Question

Suppose you are the money manager of a $4.62 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock	Investment		Beta
A	$   360,000		1.50
B	300,000		(0.50	)
C	1,560,000		1.25
D	2,400,000		0.75

If the market's required rate of return is 8% and the risk-free rate is 5%, what is the fund's required rate of return? Do not round intermediate calculations. Round your answer to two decimal places.

  %

Answer 1

Sol :

Given,

Total portfolio value = $4.62 million

Find fund's required rate of return?

In order to find und's required rate of return we have to first find weighted average beta.

Now weighted average beta = (Amount invested on each stock x beta)/Total portfolio value

Weighted average beta = [(360,000 x 1.50) + (300,000 x -050) + (1,,560,000 x 1.25) + (2,400,000 x 0.75)] / 4,620,000

Weighted average beta = $540,000 + (-150,000) + 1,950,000 + 1,800,000 / 4,620,000

Weighted average beta = 4,140,000/4,620,000 = 0.896103896

This can be work like this also,

Stock	Stock value	Weight	Beta	Weighted average
A	360000	0.077922078	1.5	0.116883117
B	300000	0.064935065	-0.5	-0.032467532
C	1560000	0.337662338	1.25	0.422077922
D	2400000	0.519480519	0.75	0.38961039
Total	4620000			0.896103896

Now fund's required rate of return (Rrr) will be,

Risk-free rate (Rfr) = 5%

Market required rate of return (Rm) = 8%

Beta of the stock (b) = 0.8961

Rrr = Rfr + (Rm - Rfr) x b

Rrr = 5% + (8% - 5%) x 0.896103896

Rrr = 5% + (3% x 0.896103896)

Rrr = 5% + 2.688311688%

Rrr = 7.69%

Therefore the fund's required rate of return (Rrr) will be 7.69%