Question

    Using CAPM, a stock has a beta of 1.13 and expected return of 12.1%. Risk-free asset currently earns 3.6%.

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

(    (b)   A portfolio of two assets has a beta of 0.50, what are portfolio weights?

(c)    If a portfolio of two assets has an expected return of 10%, what is beta?

(d)   If a portfolio of two assets has a beta of 2.26, what are portfolio weights?

Answer 1

(a)  E (RP) = 0.5{0.121+0.036}

                    = 0.0785 or 7.85%

(b) Stock beta ={0.5/1.13)}100%

                       =44.25%

     Risk free = {1-(0.5/1.13)}100%

                      =55.75%

(c)  10=12.1a+ {1-a} 3.6

   10 =12.1a+3.6-3.6a

   10=8.5a+3.6

    a =0.75

    Risk free=0.25

    Beta of portfolio = 0.75{1.13}

                                 =0.8475

(d) 2.26=1.13b+ {1-b} 0

    b=2{100%}

     =200%

Risk free rate =-100%. The amount of money is being burrowed at a risk free rate and invested in the portfolio stocks.

(a) Expected return on portfolio is 0.0785.

 (b) Portfolio weights for stock beta and risk free rate are 44.25% and 55.75% respectively.

 (c) Portfolio beta is 0.875.

(d)  Portfolio weights are 200% and -100% respectively.