Question

A stock has a beta of 1.15 and an expected return of 11.4 percent. A risk-free asset currently earns 3.5 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b.If a portfolio of the two assets has a beta of 7 what are the portfolio weights? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g.. .1616.) c. If a portfolio of the two assets has an expected return of 9 percent, what is its beta? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) d. If a portfolio of the two assets has a beta of 2.30, what are the portfolio weights? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent round to 4 decimal places, e.g.. 32.1616.) a. Expected return b. Weight of the stock Weight of the risk-free asset Beta d. Weight of the stock Weight of the risk-free asset Next

Answer 1

a.
Calculation of expected return on portfolio
Expected return on portfolio	(0.50*11.4%)+(0.5*3.5%)
Expected return on portfolio	0.057+0.0175
Expected return on portfolio	7.45%
b.
The beta of portfolio is weighted average beta of assets in the portfolio
For risk free asset the beta of portfolio is 0
Beta of portfolio	Beta of stock*Weight of stock + Beta of risk free asset*Weight of risk free asset
Let weight of stock be x and thus weight of risk free asset is (1-x)
Beta of portfolio	Beta of stock*x + Beta of risk free asset*(1-x)
0.7	(1.15x)+(0*(1-x))
0.7	1.15x
x	0.7/1.15
x	0.6087
Weight of stock	0.6087
Weight of risk free asset	0.3913	1-0.6087
c.
Using the expected return of portfolio we can calculate weight of each asset and then the beta of portfolio
Let weight of stock be x and thus weight of risk free asset is (1-x)
Expected return of portfolio	Weight of stock*Return on stock + Weight of risk free asset*Return on risk free asset
9%	11.4%x + ((1-x)*3.5%)
0.09	0.114x + 0.035 - 0.035x
0.09-0.035	0.079x
0.055	0.079x
x	0.055/0.079
x	0.6962
Weight of stock	0.6962
Weight of risk free asset	0.3038	1-0.6962
Beta of portfolio	(0.6962*1.15)+(0.3038*0)
Beta of portfolio	0.80
d.
The beta of portfolio is weighted average beta of assets in the portfolio
For risk free asset the beta of portfolio is 0
Beta of portfolio	Beta of stock*Weight of stock + Beta of risk free asset*Weight of risk free asset
Let weight of stock be x and thus weight of risk free asset is (1-x)
Beta of portfolio	Beta of stock*x + Beta of risk free asset*(1-x)
2.3	(1.15x)+(0*(1-x))
2.3	1.15x
x	2.3/1.15
x	2.0000
Weight of stock	2.0000
Weight of risk free asset	-1.0000	1-0.6087