A stock has a beta of 1.34 and an expected return of 13.2 percent. A risk-free a
ID: 2722207 • Letter: A
Question
A stock has a beta of 1.34 and an expected return of 13.2 percent. A risk-free asset currently earns 4.5 percent. Required: (a) 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).) Expected return % (b) If a portfolio of the two assets has a beta of 0.94, what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).) Weight of the stock Weight of the risk-free asset (c) If a portfolio of the two assets has an expected return of 12.4 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Beta (d) If a portfolio of the two assets has a beta of 2.54, 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).) Weight of the stock? Weight of the risk-free asset?
Explanation / Answer
a.
Calculation of expected return on a portfolio that is equally invested in the two assets:
Formula :
Expected return on a portfolio = (Return on Asset A * weight of Asset A) + (Return on risk free * weight of risk free)
Return on Assets A =
13.20%
Return on Risk Free =
4.50%
Weight of Assets A (Equal weights ) = 1/2 =
0.5
Weight of Risk Free (Equal weights ) = 1/2 =
0.5
Expected return on a portfolio = (Return on Asset A * weight of Asset A) + (Return on risk free * weight of risk free)
= (13.2% * 0.5 ) +(4.5% *0.50) =
8.85%
b.
Calculation of portfolio weights:
Formula :
Portfolio beta = (Beta of Asset A * weight of Asset A) + (Beta of Risk free * weight of risk free)
Portfolio beta =
0.94
Beta of Asset A =
1.34
Beta of Risk free Inv. =
0
Assuming Weight of Asset A =
A
hence Weight of Risk Free = 1-A
Hence,
0.94 = (1.34*A) + (0 * (1-A))
0.94 = 1.34*A
A = 0.94 / 1.34 = 0.7015
Hence weight of Asset A =
0.7015
Weight of Risk free = (1-0.7015)
0.2985
c.
Calculation of Beta;
Formula :
Expected return on a portfolio = (Return on Asset A * weight of Asset A) + (Return on risk free * weight of risk free)
Expected return on a portfolio =
12.40%
Return on Assets A =
13.20%
Return on Risk Free =
4.50%
Weight of Assets A =
A
Weight of Risk Free =
1-A
12.40%= (13.20% * A) + (4.50% * (1-A))
0.124= 0.132 * A + 0.045 - 0.045A
0.124= 0.087* A + 0.045
A = (0.124 - 0.045) / 0.087
A = 0.908046
Hence Weight of Asset A = 0.908046
And weight of Risk free = 1-0.908046 = 0.091954
Formula :
Portfolio beta = (Beta of Asset A * weight of Asset A) + (Beta of Risk free * weight of risk free)
= (1.34*0.908046) + (0*0.091954) =
1.22
d.
Calculation of portfolio weights:
Formula :
Portfolio beta = (Beta of Asset A * weight of Asset A) + (Beta of Risk free * weight of risk free)
Portfolio beta =
2.54
Beta of Asset A =
1.34
Beta of Risk free Asset. =
0
Assuming Weight of Asset A =
A
hence Weight of Risk Free = 1-A
1-A
Hence,
2.54 = (1.34 * A) + (0 * (1-A))
2.54 = (1.34 * A)
A = 2.54 / 1.34 =
1.8955
Hence weight of Assets A =
1.8955
And weight of risk free asset = 1-1.8955 =
(0.8955)
a.
Calculation of expected return on a portfolio that is equally invested in the two assets:
Formula :
Expected return on a portfolio = (Return on Asset A * weight of Asset A) + (Return on risk free * weight of risk free)
Return on Assets A =
13.20%
Return on Risk Free =
4.50%
Weight of Assets A (Equal weights ) = 1/2 =
0.5
Weight of Risk Free (Equal weights ) = 1/2 =
0.5
Expected return on a portfolio = (Return on Asset A * weight of Asset A) + (Return on risk free * weight of risk free)
= (13.2% * 0.5 ) +(4.5% *0.50) =
8.85%
b.
Calculation of portfolio weights:
Formula :
Portfolio beta = (Beta of Asset A * weight of Asset A) + (Beta of Risk free * weight of risk free)
Portfolio beta =
0.94
Beta of Asset A =
1.34
Beta of Risk free Inv. =
0
Assuming Weight of Asset A =
A
hence Weight of Risk Free = 1-A
Hence,
0.94 = (1.34*A) + (0 * (1-A))
0.94 = 1.34*A
A = 0.94 / 1.34 = 0.7015
Hence weight of Asset A =
0.7015
Weight of Risk free = (1-0.7015)
0.2985
c.
Calculation of Beta;
Formula :
Expected return on a portfolio = (Return on Asset A * weight of Asset A) + (Return on risk free * weight of risk free)
Expected return on a portfolio =
12.40%
Return on Assets A =
13.20%
Return on Risk Free =
4.50%
Weight of Assets A =
A
Weight of Risk Free =
1-A
12.40%= (13.20% * A) + (4.50% * (1-A))
0.124= 0.132 * A + 0.045 - 0.045A
0.124= 0.087* A + 0.045
A = (0.124 - 0.045) / 0.087
A = 0.908046
Hence Weight of Asset A = 0.908046
And weight of Risk free = 1-0.908046 = 0.091954
Formula :
Portfolio beta = (Beta of Asset A * weight of Asset A) + (Beta of Risk free * weight of risk free)
= (1.34*0.908046) + (0*0.091954) =
1.22
d.
Calculation of portfolio weights:
Formula :
Portfolio beta = (Beta of Asset A * weight of Asset A) + (Beta of Risk free * weight of risk free)
Portfolio beta =
2.54
Beta of Asset A =
1.34
Beta of Risk free Asset. =
0
Assuming Weight of Asset A =
A
hence Weight of Risk Free = 1-A
1-A
Hence,
2.54 = (1.34 * A) + (0 * (1-A))
2.54 = (1.34 * A)
A = 2.54 / 1.34 =
1.8955
Hence weight of Assets A =
1.8955
And weight of risk free asset = 1-1.8955 =
(0.8955)
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