To determine the expected rate of return on this stock, we use the formula for the expected value:

$E(R) = \sum P_i \cdot R_i$

Where:

• $P_i$ = Probability of scenario $i$,
• $R_i$ = Rate of return in scenario $i$.

Given the data:

• Boom: $P = 0.15$, $R = 10\% = 0.10$,
• Normal: $P = 0.70$, $R = 4\% = 0.04$,
• Recession: $P = 0.15$, $R = -4\% = -0.04$.

We calculate:

$E(R) = (0.15 \cdot 0.10) + (0.70 \cdot 0.04) + (0.15 \cdot -0.04)$

Breaking it down:

1. $0.15 \cdot 0.10 = 0.015$,
2. $0.70 \cdot 0.04 = 0.028$,
3. $0.15 \cdot -0.04 = -0.006$.

Adding these: $E(R) = 0.015 + 0.028 - 0.006 = 0.037$

Convert $0.037$ to a percentage: $E(R) = 3.70\%$

Final Answer: 3.70%

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Do you have further questions or need additional explanations?

Expanding Questions:

1. How does the expected rate of return differ from variance in assessing risk?
2. What role do probabilities play in financial decision-making for stocks?
3. How would the expected return change if the probabilities of economic states were different?
4. What is the significance of a negative expected return in investment analysis?
5. Can the expected rate of return alone determine whether this stock is a good investment?

Tip:

When calculating expected returns, always ensure probabilities sum to 1 (or 100%) to avoid errors in your computations.