Assume that you are the portfolio manager of the SF Fund,a $3 million hedge fund that contains the following stocks.The required rate of return on the market is 11.00% and the risk-free rate is 2.00%.What rate of return should investors expect (and require)on this fund? Do not round your intermediate calculations. $\begin{array}{lrl}\text { Stock }&\text { amount }&\text { Beta }\
\text { A } & \$ 1,075,000 & 1.20 \
B & \$ 675,000 & 0.50 \
\mathrm{C} & \$ 750,000 & 1.40 \
\mathrm{D} & \$ 500,000 & 0.75\&\$3,000,000
\end{array}$
?
A) 11.16%
B) 10.82%
C) 9.93%
D) 9.37%
E) 9.71%

Question

Quizplus · Accepted Answer

The expected rate of return on the fund can be calculated using the Capital Asset Pricing Model (CAPM) formula for each stock and then finding the weighted average of these expected returns based on the proportion of each stock in the portfolio. The CAPM formula is: $$E(R_i) = R_f + \beta_i(E(R_m) - R_f)$$ where $E(R_i)$ is the expected return on asset $i$, $R_f$ is the risk-free rate, $\beta_i$ is the beta of asset $i$, and $E(R_m)$ is the expected return on the market.First, calculate the weighted beta of the portfolio:- For Stock A: Weight = $1,075,000 / $3,000,000 = 0.3583, Beta = 1.20- For Stock B: Weight = $675,000 / $3,000,000 = 0.225, Beta = 0.50- For Stock C: Weight = $750,000 / $3,000,000 = 0.25, Beta = 1.40- For Stock D: Weight = $500,000 / $3,000,000 = 0.1667, Beta = 0.75Weighted Beta = (0.3583 * 1.20) + (0.225 * 0.50) + (0.25 * 1.40) + (0.1667 * 0.75) = 0.42996 + 0.1125 + 0.35 + 0.125025 = 1.017485Then, use the CAPM formula to find the expected return on the portfolio:$$E(R_p) = 2.00\% + 1.017485(11.00\% - 2.00\%)$$$$E(R_p) = 2.00\% + 1.017485 \times 9.00\%$$$$E(R_p) = 2.00\% + 9.157365\%$$$$E(R_p) = 11.157365\%$$Rounded to two decimal places, the expected rate of return on the fund is approximately 11.16%.

Assume That You Are the Portfolio Manager of the SF