Min has $5,000 to invest.The expected return on the market portfolio is 11% with a standard deviation of 15%.What are the expected return and standard deviation for the portfolio if she borrowed $2,000 at the risk-free rate of 4% to invest in the market portfolio?
A)Expected return = 19.40%; standard deviation = 15.40%
B)Expected return = 15.40%; standard deviation = 19.40%
C)Expected return = 13.80%; standard deviation = 21.00%
D)Expected return = 21.00%; standard deviation = 13.80%

Question

Quizplus · Accepted Answer

The expected return can be calculated using the formula for leveraged investments: $E(R_p) = \frac{E(R_M) \times (I+B) - R_f \times B}{I}$, where $E(R_p)$ is the expected return on the portfolio, $E(R_M)$ is the expected return on the market portfolio, $I$ is the initial investment, $B$ is the borrowed amount, and $R_f$ is the risk-free rate. Substituting the given values: $E(R_p) = \frac{0.11 \times (5000+2000) - 0.04 \times 2000}{5000} = 13.80%$. The standard deviation of the leveraged portfolio increases proportionally to the leverage ratio, which is $\frac{I+B}{I}$, so the new standard deviation is $15\% \times \frac{7000}{5000} = 21\%$.

Min Has $5,000 to Invest