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

Stock	Investment	Beta	Wt. Beta
A	25,000	0.8	0.2	<--(inv/portfolio total)*beta
B	25,000	1.2	0.3	<--(inv/portfolio total)*beta
C	25,000	NA	0.5
D	25,000	NA	<--Combined beta of these two stocks is 0.5 in the portfolio
Portfolio X	100,000	1	1
a)	Stock	Investment	Beta	Wt. Beta
	A	50%	0.8	0.4
	B	50%	1.2	0.6
	Portfolio Y beta			1.00
b)	Stock	Investment	Beta	Wt. Beta
	C	50%	0.5	0.25	<--Considering equal beta of both C & D
	D	50%	0.5	0.25
	Portfolio Y beta			0.50
c)	Stock	Investment	Beta	Wt. Beta
	A	-	0.8	0	<--No investment in A now
	B	50,000	1.2	0.6	<---25,000 from A invested in B thus wt. of B in portfolio is 50% now
	C	25,000	NA	0.5
	D	25,000	NA
	Portfolio X	100,000	1	1.1
d)	CAPM	Rf+Beta*(Rm-Rf)
	Rm	10%
	Rf	4%
	Change in expected return= New return -old expected return
	New Return	10.6%
	Old Return	10.0%
	Change	0.6%

The above table gives the answers along with the case facts

e) ONe would invest in a high beta stock when they expect the market to move up in the future and hence the stock will move up more than the market due to its higher beta.

Please reach out for any further clarifications