Stock X has a standard deviation of return of 30%. Stock Y has a standard deviation of return of 20%. The correlation coefficient between the two stocks is 0.33. If you invest 60% of your funds in Stock X and 40% in Stock Y.

The standard deviation of your portfolio is, therefore ______**%**.

(Please enter your answer as a *percentage* to two decimal places. i.e. 12.35 rather than 0.1235)

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.

Stock X has a standard deviation of return of 30%. Stock Y has a standard deviation of return of 20%. The correlation coefficient between the two stocks is 0.33. If you invest 60% of your funds in Stock X and 40% in Stock Y, the standard deviation of your portfolio is, therefore, ______%. (Please enter your answer as a percentage to two decimal places. i.e. 12.35 rather than 0.1235)

Learn how to calculate the standard deviation of a portfolio with Stock X (30% return volatility) and Stock Y (20% return volatility), using a correlation coefficient of 0.33 and weighted allocations of 60% and 40%. This step-by-step guide covers essential concepts from portfolio theory and statistics, suitable for students in advanced high school or undergraduate finance programs.

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