To calculate the expected return of Ling's portfolio, we can use the Capital Asset Pricing Model (CAPM), which is based on the following formula for the expected return of a portfolio:

$E(R_p) = R_f + \beta_p \left( E(R_m) - R_f \right)$

Where:

• $E(R_p)$ is the expected return of the portfolio,
• $R_f$ is the risk-free rate (3% or 0.03),
• $\beta_p$ is the portfolio's beta,
• $E(R_m)$ is the expected return on the market portfolio (9% or 0.09).

Step 1: Calculate the portfolio beta

First, we need to find the portfolio beta, $\beta_p$, which is a weighted average of the individual asset betas.

$\beta_p = w_{\text{MCD}} \cdot \beta_{\text{MCD}} + w_{\text{AA}} \cdot \beta_{\text{AA}} + w_{\text{Z}} \cdot \beta_{\text{Z}}$

Where:

• $w_{\text{MCD}} = 0.48$, $\beta_{\text{MCD}} = 0.57$,
• $w_{\text{AA}} = 0.32$, $\beta_{\text{AA}} = 2.35$,
• $w_{\text{Z}} = 0.20$, $\beta_{\text{Z}} = 1.48$.

Now, calculate the portfolio's beta:

$\beta_p = (0.48 \cdot 0.57) + (0.32 \cdot 2.35) + (0.20 \cdot 1.48)$

$\beta_p = 0.2736 + 0.752 + 0.296$

$\beta_p = 1.3216$

Step 2: Calculate the expected return of the portfolio

Now that we know $\beta_p = 1.3216$, we can use the CAPM formula to calculate the expected return of the portfolio.

$E(R_p) = 0.03 + 1.3216 \cdot (0.09 - 0.03)$

$E(R_p) = 0.03 + 1.3216 \cdot 0.06$

$E(R_p) = 0.03 + 0.0793$

$E(R_p) = 0.1093 \quad \text{or} \quad 10.93\%$

Conclusion:

The expected return of Ling's portfolio is 10.93%.

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Do you need further details or have any questions about the calculation? Here are some related questions you might find helpful:

1. How do you calculate the beta of an individual stock?
2. What happens to the portfolio's expected return if the risk-free rate increases?
3. How does diversification affect the beta of a portfolio?
4. How can you calculate the expected return for a single asset using CAPM?
5. What is the relationship between beta and market risk?

Tip: A portfolio with a higher beta will generally have a higher expected return but also greater risk.