W = 0.3RX +0.7Ry, where Rx is the stock return from investing in stock X and Ry is the sto investing in stock Y. The stock returns depend on the economy and are sho below. (a) What is the expected return of the portfolio, i.e. E(W)? (b) What is the variance of the portfolio, i.e. Var(W)? Assume that Rx and I dent. (c) What is the variance of the portfolio, i.e. Var(W)? Assume that Rx negative correlation where p = -0.3.
W = 0.3RX +0.7Ry, where Rx is the stock return from investing in stock X and Ry is the sto investing in stock Y. The stock returns depend on the economy and are sho below. (a) What is the expected return of the portfolio, i.e. E(W)? (b) What is the variance of the portfolio, i.e. Var(W)? Assume that Rx and I dent. (c) What is the variance of the portfolio, i.e. Var(W)? Assume that Rx negative correlation where p = -0.3.
MATLAB: An Introduction with Applications
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![## Portfolio Analysis for Stock Investment
To understand the potential returns and risks of a simple portfolio, consider the following example where we have chosen two stocks, X and Y. We will invest 30% of our money in stock X and 70% of our money in stock Y. For simplicity, suppose we invest only $1. Hence, our portfolio can be described as follows:
\[ W = 0.3R_X + 0.7R_Y, \]
where \( R_X \) is the stock return from investing in stock X and \( R_Y \) is the stock return from investing in stock Y. The stock returns vary based on the economic condition, and these conditions are classified in the table below:
| Probability | State of Economy | Stock Return \( R_X \) | Stock Return \( R_Y \) |
|-------------|------------------|------------------------|------------------------|
| 0.25 | Recession | -0.5 | -0.25 |
| 0.75 | Expansion | 0.8 | 0.3 |
### Questions to Explore
**(a) What is the expected return of the portfolio, i.e., \( E(W) \)?**
**(b) What is the variance of the portfolio, \( i.e., \ \text{Var}(W) \)?** Assume that \( R_X \) and \( R_Y \) are independent.
**(c) What is the variance of the portfolio, \( i.e., \ \text{Var}(W) \)?** Assume that \( R_X \) and \( R_Y \) have a negative correlation where \( \rho = -0.3 \).
### Analysis:
1. **Expected Return of the Portfolio:**
The expected return \( E(W) \) of the portfolio can be calculated as the weighted average of the expected returns of the individual stocks.
2. **Variance of the Portfolio (Independent Returns):**
If \( R_X \) and \( R_Y \) are independent, the variance of the portfolio can be computed considering the individual variances of the stock returns.
3. **Variance of the Portfolio (Correlated Returns):**
If \( R_X \) and \( R_Y \) have a correlation \( \rho = -0.3 \), the variance calculation must account for this correlation.
This analysis helps investors understand the trade-off between risk](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa420ac02-9353-4fae-9e0a-5b221122383e%2F86485de2-8dc8-4571-9995-21b44b66f4be%2F8dppblh_processed.png&w=3840&q=75)
Transcribed Image Text:## Portfolio Analysis for Stock Investment
To understand the potential returns and risks of a simple portfolio, consider the following example where we have chosen two stocks, X and Y. We will invest 30% of our money in stock X and 70% of our money in stock Y. For simplicity, suppose we invest only $1. Hence, our portfolio can be described as follows:
\[ W = 0.3R_X + 0.7R_Y, \]
where \( R_X \) is the stock return from investing in stock X and \( R_Y \) is the stock return from investing in stock Y. The stock returns vary based on the economic condition, and these conditions are classified in the table below:
| Probability | State of Economy | Stock Return \( R_X \) | Stock Return \( R_Y \) |
|-------------|------------------|------------------------|------------------------|
| 0.25 | Recession | -0.5 | -0.25 |
| 0.75 | Expansion | 0.8 | 0.3 |
### Questions to Explore
**(a) What is the expected return of the portfolio, i.e., \( E(W) \)?**
**(b) What is the variance of the portfolio, \( i.e., \ \text{Var}(W) \)?** Assume that \( R_X \) and \( R_Y \) are independent.
**(c) What is the variance of the portfolio, \( i.e., \ \text{Var}(W) \)?** Assume that \( R_X \) and \( R_Y \) have a negative correlation where \( \rho = -0.3 \).
### Analysis:
1. **Expected Return of the Portfolio:**
The expected return \( E(W) \) of the portfolio can be calculated as the weighted average of the expected returns of the individual stocks.
2. **Variance of the Portfolio (Independent Returns):**
If \( R_X \) and \( R_Y \) are independent, the variance of the portfolio can be computed considering the individual variances of the stock returns.
3. **Variance of the Portfolio (Correlated Returns):**
If \( R_X \) and \( R_Y \) have a correlation \( \rho = -0.3 \), the variance calculation must account for this correlation.
This analysis helps investors understand the trade-off between risk
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