-3.94%
0.000653316
0.001126
Variance = 0.001126
State
P
R A
R B
RC
Rp
P x Rp
Boom
0.58
0.07
0.15
0.33
0.183333
0.106333
Burst
0.42
0.16
0.06
-0.06
0.053333
0.0224
12.87%
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