Question

You own a portfolio consisting of the following stocks:

Stock        % of Portfolio        Beta        Historical Return   Required Return

1 13% 1.15 .11

2 44% 0.95 .08

  3 19% 1.60 .14

  4 24% 1.30 .12

The risk-free rate is 5% and the expected market return is 10%.

a. Calculate the required return for each stock.

 

b. Calculate the historical return on the portfolio.

 

c. Calculate the portfolio beta.

d. Calculate the required return on the portfolio.

 

e. Draw the SML. Plot the historical returns and the required returns of each stock and the portfolio.

f. Which investments appear to be winners and which ones appear to be losers?

 

Answer 1

A. required return = Risk free rate +Beta*(expected market return-risk free rate)

1	=0.05+1.15*(0.10-0.05)	10.75%
2	=0.05+0.95*(0.10-0.05)	9.75%
3	=0.05+1.6*(0.10-0.05)	13.00%
4	=0.05+1.30*(0.10-0.05)	11.50%

B. Historical Return of Portfolio= % of stock 1 in portfolio*historial return of 1+  % of stock 2 in portfolio*historial return of 2+ % of stock 3 in portfolio*historial return of 3+ % of stock 4 in portfolio*historial return of 4

='=0.13*0.11+0.44*.08+.19*.14+.24*.12 =10.49%

C. Portfolio Beta= % of stock 1 in portfolio* Beta of 1+% of stock 2 in portfolio* Beta of 2+% of stock 3 in portfolio* Beta of 3+% of stock 4 in portfolio* Beta of 4

='=0.13*1.15+0.44*.95+.19*1.6+.24*1.3 = 1.1835

D.required return of portfolio = Risk free rate +Beta of portfolio*(expected market return-risk free rate)

= 0.05+1.1835(.10-.05) = 10.92%

E. In the Graph Star shows historical return and Dot shows Required ReturnF. Investment 2 is losers as it is below SML, and Stock 1,2 and 3 are performing good as it is above SML.