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In this problem, you're given data about two stocks (Stock X and Stock Y) and their anticipated returns under four different economic conditions: Recession, Slow Growth, Moderate Growth, and Fast Growth. The goal is to help you develop a strategy for investing by analyzing the returns of a $1,000 investment in each stock based on these economic conditions, weighted by their associated probabilities.

The table provides the following dataIn this problem, you're given data about two stocks (Stock X and Stock Y) and their anticipated returns under four different economic conditions: Recession, Slow Growth, Moderate Growth, and Fast Growth. The goal is to help you develop a strategy for investing by analyzing the returns of a $1,000 investment in each stock based on these economic conditions, weighted by their associated probabilities.

The table provides the following 

| Probability | Economic Condition | Stock X Return (%) | Stock Y Return (%) |
|-------------|--------------------|--------------------|--------------------|
| 0.1         | Recession           | -70                | -170               |
| 0.2         | Slow Growth         | 30                 | 60                 |
| 0.4         | Moderate Growth     | 110                | 150                |
| 0.3         | Fast Growth         | 160                | 190                |

### To solve this, we can proceed with the following steps:

1. **Expected return of each stock**:
   The expected return $ E(R) $ is calculated using the formula:
   \[
   E(R) = \sum_{i} P_i \times R_i
   \]
   Where:
   - $ P_i $ is the probability of the $ i $-th economic condition,
   - $ R_i $ is the return under the $ i $-th condition.

2. **Variance and Standard Deviation**:
   The variance $ \text{Var}(R) $ measures the dispersion of returns and is calculated by:
   \[
   \text{Var}(R) = \sum_{i} P_i \times (R_i - E(R))^2
   \]
   Standard deviation is the square root of the variance and measures risk.

3. **Covariance and Correlation**:
   You might also need to compute the covariance and correlation between the returns of Stock X and Stock Y to evaluate if diversification can reduce risk.

Would you like to proceed with the calculation for expected returns, or do you need help with a specific part of the problem? Let me know if you'd like me to calculate the expected returns or any other measure! 

### Follow-up Questions:
1. How is the expected return useful in assessing investment strategies?
2. What role does the standard deviation play in understanding stock risk?
3. How do covariance and correlation between two stocks affect portfolio diversification?
4. What would be an optimal investment strategy if you prefer low risk?
5. How can probabilities of different economic conditions be forecasted?

### Tip:
When dealing with multiple investment options, always consider both the expected return and the risk (standard deviation) to make informed decisions.

You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $1,000 investment in each stock under four different economic conditions has the probability distribution shown in the table: Recession (0.1 probability), Slow growth (0.2), Moderate growth (0.4), Fast growth (0.3). Stock X has returns of -70, 30, 110, and 160, while Stock Y has returns of -170, 60, 150, and 190, respectively.

Develop an investment strategy for Stock X and Stock Y by analyzing their expected returns under different economic conditions (recession, slow growth, moderate growth, fast growth). Learn how to calculate expected returns, variance, and risk assessment using probability distributions.

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