Question

A stock has an expected return of 12.15% ,its beta is 1.31 the

risk and the expected return on the market is 10.2%. what must the
risk free rate be?

Answer 1

Using the Capital Asset Pricing Model (CAPM) the calculation for the risk-free rate based on the provided values resulted in an impractical negative value, which suggests there may be an error in the inputs or assumptions.

Step-by-step explanation:

To find the risk-free rate, we can use the Capital Asset Pricing Model (CAPM), which describes the relationship between expected return and risk of investing in a security. The CAPM formula is:

Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)

Plugging in the values provided, we get:

12.15% = Risk-Free Rate + 1.31 * (10.2% - Risk-Free Rate)

Now, we can solve for the Risk-Free Rate:

12.15% = 1.31 * 10.2% - 1.31 * Risk-Free Rate + Risk-Free Rate

12.15% = 13.362% - 1.31 * Risk-Free Rate + Risk-Free Rate

Risk-Free Rate - 1.31 * Risk-Free Rate = 13.362% - 12.15%

-0.31 * Risk-Free Rate = 1.212%

Risk-Free Rate = 1.212% / -0.31

Risk-Free Rate = -3.912%

However, a negative risk-free rate is not practical in most financial contexts; this implies there might be an error in the provided values, assumptions, or calculations. In practice, you would re-examine the inputs and context to ensure they are accurate and make sense economically. The CAPM suggests that the risk-free rate must be less than the expected return on a stock and less than the market rate of return under normal circumstances.