To find the expected return of a stock using the Capital Asset Pricing Model (CAPM), you can use the following formula:
\[ E(R_i) = R_f + \beta_i (E(R_m) - R_f) \]
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 of the market.
From your information:
- \(R_f = 2.46%\)
- \(E(R_m) = 11.80%\)
- \(\beta = 1.00\)
Now, substitute these values into the formula:
\[ E(R_i) = 2.46% + 1.00 \times (11.80% - 2.46%) \]
Calculate the market risk premium:
\[ E(R_m) - R_f = 11.80% - 2.46% = 9.34% \]
Now substitute back into the formula:
\[ E(R_i) = 2.46% + 1.00 \times 9.34% \] \[ E(R_i) = 2.46% + 9.34% \] \[ E(R_i) = 11.80% \]
Thus, the expected return of the stock with a β of 1.00 is 11.80%.