Question

uppose you manage a $3,713,350 fund that consists of four stocks with the following investments: Stock Investment Beta A $130,950 1.20 B $211,750 –0.87 C $1,016,300 2.95 D $2,354,350 0.74 If the market's required rate of return is 14.70% and the risk-free rate is 5.00%, what is the fund's required rate of return?

Answer 1

The Beta of the portfolio is the weighted average of the Beta of the individual stocks of the portfolio.

The table to thus calculate the Beta of the portfolio is :

Stock	Investment	Beta	Weights (Investment / Total Investment)	Beta * Weight
A	130950	1.2	3.53%	0.042
B	211750	0.87	5.70%	0.050
C	1016300	2.95	27.37%	0.807
D	2354350	0.74	63.40%	0.469
Total	3713350		Weighted Average Beta	1.368

Now we have calculated the :
B of portfolio = 1.368.
Also given in question, Risk free rate (Rf) = 5%.
Market rate of return (Rm)= 14.7%

Now we know, as per capital asset pricing model (CAPM),

Re = Rf + B (Rm - Rf),

Using the values we have, we get,

Re = 5% + 1.368 ( 14.7% - 5%)

or
Re = 18.27%.

Ans : As calculated the firms required rate of return is 18.27%