A stock has a beta of .6 and an expected return of 10 percent. A risk-free asset

Question

A stock has a beta of .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. Omit the "%" sign in your response.) Expected return % b. If a portfolio of the two assets has a beta of .57, what are the portfolio weights? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.) Portfolio Weight xS % xrf % c. If a portfolio of the two assets has an expected return of 8.25 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 4 decimal places.) Beta d. If a portfolio of the two assets has a beta of 1.10, what are the portfolio weights? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.) Porfolio Weight xS % xrf %

Explanation / Answer

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

=0.5*10%+0.5*4.1%

=5%+2.05%

=7.05%

Therefore the % expected return on a portfolio that is equally invested in the two assets =7.05

b)Let the weight of stock be w% therefore the weight of risk-free asset is 1-w

The portfolio beta=w*stock beta+(1-w)*risk-free asset beta

The portfolio beta=w*0.6+(1-w)*0=0.57

=>0.6w=0.57

=>w=0.57/0.6=0.95=95.00%

therefore the % Portfolio Weight in stock is 95.00 and the  % Portfolio Weight in risk-free asset is 5.00.

c)Let the weight of stock be w% therefore the weight of risk-free asset is 1-w

expected return of portfolio=w*expected return of stock+(1-w)*expected return of risk-free asset

expected return of portfolio=w*10%+(1-w)*4.1%=8.25%

=>w*10+(1-w)*4.1=8.25

=>10w-4.1w=8.25-4.1

=>5.9w=4.15

=>w=4.15/5.9

The portfolio beta=w*stock beta+(1-w)*risk-free asset beta

The portfolio beta=w*0.6+(1-w)*0

The portfolio beta=(4.15/5.9)*0.6+(1-4.15/5.9)*0

The portfolio beta=(4.15/5.9)*0.6

The portfolio beta=0.4220

Thus the portfolio of the two assets has an expected return of 8.25 percent has beta of 0.4220.

d)

Let the weight of stock be w% therefore the weight of risk-free asset is 1-w

The portfolio beta=w*stock beta+(1-w)*risk-free asset beta

The portfolio beta=w*0.6+(1-w)*0=01.1

=>0.6w=1.1

=>w=1.1/0.6=1.8333=183.33%

therefore the % Portfolio Weight in stock is 183.33 and the  % Portfolio Weight in risk-free asset is -83.33.

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