Question

Suppose you are the money manager of a $5.14 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock	Investment		Beta
A	$   420,000		1.50
B	700,000		(0.50	)
C	1,020,000		1.25
D	3,000,000		0.75

If the market's required rate of return is 13% 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

a. Calculation of portfolio beta

The beta of a portfolio is the weighted average beta of the securities which constitute the porfolio

Stock	Weight*	Beta	Weight*Beta
A	0.0817	1.5	0.12
B	0.1362	-0.5	(0.07)
C	0.1984	1.25	0.25
D	0.5837	0.75	0.44

Weight = Investment in a particular stock/total investment

Portfolio Beta = Weight*Beta

= .12-.07+.25+.44

= 0.74

Using Capital Asset Pricing Model

Required Rate of Return = Rf + b ( Rm – Rf )

Where,

Rf – Risk free return = 5%

b – Beta = .74

Rm – Expected return on market portfolio = 13%

Rm-Rf – Market risk premium

Required Rate of Return = 5+.74*(13-5)

= 5+.74*8

= 5+5.92

= 10.92%