Question

One investment adviser averaged 20% return while another one 15% return. The beta of the first adviser was 1.6, while that of the second was 1.2.

1. Which adviser was a better selector of individual stocks (ignoring general movements in the market)?

2. If the T-bill rate was 5% and the market return during the period was 13%, which adviser would be the superior stock selector?

Answer 1

Calculation of the Required rate of return of the First Adviser :

As per Capital Asset Pricing Model, required return is calculated using the following formula :

RS = RF + [ β * ( RM - RF ) ]

Where

RS = Required return ; RF = Risk free rate of return   ; β = Beta ; RM = Market Return ;

As per the information given in the question we have

RM = 13 % = 0.13 ;   RF = T – Bill rate = 5 % = 0.05 ;    β = 1.6 ;

Applying the above values in the formula we have the required rate of return as

= 5 % + [ 1.6 * ( 13 % - 5 % ) ]

= 5 % + [ 1.6 * 8 % ]

= 5 % + 12.8 %

= 17.8 %

Thus the Required rate of return for the first adviser as = 17.80 %

Calculation of Required rate of return of the Second adviser :

As per Capital Asset Pricing Model, required return is calculated using the following formula :

RS = RF + [ β * ( RM - RF ) ]

Where

RS = Required return ; RF = Risk free rate of return   ; β = Beta ; RM = Market Return ;

As per the information given in the question we have

RM = 13 % = 0.13 ;   RF = T – Bill rate = 5 % = 0.05 ;    β = 1.2 ;

Applying the above values in the formula we have the required rate of return as

= 5 % + [ 1.2 * ( 13 % - 5 % ) ]

= 5 % + [ 1.2 * 8 % ]

= 5 % + 9.6 %

= 14.6 %

Thus the Required rate of return of the second adviser as = 14.60 %

Calculation of Alpha’s:

Adviser 1 :

Actual Return = 20 %   ;   Required rate of return = 17.80 % ;

Thus Alpha of Adviser 1 = Actual Return - Required rate of return

= 20 % - 17.80 % = 2.20 %

Adviser 2 :

Actual Return = 15 % ; Required rate of return = 14.6 % ;

Thus Alpha of Adviser 2 = Actual Return - Required rate of return

= 15 % - 14.6% = 0.40 %

Since the alpha of adviser 1 is higher than the alpha of adviser 2, the adviser 1 shall be the superior stock selector.

Thus the adviser 1 shall be the superior stock selector.

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