Question

7. Stock A has an expected return of 18.6 percent and a beta of 1.2. Stock B has an expected return of 15 percent and a beta of 0.9. Both stocks are correctly priced and lie on the Security market Line (SML). What is the reward-to-risk ratio for stock A?

Answer 1

Solution :

For two stocks to be correctly priced their Reward to risk ratio should be equal

Thus equating the Reward – to – Risk ratio for the two stocks we have as follows :

( RA – RF ) / βA   = ( RB – RF ) / βB

Where RA = Expected return of stock A = 18.6 %   ;     βA   :Beta of the stock A = 1.2

Where RB = Expected return of stock B = 15.0 %   ;     βB :Beta of the stock B = 0.9

RF = Risk free rate = Let the Risk free rate be ‘ x ‘

Applying the above values in the equation we have

( 18.6 % – x ) / 1.2 = ( 15 % – x ) / 0.9

( 18.6 % – x ) * 0.9 = ( 15 % – x ) * 1.2

16.74 % - 0.9x = 18 % - 1.2x

- 0.9x + 1.20x = 18 % - 16.74 %

0.3x = 1.26 %

x = 1.26 % / 0.3

x = 4.20 %

Thus the risk-free rate for the two stocks to be correctly priced is = 4.20 %

Calculation of reward to risk ratio of Stock A :

The formula for calculating the reward-to-risk ratio is

= ( RA – RF ) / βA  

Where RA = Expected return of stock A = 18.6 % = 0.1860   ;   βA :Beta of the stock A = 1.2

RF = Risk free rate = 4.20 % = 0.0420

Applying the above values in the equation we have the reward-to-risk ratio of stock A as

= ( 0.1860 – 0.0420 ) / 1.2

= 0.1440 / 1.2

= 0.12

Thus the reward-to-risk ratio of stock A is = 0.12