Question

The risk free rate is 4%, and the required return on the market is 12%.

1. What is the required return on an asset with a beta of 1.5?
2. What is the reward/risk ratio given the required rate of return from (a)?
3. What is the required return on a portfolio consisting of 40% of the asset above and the rest in an asset with an average amount of systematic risk? (hint: asset with an average amount of systematic risk has beta of 1)
4. What is the required return on a portfolio consisting of 30% of the asset above and the rest in an asset with a risk free asset?

Answer 1

Answer a.

Risk-free Rate = 4.00%
Beta = 1.50
Market Return = 12.00%

Required Return = Risk-free Rate + Beta * (Market Return - Risk-free Rate)
Required Return = 4.00% + 1.50 * (12.00% - 4.00%)
Required Return = 16.00%

Answer b.

Reward/Risk Ratio = (Required Return - Risk-free Rate) / Beta
Reward/Risk Ratio = (0.16 - 0.04) / 1.50
Reward/Risk Ratio = 0.08

Answer c.

Required Return of Asset = 16.00%
Weight of Asset = 40%
Required Return of Market Return = 12.00%
Weight of Risk-free Asset = 60%

Required Return of Portfolio = Required Return of Asset * Weight of Asset + Required Return of Market * Weight of Market Asset
Required Return of Portfolio = 16.00% * 40% + 12.00% * 60%
Required Return of Portfolio = 13.60%

Answer d.

Required Return of Asset = 16.00%
Weight of Asset = 30%
Required Return of Risk-free Asset = 4.00%
Weight of Risk-free Asset = 70%

Required Return of Portfolio = Required Return of Asset * Weight of Asset + Required Return of Risk-free Asset * Weight of Risk-free Asset
Required Return of Portfolio = 16.00% * 30% + 4.00% * 70%
Required Return of Portfolio = 7.60%