Using CAPM A stock has a beta of 1.20 and an expected return of 14 percent. A ri

Question

Using CAPM

A stock has a beta of 1.20 and an expected return of 14 percent. A risk-free asset currently earns 3 percent.

What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))

If a portfolio of the two assets has a beta of .72, what are the portfolio weights? (Do not round intermediate calculations and round your answers to 4 decimal places. (e.g., 32.1616))

If a portfolio of the two assets has an expected return of 10 percent, what is its beta? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))

If a portfolio of the two assets has a beta of 2.40, what are the portfolio weights? (Do not round intermediate calculations and negative amount should be indicated by a minus sign.)

A stock has a beta of 1.20 and an expected return of 14 percent. A risk-free asset currently earns 3 percent.

Explanation / Answer

Answer-a:

Expected return of portfolio (of equally invested ) = (Risk free rate + Return on asset ) / 2

= (3 +14) / 2 = 8.5%

Answer-b:

Calculation of portfolio weights:

Assuming weight of Risk free investment is X (Beta for risk free investment is 0)

Hence weight for Stock =1-X

Hence ,

Portfolio beta   =Stock Beta * weight of Stock

0.72 =1.20*(1-X)

1.2 – 1.2X = 0.72

Hence X = (1.2-0.72) / 1.2

=0.40 = 40%

Hence Risk free weight = 40%

And Weight of Stock = 60%

Answer-c:

Calculation of Beta:

Expected return of portfolio = Risk free rate * weight of Risk free + Stock rate * weight of Stock

10% = 3% *X + 14% (1-X)

10 = 3 X + 14 – 14X

11X = 11

Hence X = 4/11 = 0.3636

So weight of Risk free = 0.3636

And weight of stock = 1-0.3636 = 0.6364

So beta of the project = Stock beta* stock weight

= 1.2*0.6364 = 0.76

Answer-d:

Calculation of portfolio weights:

Assuming weight of Risk free investment is X (Beta for risk free investment is 0)

Hence weight for Stock =1-X

Hence ,

Portfolio beta   = Stock Beta * weight of Stock

2.40 =1.20*(1-X)

1.2-1.2X = 2.40

Hence X = -1.2/1.2 = -1 =-100%

Hence Risk free weight = -100%

And Weight of Stock = 200%

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