Question

The risk-free rate is 2%. The β of stock 1 is 0.8 while its σ is 15%. The beta of stock 2 is 1.6 while its σ is 45%. Which of the following statements is true in equilibrium?

Select one:

a. The risk premium of stock 2 would be three times the risk premium of stock 1.

b. The risk premium of stock 2 would be twice as much as the risk premium of stock 1.

c. The expected return of stock 2 would be three times the risk premium of stock 1.

d. The expected return of stock 2 would be twice as much as the risk premium of stock 1.

Answer 1

Risk Premium of Any Stock (say Y) is given by:

Ry - Rf = Beta (Y) x [Rm - Rf] where Ry is the expected return on stock Y, Beta(Y) is stock Y's beta, Rm is the return on the market/benchmark portfolio, Rf is the risk-free rate and the term (Ry-Rf) is the risk premium of stock Y.

As is observable, the risk premium of stock Y is directly proportional to the firm's beta. In the context provided, stock 1 has a beta of 0.8 whereas stock 2 has a beta of 1.6 which is twice that of the former. Hence, it is decipherable that stock 2 will have a risk-premium twice as much as the risk-premium of stock 1.

Hence, the correct option is (b)