To find the expected return given the different economic states, their probabilities, and the potential returns, we can use the formula for the expected value. Here's the step-by-step solution:
1. List down the probabilities and the returns:
- Fast Growth: Probability = 0.40, Return = 25%
- Slow Growth: Probability = 0.55, Return = 12%
- Recession: Probability = 0.05, Return = -50%
2. Multiply each return by its respective probability:
- Fast Growth = 0.40 25 = 10.00
- Slow Growth = 0.55 12 = 6.60
- Recession = 0.05 * -50 = -2.50
3. Add these products together to get the expected return:
10.00 + 6.60 + (-2.50) = 14.10
Thus, the expected return is 14.1 percent.
The correct answer from the multiple choices given is:
14.1 percent
