A stock has a beta of 1.31 and an expected return of 12.9 percent. A risk-free a
ID: 2765590 • Letter: A
Question
A stock has a beta of 1.31 and an expected return of 12.9 percent. A risk-free asset currently earns 4.35 percent. Required: What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16). If a portfolio of the two assets has a beta of 0.91. what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).) If a portfolio of the two assets has an expected return of 12.1 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) If a portfolio of the two assets has a beta of 2.51. what are the portfolio weights? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).)Explanation / Answer
Answer
Answer a (Two decimal)
Particulars
Expected return
Proportion
Proportionate Return
A
B
A*B
Stock
12.9
0.5
6.45
Risk free asset
4.35
0.5
2.18
Expected return of portfolio
8.63
Answer b (4 decimal)
Particulars
Beta
Proportion
Weighted beta
A
B
A*B
Stock
1.31
X
1.31X
Risk free asset
0
(1-X)
0
Beta of portfolio (given)
0.91
Solving above equation
Beta of the portfolio = Sum of weighted betas
0.91 = 1.31X + 0
1.31X = 0.91
X = 0.6947
1-X = 1 - 0.6947
= 0.3053
So Stock weight = 0.6947
Risk free asset weight = 0.3053
Answer c ( two decimal)
Particulars
Expected return
Proportion
Proportionate Return
A
B
A*B
Stock
12.9
X
12.9X
Risk free asset
4.35
(1-X)
4.35(1-X)
Portfolio return (Given)
12.10
Solving Above Equation
12.10 = 12.9X + 4.35(1-X)
12.10 = 12.9X + 4.35 – 4.35X
12.10 - 4.35 = 12.9X– 4.35X
7.75 = 8.55X
X = 0.9064
1-X = 1 – 0.9064
= 0.0936
So Stock weight = 0.9064
Risk free asset weight = 0.0936
Particulars
Beta
Proportion
Weighted beta
A
B
A*B
Stock
1.31
0.9064
1.19
Risk free asset
0
0.0936
0
Beta of portfolio (given)
1.19
Answer d (4 decimal)
Particulars
Beta
Proportion
Weighted beta
A
B
A*B
Stock
1.31
X
1.31X
Risk free asset
0
(1-X)
0
Beta of portfolio (given)
2.51
Solving above equation
Beta of the portfolio = Sum of weighted betas
2.51 = 1.31X + 0
1.31X = 2.51
X = 1.9160
1-X = 1 - 1.9160
= - 0.9160
So Stock weight = 1.9160
Risk free asset weight = - 0.9160
Particulars
Expected return
Proportion
Proportionate Return
A
B
A*B
Stock
12.9
0.5
6.45
Risk free asset
4.35
0.5
2.18
Expected return of portfolio
8.63
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