A stock has an expected return of 13.8 percent, the risk-free rate is 4.5 percent, and the market risk premium is 7.5 percent. What must the beta of this stock be? (Round your answer to 2 decimal places. (e.g., 32.16)) Beta of stock=
The Correct Answer and Explanation is:
To find the beta (β) of a stock, we use the Capital Asset Pricing Model (CAPM) formula: Expected Return=Rf+β×(Rm−Rf)\text{Expected Return} = R_f + \beta \times (R_m – R_f)
Where:
- RfR_f is the risk-free rate
- Rm−RfR_m – R_f is the market risk premium
- β\beta is the beta of the stock
- Expected Return is the return investors expect from the stock
Given:
- Expected Return = 13.8%
- Risk-free rate (RfR_f) = 4.5%
- Market Risk Premium = 7.5%
Now plug the values into the CAPM formula and solve for beta (β\beta): 13.8%=4.5%+β×7.5%13.8\% = 4.5\% + \beta \times 7.5\% 13.8%−4.5%=β×7.5%13.8\% – 4.5\% = \beta \times 7.5\% 9.3%=β×7.5%9.3\% = \beta \times 7.5\% β=9.3%7.5%=1.24\beta = \frac{9.3\%}{7.5\%} = 1.24
✅ Final Answer:
Beta of stock = 1.24
The beta (β) of a stock is a measure of its sensitivity to movements in the overall market. A beta of 1.0 means the stock’s price moves exactly with the market. A beta greater than 1 indicates that the stock is more volatile than the market, while a beta less than 1 means it is less volatile.
In this case, we use the Capital Asset Pricing Model (CAPM) to determine the stock’s beta. CAPM is a widely-used model in finance that relates the expected return on a security to its systematic risk, measured by beta. The model assumes that investors require compensation for time value of money (captured by the risk-free rate) and risk (captured by the market risk premium).
The expected return of the stock is 13.8%, the risk-free rate is 4.5%, and the market risk premium is 7.5%. The market risk premium represents the additional return investors expect for taking on the risk of investing in the stock market as a whole, above the risk-free rate.
We rearranged the CAPM formula to isolate beta and solved: β=Expected Return−RfMarket Risk Premium=13.8%−4.5%7.5%=1.24\beta = \frac{\text{Expected Return} – R_f}{\text{Market Risk Premium}} = \frac{13.8\% – 4.5\%}{7.5\%} = 1.24
This tells us that the stock has a beta of 1.24, meaning it is 24% more volatile than the market. If the market increases by 1%, this stock is expected to increase by approximately 1.24%, and vice versa for decreases.
