Suppose an investor wants to include Bartman Industries's stock in his portfolio. Stocks A, B, and C are currently in the portfolio, and their betas are 0.761, 0.967, and 1.353, respectively. Calculate the new portfolio's required return if it consists of 20% of Bartman, 15% of Stock A, 40% of Stock B, and 25% of Stock C. Round your answer to two decimal places.

To calculate the new portfolio's required return, we need to follow these steps:

### Step 1: Identify the components
We have the following information:

- **Stock A Beta**: \( \beta_A = 0.761 \)
- **Stock B Beta**: \( \beta_B = 0.967 \)
- **Stock C Beta**: \( \beta_C = 1.353 \)

- **Weights of stocks** in the portfolio:
  - Bartman Industries: 20% or \( W_{\text{Bartman}} = 0.20 \)
  - Stock A: 15% or \( W_A = 0.15 \)
  - Stock B: 40% or \( W_B = 0.40 \)
  - Stock C: 25% or \( W_C = 0.25 \)

We also assume the **market risk premium** (the expected return on the market minus the risk-free rate) and the **risk-free rate** are known or provided, but you haven't given that information. Let's assume:
- **Market risk premium**: 8% or \( R_{\text{M}} - R_{\text{RF}} = 8\% = 0.08 \)
- **Risk-free rate**: 5% or \( R_{\text{RF}} = 5\% = 0.05 \)

### Step 2: Calculate the weighted average beta for the portfolio

The beta of a portfolio is the weighted sum of the betas of the individual assets. Since Bartman's beta is not provided, we will assume it as \( \beta_{\text{Bartman}} \), and include it in our calculation.

\[
\beta_{\text{portfolio}} = W_{\text{Bartman}} \cdot \beta_{\text{Bartman}} + W_A \cdot \beta_A + W_B \cdot \beta_B + W_C \cdot \beta_C
\]

Substituting the given values:

\[
\beta_{\text{portfolio}} = 0.20 \cdot \beta_{\text{Bartman}} + 0.15 \cdot 0.761 + 0.40 \cdot 0.967 + 0.25 \cdot 1.353
\]

Simplifying the right-hand side:

\[
\beta_{\text{portfolio}} = 0.20 \cdot \beta_{\text{Bartman}} + 0.11415 + 0.3868 + 0.33825
\]

\[
\beta_{\text{portfolio}} = 0.20 \cdot \beta_{\text{Bartman}} + 0.8392
\]

### Step 3: Use the Capital Asset Pricing Model (CAPM) to calculate the required return

The formula for the required return using CAPM is:

\[
R_{\text{portfolio}} = R_{\text{RF}} + \beta_{\text{portfolio}} \cdot (R_{\text{M}} - R_{\text{RF}})
\]

Substituting values:

\[
R_{\text{portfolio}} = 0.05 + \left( 0.20 \cdot \beta_{\text{Bartman}} + 0.8392 \right) \cdot 0.08
\]

Now, you can either provide the beta for Bartman Industries, or I can help you solve this equation further by assuming a value for it.

Do you want to proceed with an assumed beta for Bartman, or do you have the value of its beta available?

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Would you like more details on these concepts? Here are some related questions:

1. What factors affect a stock's beta?
2. How is the market risk premium determined?
3. What assumptions are made in CAPM?
4. How can portfolio beta be interpreted?
5. What happens to a portfolio's return if a higher beta stock is added?

**Tip**: A stock's beta is a measure of its volatility relative to the market, with the market having a beta of 1.

Learn how to calculate a portfolio's required return when Bartman Industries is added alongside stocks A, B, and C. This problem applies the Capital Asset Pricing Model (CAPM) and portfolio beta concepts to determine the expected return with specific weights and betas.

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