Question

5. You have been managing a $5million portfolio that has a beta of 1.25 and a required rate of return of 12%. The current risk-free rate is 5.25%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 0.75, what will be the required return on your $5.5 million portfolio? Show work. a. 10.43% b. 11.75% c. 9.62% d. 10.17%

Answer 1

In the Queation Required rate of return will be calculated through CAPM Equation
Ke   =	Rf+ B( ER(M)-RF)
Ke represent Required rate of Return
Rf represent Risk free rate of Return
ER(M) reprersent Expected rate of Market
Given in the question , following Figure ( Risk free return =5.25 , Required rate of return =12, Beta =1.25 but Expected rate of market are not defined, so it need to calulate:_
Ke   =	Rf+ B( ER(M)-RF)
12=	5.25+1.25(ER(M)-5.25)
6.75	1.25(ER(M)-5.25)		10.65	6.5625
5.4	ER(M)-5.25		13.3125	1.25 ER(M)
10.65	ER(M)		10.6500
Expected rate of Market will be 10.65 %
Solution for case mentioned where Beta= 0.75, Risk free return =5.25% , Required rate of return need to be calculated=?
Ke   =	Rf+ B( ER(M)-RF)
	5.25+ 0.75( 10.65-5.25)
=	9.30
Hence, Required rate of return for $5 Million portfolio will be 12% and $0.5 Million portfolio will be 9.30%
Required rate of retun for $5.5 Million Portfolio will be =
	12%*$5 Million/$5.5 Million + 9.30% * $0.5 Million/$5.5 Million)
	0.117545455
	11.75%