Question

Suppose you are the money manager of a $3.86 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock	Investment		Beta
A	$   380,000		1.50
B	500,000		(0.50	)
C	1,180,000		1.25
D	1,800,000		0.75

If the market's required rate of return is 9% 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
A	380000	1.5
B	500000	-0.5
C	1180000	1.25
D	1800000	0.75

Total amount invested in the portfolio = $3860000

Weight of stock A in the portfolio = wA = 380000/3860000 = 0.0984455958549223

Weight of stock B in the portfolio = wB = 500000/3860000 = 0.129533678756477

Weight of stock C in the portfolio = wC = 1180000/3860000 = 0.305699481865285

Weight of stock D in the portfolio = wD = 1800000/3860000 = 0.466321243523316

Beta of stock A = βA = 1.5

Beta of stock B = βB = -0.5

Beta of stock C = βC = 1.25

Beta of stock D = βD = 0.75

Beta of the portfolio is calculated using the formula:

Portfolio beta = βP = wA*βA + wB*βB + wC*βC + wD*βD = 0.0984455958549223*1.5 + 0.129533678756477*(-0.5) + 0.305699481865285*1.25 + 0.466321243523316*0.75 = 0.814766839378238

Risk-free rate = RF = 6%

Market return = RM = 9%

Fund's or the portfoli's required rate of return is calculated using CAPM as shown below:

Return on portfolio = RP = RF + βP*(RM-RF) = 6% + 0.814766839378238*(9%-6%) = 8.44430051813472% ~ 8.44% (Rounded to two decimals)

Answer (%) -> 8.44