Question

Stock Y has a beta of 0.6 and an expected return of 9.7 percent. Stock Z has a beta of 2.4 and an expected return of 14.97 percent. What would the risk-free rate (in percent) have to be for the two stocks to be correctly priced relative to each other? Answer to two decimals.

Answer 1

Let the risk free rate be Rf

As per CAPM, price of a stock is given by

Re = Rf + (Rm – Rf) x Beta

Where,

Re = Expected return on the stock

Rf = Risk free rate of return

Rm – Rf = Market risk premium

Beta = Beta of the stock

So, price of stock Y will be given by

9.7 = Rf + (Rm – Rf) x 0.60 ---------- ( 1 ) and price of stock Z will be given by

14.97 = Rf + (Rm – Rf) x 2.4 ------- ( 2 )

( 2 ) - ( 1 )

5.27 = Rf – Rf + (Rm – Rf) x (2.4 – 0.60)

So, Rm – Rf = 5.27 / 1.80

= 2.93

So, putting the value of Rm – Rf in equation 1 we get

9.7 = Rf + 2.93 x 0.60

So, Rf = 9.7 – 1.76

= 7.94 percent