A stock has a beta of 1.29 and an expected return of 12.7 percent. A risk-free a

Question

A stock has a beta of 1.29 and an expected return of 12.7 percent. A risk-free asset currently earns 4.25 percent.

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 0.89, 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 11.9 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 2.49, 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).)

A stock has a beta of 1.29 and an expected return of 12.7 percent. A risk-free asset currently earns 4.25 percent.

Explanation / Answer

Answer:

a) Expected return on a portfolio that is equally invested in the two assets =

weight of risky stock * Expected return on risky stock + weight of riskfree stock * Expected return on riskfree stock

= 0.5 * 12.7% + 0.5 * 4.25% = 8.475%

b) In portfolio beta is the weighted average beta of all stocks in the portfolio:

Beta of a risk free asset is 'Zero"

Now : Portfolio beta = Weight of risky asset * Beta of risky asset =>0.89 = Weight * 1.29

=>Weight of risky stock = 68.99%

so Weight of risk free stock = 100%-68.99% = 31.01%

c) Let the weight of risky asset = "x" , so the weight of risk free asset = (1-x)

So the expected return of the portfolio = X * 12.7% + (1-X)*4.25% = 11.9%

=> 12.7% X - 4.25% X = 11.9% - 4.25% =>0.127X - 0.0425X = 0.0765 => 0.9053 = 90.53%

(1-X) = 1-0.9053 = 0.0947 = 9.47%

So the portfolio beta = Weight of risky asset* Beta of risky asset = 90.53%*1.29 = 1.17

d)

Portfolio beta = Weight of risky asset * Beta of risky asset =>2.49 = Weight * 1.29

=>Weight of risky stock = 1.9302

so Weight of risk free stock = 1 - 1.9302 = - 0.9302

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