1. **State the problem:** We need to find the fund's required rate of return given the investments and betas of four stocks, the market's required rate of return, and the risk-free rate. 2. **Formula used:** The required rate of return for a portfolio is given by the Capital Asset Pricing Model (CAPM): $$ R_p = R_f + \beta_p (R_m - R_f) $$ where: - $R_p$ is the portfolio's required rate of return, - $R_f$ is the risk-free rate, - $\beta_p$ is the portfolio beta, - $R_m$ is the market's required rate of return. 3. **Calculate the portfolio beta $\beta_p$:** The portfolio beta is the weighted average of the individual stock betas: $$ \beta_p = \frac{\sum (Investment_i \times \beta_i)}{\sum Investment_i} $$ 4. **Calculate numerator:** $$ 400,000 \times 1.50 = 600,000 $$ $$ 600,000 \times (-0.50) = -300,000 $$ $$ 1,000,000 \times 1.25 = 1,250,000 $$ $$ 2,000,000 \times 0.75 = 1,500,000 $$ Sum of weighted betas: $$ 600,000 - 300,000 + 1,250,000 + 1,500,000 = 3,050,000 $$ 5. **Calculate portfolio beta:** Total investment = $4,000,000$ $$ \beta_p = \frac{3,050,000}{4,000,000} = 0.7625 $$ 6. **Calculate the fund's required rate of return:** Given $R_f = 6\% = 0.06$, $R_m = 14\% = 0.14$, and $\beta_p = 0.7625$: $$ R_p = 0.06 + 0.7625 \times (0.14 - 0.06) $$ $$ R_p = 0.06 + 0.7625 \times 0.08 $$ $$ R_p = 0.06 + 0.061 = 0.121 $$ 7. **Final answer:** The fund's required rate of return is **12.1%**.