The formula for the standard deviation of a two-asset portfolio is given by:

$\sigma_p = \sqrt{w_X^2 \cdot \sigma_X^2 + w_Y^2 \cdot \sigma_Y^2 + 2 \cdot w_X \cdot w_Y \cdot \sigma_X \cdot \sigma_Y \cdot \rho_{XY}}$

Where:

• $\sigma_p$ is the standard deviation of the portfolio,
• $w_X$ and $w_Y$ are the weights of Stock X and Stock Y, respectively,
• $\sigma_X$ and $\sigma_Y$ are the standard deviations of Stock X and Stock Y, respectively,
• $\rho_{XY}$ is the correlation coefficient between Stock X and Stock Y.

Given dataThe formula for the standard deviation of a two-asset portfolio is given by:

$\sigma_p = \sqrt{w_X^2 \cdot \sigma_X^2 + w_Y^2 \cdot \sigma_Y^2 + 2 \cdot w_X \cdot w_Y \cdot \sigma_X \cdot \sigma_Y \cdot \rho_{XY}}$

Where:

• $\sigma_p$ is the standard deviation of the portfolio,
• $w_X$ and $w_Y$ are the weights of Stock X and Stock Y, respectively,
• $\sigma_X$ and $\sigma_Y$ are the standard deviations of Stock X and Stock Y, respectively,
• $\rho_{XY}$ is the correlation coefficient between Stock X and Stock Y.

Given

• $w_X = 0.60$,
• $w_Y = 0.40$,
• $\sigma_X = 30\% = 0.30$,
• $\sigma_Y = 20\% = 0.20$,
• $\rho_{XY} = 0.33$.

Now, substituting the values into the formula:

$\sigma_p = \sqrt{(0.60)^2 \cdot (0.30)^2 + (0.40)^2 \cdot (0.20)^2 + 2 \cdot 0.60 \cdot 0.40 \cdot 0.30 \cdot 0.20 \cdot 0.33}$

Let's break it down step by step:

1. $(0.60)^2 \cdot (0.30)^2 = 0.36 \cdot 0.09 = 0.0324$,
2. $(0.40)^2 \cdot (0.20)^2 = 0.16 \cdot 0.04 = 0.0064$,
3. $2 \cdot 0.60 \cdot 0.40 \cdot 0.30 \cdot 0.20 \cdot 0.33 = 2 \cdot 0.072 \cdot 0.33 = 0.04752$.

Now, summing these:

$\sigma_p^2 = 0.0324 + 0.0064 + 0.04752 = 0.08632$

Taking the square root:

$\sigma_p = \sqrt{0.08632} \approx 0.2938$

Converting this to a percentage:

$\sigma_p \approx 29.38\%$

Therefore, the standard deviation of your portfolio is 29.38%.

Would you like more details or have any questions?

Here are 5 related questions:

1. How does the correlation coefficient between two stocks affect the portfolio's standard deviation?
2. What would happen to the portfolio risk if the correlation coefficient was negative?
3. How do you compute the expected return of a portfolio?
4. Can you explain the significance of diversification in reducing portfolio risk?
5. How would the portfolio's risk change if Stock X had a lower standard deviation?

Tip: Lower correlation between assets generally leads to better diversification and lower overall portfolio risk.