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This is a Capital Asset Pricing Model (CAPM) question where we need to calculate the required rate of return for a fund that consists of four stocks. We will follow these steps:

1. **Calculate the portfolio's beta**:
   The portfolio's beta is a weighted average of the individual betas, based on the proportion of the total fund each stock represents.

2. **Use the CAPM formula** to find the required rate of return for the portfolio:
   
   \[
   R_p = R_f + \beta_p (R_m - R_f)
   \]
   
   where:
   - $ R_p $ is the required return for the portfolio,
   - $ R_f $ is the risk-free rate,
   - $ \beta_p $ is the portfolio's beta,
   - $ R_m $ is the market's required rate of return.

---

### Step 1: Calculate the portfolio's beta.

We need the weighted beta of the portfolio. First, determine each stock's weight in the portfolio:

- Total investment = \$5,000,000.
  
  \[
  \text{Weight of A} = \frac{250,000}{5,000,000} = 0.05
  \]
  \[
  \text{Weight of B} = \frac{1,000,000}{5,000,000} = 0.20
  \]
  \[
  \text{Weight of C} = \frac{1,750,000}{5,000,000} = 0.35
  \]
  \[
  \text{Weight of D} = \frac{2,000,000}{5,000,000} = 0.40
  \]

Now calculate the portfolio's beta:

\[
\beta_p = (0.05 \times 1.50) + (0.20 \times -0.50) + (0.35 \times 1.25) + (0.40 \times 0.75)
\]

### Step 2: Use the CAPM formula.

Once we have the portfolio's beta, we plug it into the CAPM formula using:
- $ R_f = 7\% $,
- $ R_m = 12\% $.

Let's calculate this now.The portfolio's beta is $ 0.71 $.

Using the Capital Asset Pricing Model (CAPM), the fund's required rate of return is approximately **10.56%**.

Would you like further details or have any questions?

Here are 5 related questions you might explore:
1. How does changing the weight of a stock affect the portfolio's beta?
2. What would happen if the market's required rate of return increased to 15%?
3. How do negative betas, like that of stock B, affect the overall portfolio risk?
4. Can we reduce risk by increasing investment in stocks with low beta?
5. What other factors might influence the required rate of return besides beta?

**Tip:** Diversifying a portfolio by including assets with different betas can help manage risk and target specific returns.

Suppose you manage a $5 million fund that consists of four stocks with investments in Stock A ($250,000), Stock B ($1,000,000), Stock C ($1,750,000), and Stock D ($2,000,000). Each stock has a beta, and the market's required rate of return is 12%, with a risk-free rate of 7%. What is the fund's required rate of return?

Learn how to calculate the required rate of return for a $5 million fund consisting of four stocks. This example uses the Capital Asset Pricing Model (CAPM) and portfolio beta calculation to derive the solution. Suitable for finance and economics students.

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