Question

A stock has an expected return of 13.00%. The risk-free rate is 3.99% and the market risk premium is 7.58%. What is the β of the stock?

Answer 1

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

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

From the information provided:

- Expected Return (ER) = 13.00% = 0.13
- Risk-Free Rate (RFR) = 3.99% = 0.0399
- Market Risk Premium (MRP) = 7.58% = 0.0758

We can plug these values into the CAPM formula and solve for β:

\[
0.13 = 0.0399 + \beta \times 0.0758
\]

Subtract the risk-free rate from both sides:

\[
0.13 - 0.0399 = \beta \times 0.0758
\]

\[
0.0901 = \beta \times 0.0758
\]

Now, solve for β by dividing both sides by the market risk premium:

\[
\beta = \frac{0.0901}{0.0758}
\]

\[
\beta \approx 1.188
\]

Thus, the beta (β) of the stock is approximately **1.19**.