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.
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