An investor has a portfolio with an expected return of 11.19%. The portfolio is evenly invested in a stock and a risk-free asset. The market has an expected return of 17% and the risk-free asset has an expected return of 3%. What is the beta of the stock?

Question

Quizplus · Accepted Answer

The beta of the stock can be calculated using the formula for the expected return of a portfolio, which is $E(R_p) = w_1E(R_1) + w_2E(R_2)$, where $E(R_p)$ is the expected return of the portfolio, $w_1$ and $w_2$ are the weights of the stock and the risk-free asset respectively, and $E(R_1)$ and $E(R_2)$ are their expected returns. Given that the portfolio is evenly invested, $w_1 = w_2 = 0.5$. The expected return of the portfolio is 11.19%, the expected return of the risk-free asset is 3%, and the market's expected return is 17%. The expected return of the stock can be found by rearranging the formula: $E(R_1) = \frac{E(R_p) - w_2E(R_2)}{w_1}$. Substituting the given values, we find $E(R_1) = \frac{11.19 - 0.5*3}{0.5} = 16.38%$.The beta of the stock ($\beta$) can then be calculated using the Capital Asset Pricing Model (CAPM) formula: $E(R_1) = R_f + \beta(E(R_m) - R_f)$, where $E(R_m)$ is the expected return of the market and $R_f$ is the risk-free rate. Rearranging for $\beta$ gives $\beta = \frac{E(R_1) - R_f}{E(R_m) - R_f}$. Substituting the given and calculated values, we get $\beta = \frac{16.38 - 3}{17 - 3} = 1.17$.

An Investor Has a Portfolio with an Expected Return of 11.19