Question

The risk-free rate is 2.46% and the expected return on the market 11.80%. A stock with a β of 1.00 will have an expected return of ____%.

Answer 1

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%**.