Question

There is a 30 percent probability that a particular stock will earn a 17 percent return and a 70 percent probability that it will earn 11 percent. What is the risk-free rate if the risk premium on the stock is 8.60 percent?

Multiple Choice

4.20 percent

4.80 percent

5.20 percent

5.40 percent

Answer 1

Solution :

Assuming that the return on stock given in the question are market returns we have expected market return as

R_M = (17 % * 0.3) + (11 % * 0.7) = 5.1 + 7.7 = 12.8 %

Given that R_F = Risk premium on stock = 8.60 % .

Risk premium as per Capital Asset Pricing Model (CAPM) is calculated as follows:

Risk premium = (Return on market - Risk free rate of Interest or return)

                        = (Market Return - Risk free rate)   = ( R_M - R_F )

Thus Risk premium = 5.60 = ( 12.8 - R_F )

5.60 = ( 12.8 - R_F )

R_F = 12.8 - 5.60 = 4.2 %

Thus risk free rate = 4. 2 %

Hence, the solution is option 1 = 4.2 % = Risk free rate.