Question

Suppose you are the money manager of a $4.83 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock	Investment	Beta
A	$   220,000	1.50
B	740,000	(0.50)
C	1,220,000	1.25
D	2,650,000	0.75

If the market's required rate of return is 9% and the risk-free rate is 3%, what is the fund's required rate of return? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Solution :

Calculation of beta of the fund :

The formula for calculating the beta of the fund is

Β_F = [ ( W_A * β_A ) + ( W_B * β_B ) + ( W_C * β_C ) + ( W_D * β_D ) ]

where

β_F = Beta of the fund

W_A = Weight of Investment in Stock A = ( 220,000 / 4,830,000 ) = 0.0455 ;      

β_A = Beta of the Stock A = 1.50    ;

W_B = Weight of Investment in Stock B = ( 740,000 / 4,830,000 ) = 0.1532 ;       

Β_B = Beta of the Stock B = - 0.50     ;

W_C = Weight of Investment in Stock C = ( 1,220,000 / 4,830,000 ) = 0.2526 ;      

β_C = Beta of the Stock C = 1.25 ;

W_D = Weight of Investment in Stock D = ( 2,650,000 / 4,830,000 ) = 0.5487 ;   

β_D = Beta of the Stock D = 0.75 ;

Applying the above vales in the formula we have

= ( 0.0455 * 1.50 )   + ( 0.1532 * - 0.50 )   + ( 0.2526 * 1.25 ) + ( 0.5487 * 0.75 )

= 0.0683 – 0.0766 + 0.3158 + 0.4115

= 0.7189

Thus beta of the Fund is = 0.7189

Calculation of required rate of return of the fund :

The required rate of return on a given fund is calculated using the following formula :

RR= R_F + [ β * ( R_M - R_F ) ]

Where

RR = Required rate of return on a fund; R_F = Risk free rate f return   ; β = Beta of the fund ;   R_M = Market required rate of return

As per the information given in the question we have

R_F = 3 %   ; R_M = 9 %   ; β = 0.7189

Applying the above values in the formula we have

= 3 % + [ 0.7189 * ( 9 % - 3 % ) ]

= 3 % + [ 0.7189 * ( 6 % ) ]

= 3 % + 4.3134 % = 7.3134 %

= 7.31 % (When rounded off to two decimal places)

Thus, the fund's required rate of return = 7.31 %