The expected return for a stock calculated using the CAPM is 11.5%. The market return is 8.0% and the beta of the stock is 1.50. Calculate the implied risk-free rate (as a percentage).

The Capital Asset Pricing Model (CAPM) is given by the formula:

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

We can rearrange this formula to solve for the risk-free rate:

Risk-Free Rate = (Expected Return - Beta * Market Return) / (1 - Beta)

Substituting the given values into this formula:

Risk-Free Rate = (11.5% - 1.50 * 8.0%) / (1 - 1.50)

Risk-Free Rate = (11.5% - 12.0%) / -0.50

Risk-Free Rate = -0.5% / -0.50

Risk-Free Rate = 1.0%

So, the implied risk-free rate is 1.0%.

The Capital Asset Pricing Model (CAPM) is given by the formula:

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

We can rearrange this formula to solve for the risk-free rate:

Risk-Free Rate = (Expected Return - Beta * Market Return) / (1 - Beta)

Substituting the given values:

Risk-Free Rate = (11.5% - 1.50 * 8.0%) / (1 - 1.50)

Risk-Free Rate = (11.5% - 12.0%) / -0.50

Risk-Free Rate = -0.5% / -0.50

Risk-Free Rate = 1.0%

So, the implied risk-free rate is 1.0%.

The Capital Asset Pricing Model (CAPM) is expressed as:

Expected Return = Risk-free rate + Beta * (Market Return - Risk-free rate)

We can rearrange this formula to solve for the risk-free rate:

Risk-free rate = (Expected Return - Beta * Market Return) / (1 - Beta)

In this case, the expected return is 11.5%, the market return is 8.0%, and the beta is 1.50.

Step 1: Convert the percentages to decimals. 11.5% becomes 0.115, and 8.0% becomes 0.08.

Step 2: Substitute the values into the rearranged CAPM formula:

Risk-free rate = (0.115 - 1.50 * 0.08) / (1 - 1.50)

Step 3: Calculate the value:

Risk-free rate = (0.115 - 0.12) / (1 - 1.50) = -0.005 / -0.50 = 0.01

Step 4: Convert the decimal back to a percentage:

Risk-free rate = 0.01 * 100 = 1%

So, the implied risk-free rate is 1%.