Question

The stock of United Industries has a beta a 1.14 and an expected return of 11.2. The risk-free rate of return is 4 percent. What is the expected return on the market?

Answer 1

Solution:          

As per Capital Asset Pricing model the Expected return on stock is calculated using the following formula :

E(R) = R_F + [ β * ( R_M - R_F ) ]

Where

E(R) = Expected Return on stock ; R_F = Risk free rate   ; β = Beta of the stock ;  

R_M = Expected Return on the market ;

As per the information given in the question we have

R_F = 4 %   ; β = 1.14 ;    E(R ) = 11.2 % ; R_M = To find ;

Applying the above values in the formula we have

11.2 % = 4 % + [ 1.14 * ( R_M - 4 % ) ]

11.2 % - 4 % = [ 1.14 * ( R_M - 4 % ) ]

7.2 % = 1.14 * (R_M - 4 % )

7.2 % / 1.14 = ( R_M - 4 % )

6.315789 % = ( R_M - 4 % )

( R_M - 4 % ) = 6.315789 %

R_M = 4 % + 6.315789 %

R_M = 10.315789 %

Thus the Expected Return on the market is

= 10.3158 % ( when rounded off to four decimal places )

= 10.32 % ( when rounded off to two decimal places )