Question

Suppose you are the money manager of a $4.95 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock	Investment	Beta
A	$   320,000	1.50
B	780,000	(0.50)
C	900,000	1.25
D	2,950,000	0.75

If the market's required rate of return is 9% and the risk-free rate is 3%, what is the fund's required rate of return? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Beta of portfolio is calculated as = Summision of Weight of each stock in the portfolio * beta of each stock

where weight of each stock is determined as = Investment in each stock / Total investement in portfolio

Hence beta calculation is given as-

Stock	Investement	Weight	Beta	W*B
		(W)	(B)
A	320000	0.06464646	1.5	0.096969697
B	780000	0.15757576	-0.5	-0.078787879
C	900000	0.18181818	1.25	0.227272727
D	2950000	0.5959596	0.75	0.446969697
Total	4950000	1		0.692424242

Hence the beta of the stock is 0.692424242

Required rate of return is given as = Risk free return+ (Market rate of return - Risk free return)*Beta

hence in this case

Required return = 3%+(9%-3%)*0.692424242

=3%+4.1545%

=7.1545%

or 7.15%(Rounded off to two decimals)