The risk-free rate is 2.96% and the expected return on the market 11.23%. A stock with a β of 1.23 will have an expected return of ____%.

Answer 1

To calculate the expected return of a stock using the Capital Asset Pricing Model (CAPM), the formula is:

\[ E(R_i) = R_f + \beta_i (E(R_m) - R_f) \]

Where:

• \(E(R_i)\) is the expected return of the stock.
• \(R_f\) is the risk-free rate.
• \(\beta_i\) is the beta of the stock.
• \(E(R_m)\) is the expected return on the market.

Given:

• \(R_f = 2.96%\)
• \(E(R_m) = 11.23%\)
• \(\beta_i = 1.23\)

Now, plug in the values:

1. Calculate the market risk premium (\(E(R_m) - R_f\)): \[ E(R_m) - R_f = 11.23% - 2.96% = 8.27% \]

2. Now substitute back into the CAPM formula: \[ E(R_i) = 2.96% + 1.23 \times 8.27% \]

3. Calculate the product: \[ 1.23 \times 8.27% = 10.18% \]

4. Finally, sum it up: \[ E(R_i) = 2.96% + 10.18% = 13.14% \]

So, the expected return of the stock is 13.14%.