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

\begin{tabular}{lcr}
\hline
Economic State & Probability & Return \\
\hline
Fast Growth & 0.40 & [tex]$25 \%$[/tex] \\
Slow Growth & 0.55 & [tex]$12 \%$[/tex] \\
Recession & 0.05 & [tex]$-50 \%$[/tex] \\
\hline
\end{tabular}

Multiple Choice:
A. -4.3 percent
B. 14.1 percent
C. 19.1 percent



Answer :

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