Question

Two investment advisers are comparing performance. One averaged a 19% return and the other a 16% return. However, the beta of the first adviser was 1.5, while that of the second was 1.0. If the T-bill rate were 3% and the market return were 15%, which adviser would be the superior stock selector?

Answer 1

Solution :

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 = 15 % = 0.15 ;   RF = T – Bill rate = 3 % = 0.03 ;    β = 1.5   ;

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

= 3 % + [ 1.5 * ( 15 % - 3 % ) ]

= 3 % + [ 1.5 * 12 % ]

= 3 % + 18 %

= 21 %

Thus the Required rate of return for the first adviser as = 21 %

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 = 15 % = 0.15 ;   RF = T – Bill rate = 3 % = 0.03 ;    β = 1.0   ;

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

= 3 % + [ 1.0 * ( 15 % - 3 % ) ]

= 3 % + [ 1.0 * 12 % ]

= 3 % + 12 %

= 15 %

Thus the Required rate of return of the second adviser as = 15 %

Calculation of Alpha’s:

Adviser 1 :

Actual Return = 19 %   ;   Required rate of return = 21 % ;

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

= 19 % - 21 % = - 2 %

Adviser 2 :

Actual Return = 16 % ; Required rate of return = 15 % ;

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

= 16 % - 15% = 1 %

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

Thus the adviser 2 shall be the superior stock selector.