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Compute the expected return given these three economic states, their likelihoods, and the potential returns:

[tex]\[
\begin{tabular}{lcc}
\hline
Economic State & Probability & Return \\
\hline
Fast Growth & 0.2 & 23\% \\
Slow Growth & 0.6 & 14\% \\
Recession & 0.2 & -30\% \\
\hline
\end{tabular}
\][/tex]

Multiple Choice:

A. 3.5 percent

B. 7.0 percent

C. 7.5 percent


Sagot :

To compute the expected return given the different economic states, their probabilities, and the potential returns, we follow these steps:

1. Identify the probabilities and returns for each state:

- Fast Growth: Probability = 0.2, Return = 23%
- Slow Growth: Probability = 0.6, Return = 14%
- Recession: Probability = 0.2, Return = -30%

2. Use the formula for the expected return:

[tex]\[ \text{Expected Return} = (\text{Probability of Fast Growth} \times \text{Return in Fast Growth}) + (\text{Probability of Slow Growth} \times \text{Return in Slow Growth}) + (\text{Probability of Recession} \times \text{Return in Recession}) \][/tex]

3. Plug in the values and compute the expected return:

- Contribution of Fast Growth: [tex]\(0.2 \times 23\% = 0.2 \times 0.23 = 0.046\)[/tex]
- Contribution of Slow Growth: [tex]\(0.6 \times 14\% = 0.6 \times 0.14 = 0.084\)[/tex]
- Contribution of Recession: [tex]\(0.2 \times -30\% = 0.2 \times -0.30 = -0.060\)[/tex]

4. Sum these contributions:

[tex]\[ \text{Expected Return} = 0.046 + 0.084 + (-0.060) \][/tex]

5. Calculate the final expected return:

[tex]\[ \text{Expected Return} = 0.046 + 0.084 - 0.060 = 0.070 \][/tex]

6. Express the expected return as a percentage:

[tex]\[ \text{Expected Return as a percentage} = 0.070 \times 100\% = 7.0\% \][/tex]

Therefore, the expected return given the economic states, probabilities, and returns is [tex]\( \boxed{7.0 \%} \)[/tex].