To calculate the portfolio's expected return, we need to first determine the expected return for each stock using the Capital Asset Pricing Model (CAPM), and then calculate the weighted average of these returns based on the investment amounts in each stock.

Step 1: Apply the CAPM formula for each stock

The CAPM formula is:

$R_{\text{expected}} = R_f + \beta \times (R_m - R_f)$

Where:

• $R_{\text{expected}}$ is the expected return of the stock.
• $R_f$ is the risk-free rate (T-Bill yield = 3.5% or 0.035).
• $\beta$ is the stock's beta.
• $R_m - R_f$ is the market risk premium (7.2% or 0.072).

For Stock A:

• $\beta_A = 0.77$
• $R_f = 0.035$
• $R_m - R_f = 0.072$

$R_{\text{A, expected}} = 0.035 + 0.77 \times 0.072 = 0.035 + 0.05544 = 0.09044$

So, the expected return for Stock A is 0.09044 or 9.044%.

For Stock B:

• $\beta_B = 1.43$
• $R_f = 0.035$
• $R_m - R_f = 0.072$

$R_{\text{B, expected}} = 0.035 + 1.43 \times 0.072 = 0.035 + 0.10296 = 0.13796$

So, the expected return for Stock B is 0.13796 or 13.796%.

Step 2: Calculate the portfolio's expected return

Now we calculate the portfolio's expected return by weighting the expected returns of each stock based on their investment amounts.

Total portfolio value = $20,000 (Stock A) + $12,000 (Stock B) = $32,000

Weight of Stock A in the portfolio:

$w_A = \frac{20,000}{32,000} = 0.625$

Weight of Stock B in the portfolio:

$w_B = \frac{12,000}{32,000} = 0.375$

Portfolio's expected return:

$R_{\text{portfolio}} = w_A \times R_{\text{A, expected}} + w_B \times R_{\text{B, expected}}$

$R_{\text{portfolio}} = 0.625 \times 0.09044 + 0.375 \times 0.13796$

$R_{\text{portfolio}} = 0.056525 + 0.051735 = 0.10826$

Final Answer:

The portfolio's expected return is 0.1083 (rounded to four decimal places).

Would you like further details on the calculations, or have any other questions?

Related Questions:

1. How would the portfolio's expected return change if you adjusted the investment in Stock A to $15,000?
2. What would happen to the portfolio's risk if Stock A had a higher volatility than Stock B?
3. How do you calculate the beta of a portfolio consisting of multiple stocks?
4. How would the expected return change if the market risk premium were 10% instead of 7.2%?
5. What is the relationship between beta and portfolio risk?

Tip: The expected return of a portfolio depends not just on the returns of individual assets, but also on their respective weights in the portfolio. Consider this when balancing risk and return in investment decisions.