Question

7.7

Suppose you are the money manager of a $4.22 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock	Investment		Beta
A	$   560,000		1.50
B	600,000		(0.50	)
C	1,260,000		1.25
D	1,800,000		0.75

If the market's required rate of return is 11% and the risk-free rate is 4%, what is the fund's required rate of return? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Given the following information,

Stock	Investment	Beta
A	5,60,000	1.50
B	6,00,000	-0.50
C	12,60,000	1.25
D	18,00,000	0.75

In order to calculate the funds required rate of return, we need to use the following formula,

Fund's Required return = Risk free Return + (Market Return - Risk free return)* Beta of fund

Where

Risk free rate = 4% = 0.04

Market's return = 11% = 0.11

and

Beta of fund = Σ (Investment in stock * beta of stock)/ Total investment

Where

Σ (Investment in stock * beta of stock) = (5,60,000*1.50) + (6,00,000*(-0.50)) + (12,60,000*1.25) + (18,00,000*0.75)

Σ (Investment in stock * beta of stock) = 8,40,000 + (-3,00,000) + 15,75,000 + 13,50,000

Σ (Investment in stock * beta of stock) = 34,65,000

Total investment = 4.22 million = 42,20,000

Now,

Beta of fund = 34,65,000/ 42,20,000

Beta of fund = 0.8210900

Substituting these values in the funds required rate equation, we get

Fund's Required return = 0.04 + (0.11 - 0.04)* 0.8210900

Fund's Required return = 0.04 + (0.07)* 0.8210900

Fund's Required return = 0.04 + 0.0575

Fund's Required return = 0.0975

Fund's Required return = 9.75%

Therefore, the funds required rate of return is 9.75%