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.