Final answer:
The risk-free rate, given a stock's beta of .90, an expected return of 9.22 percent, and a reward-to-risk ratio of 6.20 percent is calculated to be 3.64 percent using the Capital Asset Pricing Model.
Step-by-step explanation:
The question involves calculating the risk-free rate given a stock's beta, expected return, and reward-to-risk ratio. to find the risk-free rate we use the Capital Asset Pricing Model (CAPM), which states that the expected return of a security is equal to the risk-free rate plus the product of the security's beta and the market risk premium. the market risk premium is the difference between the expected market return and the risk-free rate.
Using the CAPM formula:
Expected Return = Risk-Free Rate + Beta x (Market Return - Risk-Free Rate)
We can rearrange this to solve for the risk-free rate:
Risk-Free Rate = Expected Return - Beta x Reward-to-Risk Ratio
In this case:
Risk-Free Rate = 9.22% - 0.90 x 6.20%
Calculating this:
Risk-Free Rate = 9.22% - (0.90 x 6.20%)
Risk-Free Rate = 9.22% - 5.58%
Risk-Free Rate = 3.64%
Therefore, the risk-free rate is 3.64 percent.