To calculate the expected return of the portfolio, follow these steps:

Formula for Expected Return of Portfolio:

$E(R_{\text{portfolio}}) = \sum \text{(Weight of Stock)} \times \text{(Expected Return of Stock)}$

1. Step 1: Calculate the portfolio return for each economic state. For each economic state, the return of the portfolio is: $R_{\text{portfolio}} = (Weight_A \times R_A) + (Weight_B \times R_B) + (Weight_C \times R_C)$

   • Weight of Stock A: $30\% = 0.30$
   • Weight of Stock B: $30\% = 0.30$
   • Weight of Stock C: $40\% = 1 - 0.30 - 0.30 = 0.40$

   Substitute the returns for each state:

   • Boom: = -4.98\% - 0.84\% - 8.68\% = -14.5\%$$
   • Normal: = 3.72\% + 2.22\% + 6.40\% = 12.34\%$$
   • Recession: = 7.92\% + 4.41\% + 12.24\% = 24.57\%$$

2. Step 2: Use probabilities to calculate the expected return.

   + (\text{Probability}_{\text{Normal}} \times R_{\text{Normal}}) + (\text{Probability}_{\text{Recession}} \times R_{\text{Recession}})$$ Substitute the values: $$E(R_{\text{portfolio}}) = (0.20 \times -14.5\%) + (0.53 \times 12.34\%) + (0.27 \times 24.57\%)$$ Calculate each term: - $$0.20 \times -14.5\% = -2.90\%$$ - $$0.53 \times 12.34\% = 6.54\%$$ - $$0.27 \times 24.57\% = 6.63\%$$ Add them up: $$E(R_{\text{portfolio}}) = -2.90\% + 6.54\% + 6.63\% = 10.27\%$$

Final Answer:

$\boxed{10.27\%}$

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Do you want further clarification on the steps? Here are some related questions to expand your understanding:

1. How do portfolio weights affect overall portfolio returns?
2. Why is probability multiplied with returns in the expected return formula?
3. What happens if one stock's return significantly deviates from others?
4. How would a change in the weights of the stocks impact the portfolio's expected return?
5. Can this method be extended to calculate portfolio variance or risk?

Tip: Always ensure the sum of weights equals 100% (or 1) when allocating investments in a portfolio.