Question

In: Finance

A stock has a beta of 0.9 and an expected return of 9 percent. A risk-free...

A stock has a beta of 0.9 and an expected return of 9 percent. A risk-free asset currently earns 4 percent.

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 percent rounded to 2 decimal places.) b. If a portfolio of the two assets has a beta of 0.5, what are the portfolio weights? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

c. If a portfolio of the two assets has an expected return of 8 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Expert Solution

a) The return of a portfolio is the weighted average return of the securities which constitute the porfolio.

Security	Weight	Expected Return(%)	*WeightExpected Return**
Stock	0.5	9	4.5
Risk free asset	0.5	4	2

Portfolio Return = 6.50 % (4.50+2.00)

b) The beta of a portfolio is the weighted average beta of the securities which constitute the porfolio.

Let weight of Stock be x, weight of risk free asset is 1-x

Security	Weight	Beta	*WeightBeta**
Stock	x	0.9	.9x
Risk free asset	1-x	0	0

.9x + 0 =.5

x = 55.56%

weight of Stock is 55.56% and weight of risk free asset is 44.44%

note: beta of risk free asset is zero

c) Calculation of portfolio beta

a) Find weight under given portfolio return

Let weight of Stock be x, weight of risk free asset is 1-x

Security	Weight	Expected Return	*WeightExpected Return**
Stock	x	9	9x
Risk free asset	1-x	4	4(1-x)

9x + 4 - 4x = 8

5x = 4

x = .80

weight of Stock is 80% and weight of risk free asset is 20%

b) Calculation of portfolio beta

Security	Weight	Beta	*Weightbeta**
Stock	0.8	0.9	0.72
Risk free asset	0.2	0	0

Portfolio Beta = 0.72

jeff jeffy answered 2 years ago

A stock has a beta of 1.6 and an expected return of 14 percent. A risk-free...

A stock has a beta of 1.6 and an expected return of 14 percent. A risk-free asset currently earns 4 percent. a) What is the expected return on a portfolio that is equally invested in the two assets? b) If a portfolio of the two assets has a beta of 0.8, what are the portfolio weights? c) If a portfolio of the two assets has an expected return of 10 percent, what is its beta? d) If all assets in...

A stock has a beta of 0.6 and an expected return of 10 percent. A risk-free...

A stock has a beta of 0.6 and an expected return of 10 percent. A risk-free asset currently earns 4.1 percent. 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 percent rounded to 2 decimal places.) b. If a portfolio of the two assets has a beta of 0.57, what are the portfolio weights? (Do not round intermediate calculations. Enter your answers...

A stock has a beta of 1.38 and an expected return of 13.6 percent. A risk-free...

A stock has a beta of 1.38 and an expected return of 13.6 percent. A risk-free asset currently earns 4.7 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.) Expected return % b. If a portfolio of the two assets has a beta of .98, what are the portfolio weights? (Do not...

A stock has a beta of 1.3 and an expected return of 12.8 percent. A risk-free...

A stock has a beta of 1.3 and an expected return of 12.8 percent. A risk-free asset currently earns 4.3 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.) Expected return % b. If a portfolio of the two assets has a beta of .90, what are the portfolio weights? (Do not...

A stock has a beta of 0.5 and an expected return of 9.6 percent. A risk-free...

A stock has a beta of 0.5 and an expected return of 9.6 percent. A risk-free asset currently earns 3.3 percent. If a portfolio of the two assets has an expected return of 12 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

A stock has a beta of 2.2, the risk-free rate is 6 percent, and the expected...

A stock has a beta of 2.2, the risk-free rate is 6 percent, and the expected return on the market is 12 percent. Using the CAPM, what would you expect the required rate of return on this stock to be? What is the market risk premium?

Evaluating risk and return. Stock X has an expected return of 9.5 percent, a beta coefficient...

Evaluating risk and return. Stock X has an expected return of 9.5 percent, a beta coefficient of 0.9, and a 30 percent standard deviation of expected returns. Stock Y has a 13 percent expected return, a beta coefficient of 1.3, and a 20 percent standard deviation. The risk-free rate is 5 percent, and the market risk premium is 5.5 percent. a) Calculate the coefficient of variation of each stock. b) Which stock is riskier for diversified investors? Which stock is...

A stock has an expected return of 0.07, its beta is 0.75, and the risk-free rate...

A stock has an expected return of 0.07, its beta is 0.75, and the risk-free rate is 0.03. What must the expected return on the market be? Enter the answer with 4 decimals (e.g. 0.0567).

A stock has an expected return of 0.06, its beta is 1.12, and the risk-free rate...

A stock has an expected return of 0.06, its beta is 1.12, and the risk-free rate is 0.03. What must the expected return on the market be? Enter the answer with 4 decimals (e.g. 0.0567). You own a stock portfolio invested 32 percent in Stock Q, 22 percent in Stock R, 19 percent in Stock S, and 27 percent in Stock T. The betas for these four stocks are 1.87, 1.81, 2.64, and 0.99, respectively. What is the portfolio beta?...

A stock has an expected return of 0.12, its beta is 0.94, and the risk-free rate...

A stock has an expected return of 0.12, its beta is 0.94, and the risk-free rate is 0.02. What must the expected return on the market be? Enter the answer with 4 decimals (e.g. 0.0567). You own a stock portfolio invested 32 percent in Stock Q, 22 percent in Stock R, 19 percent in Stock S, and 27 percent in Stock T. The betas for these four stocks are 1.93, 1.64, 0.91, and 1.42, respectively. What is the portfolio beta?...