Question

A sock has an expected return of 18.00%. The risk free rate is 2.05% and the market premium is 7.19%. What is the beta of the stock?

Answer 1

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:

1. Subtract the risk-free rate from both sides:

\[
0.18 - 0.0205 = \beta \times 0.0719
\]

\[
0.1595 = \beta \times 0.0719
\]

2. Now, divide both sides by the market premium to solve for β:

\[
\beta = \frac{0.1595}{0.0719}
\]

3. Performing the calculation:

\[
\beta \approx \frac{0.1595}{0.0719} \approx 2.2
\]

Thus, the beta of the stock is approximately **2.2**.