Consider the following information about three stocks: Rate of Return If State O
ID: 2715172 • Letter: C
Question
Consider the following information about three stocks: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C Boom .25 .22 .34 .56 Normal .48 .19 .17 .15 Bust .27 .03 .35 .44 a-1 If your portfolio is invested 45 percent each in A and B and 10 percent in C, what is the portfolio expected return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Portfolio expected return % a-2 What is the variance? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) Variance a-3 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.) Standard deviation % b. If the expected T-bill rate is 3.90 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected risk premium % c-1 If the expected inflation rate is 3.50 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Approximate expected real return % Exact expected real return % c-2 What are the approximate and exact expected real risk premiums on the portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Approximate expected real risk premium % Exact expected real risk premium %
Explanation / Answer
Portfolio Return Rp = WA x RA + WB x RB + WC x RC
State
P
A
B
C
Rp
Boom
0.25
0.22
0.34
0.56
0.308
Normal
0.48
0.19
0.17
0.15
0.177
Bust
0.27
0.03
-0.35
-0.44
-0.188
State
P
Rp
P x Rp
Rp-ER
P x (Rp-ER)^2
Boom
0.25
0.308
0.077
0.1968
0.00968256
Normal
0.48
0.177
0.08496
0.0658
0.002078227
Bust
0.27
-0.188
-0.05076
-0.2992
0.024170573
Er
0.1112
Variance
0.03593
Portfolio Expected return Er= Sum of P x Rp
= 11.12%
Variance = P x (Rp-ER)^2
= 0.03593
Standard deviation = variance ^0.50
= 0.03593^0.50
= 18.96%
Risk premium = portfolio expected return – risk free rate
= 11.12% -3.90%
= 7.22%
State
P
A
B
C
Rp
Boom
0.25
0.22
0.34
0.56
0.308
Normal
0.48
0.19
0.17
0.15
0.177
Bust
0.27
0.03
-0.35
-0.44
-0.188
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