The expected return of a portfolio on the Capital Market Line (CML)is 14% with a standard deviation of 25%.The risk-free rate is 6%.What is the expected return on an efficient portfolio with a standard deviation of 30%?
A)9.6%
B)15.6%
C)22.8%
D)16.8%

Question

Quizplus · Accepted Answer

The Capital Market Line (CML) equation is given by: $E(R_p) = R_f + \frac{E(R_m) - R_f}{\sigma_m} \times \sigma_p$, where $E(R_p)$ is the expected return on the portfolio, $R_f$ is the risk-free rate, $E(R_m)$ is the expected return on the market portfolio, $\sigma_m$ is the standard deviation of the market portfolio, and $\sigma_p$ is the standard deviation of the portfolio. Given $E(R_p) = 14\%$, $R_f = 6\%$, and $\sigma_m = 25\%$, for a portfolio with $\sigma_p = 30\%$, we find the expected return by substituting the given values into the equation. The slope of the CML is $\frac{14\% - 6\%}{25\%} = \frac{8\%}{25\%} = 0.32$. Therefore, the expected return on the portfolio with a standard deviation of 30% is $6\% + 0.32 \times 30\% = 6\% + 9.6\% = 15.6\%$.

The Expected Return of a Portfolio on the Capital Market