To calculate the return on the portfolio, we'll use the Capital Asset Pricing Model (CAPM) formula:

$\text{Expected Return} = \text{Risk-Free Rate} + \text{Beta} \times \text{Market Risk Premium}$

Given dataTo calculate the return on the portfolio, we'll use the Capital Asset Pricing Model (CAPM) formula:

$\text{Expected Return} = \text{Risk-Free Rate} + \text{Beta} \times \text{Market Risk Premium}$

Given

• Risk-Free Rate (Rf): 3%
• Market Risk Premium (Rm - Rf): 9%
• Beta of ABC stock (β$_{\text{ABC}}$): 1.3
• Beta of XYZ stock (β$_{\text{XYZ}}$): -0.2
• Portfolio Weights: 50% in ABC, 50% in XYZ

Step 1: Calculate the Portfolio Beta

The portfolio beta (β$_{\text{portfolio}}$) is the weighted average of the individual betas:

$\beta_{\text{portfolio}} = (0.5 \times 1.3) + (0.5 \times -0.2)$

$\beta_{\text{portfolio}} = 0.65 - 0.1 = 0.55$

Step 2: Calculate the Expected Return of the Portfolio

Using the CAPM formula with the portfolio beta:

$\text{Expected Return}_{\text{portfolio}} = \text{Risk-Free Rate} + \beta_{\text{portfolio}} \times \text{Market Risk Premium}$

$\text{Expected Return}_{\text{portfolio}} = 3\% + (0.55 \times 9\%)$

$\text{Expected Return}_{\text{portfolio}} = 3\% + 4.95\% = 7.95\%$

Conclusion

The expected return on the portfolio is 7.95%.

Would you like further details or have any questions?

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Here are five related questions to explore:

1. What would happen to the portfolio return if the weight in ABC stock increased to 70%?
2. How would the portfolio beta change if both stocks had positive betas?
3. What does a negative beta mean, and how does it affect portfolio risk?
4. How would the expected return change if the market risk premium increased to 10