Question

Suppose you manage a $4.485 million fund that consists of four stocks with the following investments:

Stock	Investment		Beta
A	$220,000		1.50
B	775,000		-0.50
C	1,340,000		1.25
D	2,150,000		0.75

If the market's required rate of return is 13% and the risk-free rate is 6%, what is the fund's required rate of return? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Stock	Investment	Beta	Weights
A	220000	1.5	4.91%
B	775000	-0.5	17.28%
C	1340000	1.25	29.88%
D	2150000	0.75	47.94%

We can calculate the weights of individual stocks in the portfolio

Weight of A = w_A = 220000/4485000 = 4.91%, Beta of A = β_A = 1.5

Weight of B = w_B = 775000/4485000 = 17.28%, Beta of B = β_B = -0.5

Weight of C = w_C = 1340000/4485000 = 29.88%, Beta of C = β_C = 1.25

Weight of D = w_D = 2150000/4485000 = 47.94%, Beta of D = β_D​​​​​​​ = 0.75

We need to calculate the beta of the portfolio, using the formula:

β_P = w_A*β_A + w_B*β_B + w_C*β_C + w_D*β_D = 4.91%*1.5 + 17.28%*(-0.5) + 29.88%*1.25 + 47.94%*0.75 = 0.720178372352285

Fund's required rate of return can be calculated using the CAPM Equation

E[R_P] = R_F + β_P*(R_M - R_F)

Risk-free rate = R_F = 6%, Market's return = R_M = 13%

E[R_P] = 6% + 0.720178372352285*(13% - 6%) = 11.041248606466%

Answer -> Fund's required rate of return = 11.04%