Question

A stock has an expected return of 12.00%. The risk-free rate is 2.82% and the market risk premium is 6.92%. What is the β of the stock?

Answer 1

To find the beta (\(\beta\)) of the stock, we can use the Capital Asset Pricing Model (CAPM), which is expressed by the formula:

\[
\text{Expected Return} = \text{Risk-free Rate} + \beta \times \text{Market Risk Premium}
\]

We can rearrange this formula to solve for \(\beta\):

\[
\beta = \frac{\text{Expected Return} - \text{Risk-free Rate}}{\text{Market Risk Premium}}
\]

Substituting the values provided:

- Expected Return = 12.00% = 0.12
- Risk-free Rate = 2.82% = 0.0282
- Market Risk Premium = 6.92% = 0.0692

Now, substituting these values into the formula:

\[
\beta = \frac{0.12 - 0.0282}{0.0692}
\]

Calculating the numerator:

\[
0.12 - 0.0282 = 0.0918
\]

Now divide this by the market risk premium:

\[
\beta = \frac{0.0918}{0.0692} \approx 1.326
\]

Thus, the beta (\(\beta\)) of the stock is approximately **1.33**.