Bot GPT 4-o mini To find the beta (β) of the stock, we can use the Capital Asset Pricing Model (CAPM) formula, which is:
\[ \text{Expected return} = \text{Risk-free rate} + \beta \times \text{Market premium} \]
Given the values:
- Expected return of the stock (E) = 18.00% = 0.18
- Risk-free rate (R_f) = 2.05% = 0.0205
- Market premium (E_m - R_f) = 7.19% = 0.0719
Let's plug the values into the CAPM equation:
\[ 0.18 = 0.0205 + \beta \times 0.0719 \]
Now, we will isolate β:
- Subtract the risk-free rate from both sides:
\[ 0.18 - 0.0205 = \beta \times 0.0719 \]
\[ 0.1595 = \beta \times 0.0719 \]
- Now, divide both sides by the market premium to solve for β:
\[ \beta = \frac{0.1595}{0.0719} \]
- Performing the calculation:
\[ \beta \approx \frac{0.1595}{0.0719} \approx 2.2 \]
Thus, the beta of the stock is approximately 2.2.
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