Question

3. The risk-free rate is 2%, and the required return on the market is 8%. What is the required return on an asset with a beta of 1.2? What is the reward/risk ratio? What is the required return on a portfolio consisting of 80% of the asset with a beta of 1.2 and the rest in an asset with an average amount of systematic risk?

4. Using the CAPM, show that the ratio of the risk premiums on the two assets in Question 3 is equal to the ratio of their betas.

Can you solve these two problems with detailed solutions?

Answer 1

Answer 3 (a):

Using CAPM model:

Required return = Risk free rate + Beta * (Market rate of return - Risk free rate)

= 2% + 1.2 * (8% - 2%)

= 9.20%

Required return = 9.20%

Answer 3 (b):

Reward Risk ratio = (Required return - Risk free rate) / Beta = (9.20% - 2%) / 1.2 = 6%

Reward Risk ratio = 6%

Answer 3 (c):

Required return on a portfolio consisting of 80% of the asset with a beta of 1.2 and the rest in an asset with an average amount of systematic risk:

Required return of the asset with a beta of 1.2 = 9.20%

Required return on average amount of systematic risk = Market rate of return = 8%

Required return = 80% *9.20% + 20% * 8%

= 8.96%

Required return = 8.96%

Answer 4:

Risk premium of the asset with a beta of 1.2 = Required return - Risk free rate = 9.20% - 2% = 7.20%

Risk premium of the asset of average amount of systematic risk = 8% - 2% = 6%

The ratio of the risk premiums on the two assets = 7.20% / 6% = 1.20 / 1

As such ratio of the risk premiums on the two assets is equal to the ratio of their betas.