Question

Portfolio X consists of 4 stocks which are A, B, C, and D. The information pertaining to the stocks, the portfolio and the market are given below:

Stock	Investment	Beta
A	$25,000	0.8
B	$25,000	1.2
C	$25,000	Not Available
D	$25,000	Not Available
Portfolio X	$100,000	1

Expected return of the market = 10%
Risk-free rate = 4%

(a) Calculate the beta of Portfolio Y that is equally invested in stock A and stock B.

b) Compute the beta of Portfolio Z that is equally invested in stock C and stock D.

(c) Suppose you sell all $25,000 invested in Stock A and use the proceeds to invest in Stock B. Calculate the resulting value of the beta of Portfolio X.

(d) Compute the change in the expected return of Portfolio X resulting from your actions in part (c).

(e) Discuss the likely circumstances where you would sell a stock with a lower beta and invest the proceeds in a stock with a higher beta, as in part (c).

Answer 1

(a) Calculate the beta of Portfolio Y that is equally invested in stock A and stock B.
=(0.8+1.2)/2
=1.00

b) Compute the beta of Portfolio Z that is equally invested in stock C and stock D.
Average beta of C and D has to be 1 for Portfolio X to have beta of 1 and given A and B have average beta of 1
=1.00

(c) Suppose you sell all $25,000 invested in Stock A and use the proceeds to invest in Stock B. Calculate the resulting value of the beta of Portfolio X.
Beta will increase by (1.2-0.8)*0.25=0.1
New beta=1.1

(d) Compute the change in the expected return of Portfolio X resulting from your actions in part (c).
=change in beta*(market return-risk free rate)
=0.1*(10%-4%)
=0.60%

(e) Discuss the likely circumstances where you would sell a stock with a lower beta and invest the proceeds in a stock with a higher beta, as in part (c).
When returns has to be increased