A stock has a beta of .9 and an expected return of 11 percent. A risk-free asset

Question

A stock has a beta of .9 and an expected return of 11 percent. A risk-free asset currently earns 3.5 percent.

What is the expected return on a portfolio that is equally invested in the two assets? (

If a portfolio of the two assets has a beta of .29, what are the portfolio weights?

If a portfolio of the two assets has an expected return of 11.75 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

If a portfolio of the two assets has a beta of 1.38, what are the portfolio weights?

A stock has a beta of .9 and an expected return of 11 percent. A risk-free asset currently earns 3.5 percent.

Explanation / Answer

a. In present case portfolio has equal weight so we can sum the returns of each asset and divide by the number of assets.The expected return of the portfolio = E(Rp) = (11%+3.5%)/2 = 7.25%

b.We need to find out the portfolio weights that result in portfolio's Beta 0.29. We know the risk free asset beta is zero and we know that portfolio total wieght is 1 so weight of risk free asset is 1 - weight of stck.

Beta of portfolio = wS* Beta S +w Rf * Beta Rf

0.29 = wS*0.9 +(1-ws) * 0

ws = 0.29/0.9

ws = 0.3222

and weight of risk free asset is = 1 - 0.3222 =0.6777

c. We need to find out the portfolio weight that result in a portfolio with an expected return of 11.75%.We know the risk free asset beta is zero and we know that portfolio total wieght is 1 so weight of risk free asset is 1 - weight of stck.

E(Rp) = 11.75% = 11%ws +3.5% (1-ws)

0.1175 = 0.11 ws + 0.035- 0.035ws

0.0825 = 0.075 ws

ws = 1.1

W Rp = 1-1.1 = 0.10

So the beta of the portfolio =

Beta of portfolio = wS* Beta S +w Rf * Beta Rf

=1.1*0.9 +( -.10 *0)

=0.99

d. Beta of portfolio = wS* Beta S +w Rf * Beta Rf

1.38 = wS* Beta S +(1-ws) * Beta Rf

1.38= 0.9 ws + (1-ws) *0

1.38 = 0.9ws

ws =1.53

Wrf = 1- 1.53 = -0.53

c. We need to find out the portfolio weight that result in a portfolio with an expected return of 11.75%.We know the risk free asset beta is zero and we know that portfolio total wieght is 1 so weight of risk free asset is 1 - weight of stck.

E(Rp) = 11.75% = 11%ws +3.5% (1-ws)

0.1175 = 0.11 ws + 0.035- 0.035ws

0.0825 = 0.075 ws

ws = 1.1

W Rp = 1-1.1 = 0.10

So the beta of the portfolio =

Beta of portfolio = wS* Beta S +w Rf * Beta Rf

=1.1*0.9 +( -.10 *0)

=0.99

d. Beta of portfolio = wS* Beta S +w Rf * Beta Rf

1.38 = wS* Beta S +(1-ws) * Beta Rf

1.38= 0.9 ws + (1-ws) *0

1.38 = 0.9ws

ws =1.53

Wrf = 1- 1.53 = -0.53

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