Consider the single-index model. The alpha of a stock is 0%. The return on the market index is 10%. The risk-free rate of return is 5%. The stock earns a return that exceeds the risk-free rate by 5%, and there are no firm-specific events affecting the stock performance. The β of the stock is
A) 0.67.
B) 0.75.
C) 1.0.
D) 1.33.
E) 1.50.

Question

Quizplus · Accepted Answer

The single-index model is represented by the equation $R_i = \alpha_i + \beta_i(R_m - R_f) + \epsilon_i$, where $R_i$ is the return on the stock, $\alpha_i$ is the stock's alpha, $\beta_i$ is the stock's beta, $R_m$ is the return on the market index, $R_f$ is the risk-free rate, and $\epsilon_i$ is the error term representing firm-specific events. Given that the alpha ($\alpha_i$) is 0%, the return on the market index ($R_m$) is 10%, the risk-free rate ($R_f$) is 5%, and the stock earns a return that exceeds the risk-free rate by 5% without firm-specific events ($\epsilon_i = 0$), the equation simplifies to $5\% = \beta_i(10\% - 5\%)$. Solving for $\beta_i$ gives $\beta_i = 1.0$, indicating that the stock moves in perfect correlation with the market.

Consider the Single-Index Model