To calculate the standard deviation of a portfolio with two stocks, you can use the following formula:

$\sigma_p = \sqrt{(w_X^2 \cdot \sigma_X^2) + (w_Y^2 \cdot \sigma_Y^2) + 2 \cdot w_X \cdot w_Y \cdot \text{Corr}(X,Y) \cdot \sigma_X \cdot \sigma_Y}$

Where:

• $\sigma_p$ is the standard deviation of the portfolio,
• $w_X$ and $w_Y$ are the weights of Stock X and Stock Y in the portfolio (60% and 40%, respectively),
• $\sigma_X$ and $\sigma_Y$ are the standard deviations of Stock X and Stock Y (10% and 20%, respectively),
• $\text{Corr}(X,Y)$ is the correlation coefficient between Stock X and Stock Y (0.5).

Step-by-step calculation:

1. Given values:

   • $w_X = 0.60$
   • $w_Y = 0.40$
   • $\sigma_X = 10\% = 0.10$
   • $\sigma_Y = 20\% = 0.20$
   • $\text{Corr}(X,Y) = 0.5$

2. Substitute values into the formula:

$\sigma_p = \sqrt{(0.60^2 \cdot 0.10^2) + (0.40^2 \cdot 0.20^2) + 2 \cdot 0.60 \cdot 0.40 \cdot 0.5 \cdot 0.10 \cdot 0.20}$

3. Calculate each term:

   • $(0.60^2 \cdot 0.10^2) = 0.36 \cdot 0.01 = 0.0036$
   • $(0.40^2 \cdot 0.20^2) = 0.16 \cdot 0.04 = 0.0064$
   • $2 \cdot 0.60 \cdot 0.40 \cdot 0.5 \cdot 0.10 \cdot 0.20 = 2 \cdot 0.60 \cdot 0.40 \cdot 0.5 \cdot 0.02 = 0.0048$

4. Add these results:

$\sigma_p = \sqrt{0.0036 + 0.0064 + 0.0048} = \sqrt{0.0148}$

5. Final result:

$\sigma_p = \sqrt{0.0148} \approx 0.1217 \text{ or } 12.17\%$

Answer:

The standard deviation of the portfolio is approximately 12.17%.

---

Would you like a more detailed explanation of the steps or have any questions about the process?

Here are 5 related questions you could explore:

1. How would the portfolio standard deviation change if the correlation between the stocks were 1 or -1?
2. What is the effect of increasing or decreasing the weight of Stock X on the portfolio's standard deviation?
3. How does diversification impact the portfolio standard deviation in this case?
4. How can you calculate the expected return of this portfolio?
5. What are some other methods for reducing the risk in a portfolio?

Tip: To reduce portfolio risk, you can focus on increasing diversification by adding more assets with lower correlations to the existing ones.