Question

Suppose you are the money manager of a $3.74 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock	Investment	Beta
A	$   400,000	1.50
B	320,000	(0.50)
C	1,220,000	1.25
D	1,800,000	0.75

If the market's required rate of return is 10% 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

Given that the total investment amount=3.74 million or 3.74*1000000=3740000
Percentage invested in stock A =400000/3740000=0.106951872 or 10.70%
Percentage invested in stock B =320000/3740000=0.085561497 or 8.56%
Percentage invested in stock C =1220000/3740000=0.326203209 or 32.62%
Percentage invested in stock D =1800000/3740000=0.481283422 or 48.13%

Expected return of the stocks is calculated as:
Risk free rate + Beta*(Market return-Risk free rate)
= 5% + Beta*(10% - 5%)
= 5% + Beta*0.05

Expected return for stock A=5% + Beta*0.05=5% + 1.5*0.05=0.125
Expected return for stock B=5% + Beta*0.05=5% + (-.5)*0.05=0.025
Expected return for stock C=5% + Beta*0.05=5% + 1.25*0.05=0.1125
Expected return for stock D=5% + Beta*0.05=5% + 0.75*0.05=0.0875

Fund's required rate of return= Summation of (Percentage invested in a stock)*(Expected return of the stock)
=0.106951872*0.125+0.085561497*0.025+0.326203209*0.1125+0.481283422*0.0875
=0.013368984+0.002139037+0.036697861+0.042112299
=0.094318181 or 9.43% (Rounded to two decimal places)

So, the fund's required rate of return is 9.43%