Question

The expected return on Justus, Inc. stock is 15.63% while the expected return on the market is 12.4%. The beta of Justus's stock is 1.48. What is the risk-free rate of return?

Answer 1

Solution :

As per Capital Asset Pricing Model, Expected return of a stock is calculated using the following formula :

R_S = R_F + [ β * ( R_M - R_F ) ]

Where

R_S = Expected return on stock ; R_F = Risk free rate of return   ; β = Beta of the stock ;

R_M = Expected return on the market

As per the information given in the question we have

R_S = 15.63 % = 0.1563 ;   R_M = 12.4 % = 0.124 ; β = 1.48

R_F = To find   ; Let R_F be ‘X’

Applying the above values in the formula we have

0.1563 = X + [ 1.48 * ( 0.124 – X) ]

0.1563 = X + 0.183520 – 1.48X

0.1563 = 0.183520 – 0.48X

0.48X = 0.183520 – 0.1563

0.48X = 0.027220

X = 0.027220 / 0.48

X = 0.056708

X = 5.6708 %

Thus the Risk free rate = 5.6708 %

= 5.67 % ( when rounded off to two decimal places )