You have decided to invest 30 percent in X; 30 percent in Y; and 40 percent in Z
ID: 2652181 • Letter: Y
Question
You have decided to invest 30 percent in X; 30 percent in Y; and 40 percent in Z. The probability of the state of the economy is Boom 25%; Normal 60%; and, Bust 15%. The rate of return for stock X is Boom .20; Normal .15; and, Bust .00. The rate of return for stock Y is Boom .35; Normal .10; and, Bust -.30. The rate of return for stock Z is Boom .60; Normal .05; Bust -.40.
A] What is the portfolio expected return?
B] If the expected T-bill rate is 1.5 percent, what is the expected risk premium on the portfolio?
Explanation / Answer
Answer:
A
Calculation of Expected Return of portfolio
State of Economy
Probability of
Stock X
Stock Y
Stock Z
Return
Expected Return (A)
Return
Expected Return (B)
Return
Expected Return (C)
A
B
A*B
C
A*C
D
A*D
Boom
25.00%
0.20
5.00%
0.35
8.75%
0.60
15.00%
Normal
60.00%
0.15
9.00%
0.10
6.00%
0.05
3.00%
Bust
15.00%
-
0.00%
(0.30)
-4.50%
(0.40)
-6.00%
Expected returns (E)
14.00%
10.25%
12.00%
Weights (F)
30.00%
30.00%
40.00%
E*F
4.20%
3.08%
4.80%
Expected return of portfolio = Sum of E *F
12.08%
B
Expected risk premium on the portfolio = Expected Return of Portfolio - Risk Free rate
= 12.08% -1.5%
10.58%
A
Calculation of Expected Return of portfolio
State of Economy
Probability of
Stock X
Stock Y
Stock Z
Return
Expected Return (A)
Return
Expected Return (B)
Return
Expected Return (C)
A
B
A*B
C
A*C
D
A*D
Boom
25.00%
0.20
5.00%
0.35
8.75%
0.60
15.00%
Normal
60.00%
0.15
9.00%
0.10
6.00%
0.05
3.00%
Bust
15.00%
-
0.00%
(0.30)
-4.50%
(0.40)
-6.00%
Expected returns (E)
14.00%
10.25%
12.00%
Weights (F)
30.00%
30.00%
40.00%
E*F
4.20%
3.08%
4.80%
Expected return of portfolio = Sum of E *F
12.08%
B
Expected risk premium on the portfolio = Expected Return of Portfolio - Risk Free rate
= 12.08% -1.5%
10.58%
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