To calculate the standard deviation of a portfolio consisting of two assets, we use the following formula:

$\sigma_p = \sqrt{w_1^2 \cdot \sigma_1^2 + w_2^2 \cdot \sigma_2^2 + 2 \cdot w_1 \cdot w_2 \cdot \sigma_1 \cdot \sigma_2 \cdot \rho}$

Where:

• $\sigma_p$ is the standard deviation of the portfolio,
• $w_1$ and $w_2$ are the weights of Cisco and Apple in the portfolio,
• $\sigma_1$ and $\sigma_2$ are the standard deviations of Cisco and Apple, respectively,
• $\rho$ is the correlation between the two stocks.

Given values:

• $w_1 = 0.31$ (Cisco Systems weight),
• $w_2 = 0.69$ (Apple Computer weight),
• $\sigma_1 = 0.36$ (standard deviation of Cisco Systems stock),
• $\sigma_2 = 0.29$ (standard deviation of Apple Computer stock),
• $\rho = 0.50$ (correlation between Cisco and Apple).

Let’s calculate the portfolio’s standard deviation.

First, compute each term separately and then sum them up.The standard deviation of the portfolio is approximately 27.35%.

Would you like more details on this calculation, or do you have any further questions?

Here are 5 related questions to deepen your understanding:

1. How does changing the correlation between two stocks affect the portfolio’s risk?
2. What happens to the portfolio standard deviation if both stocks had a correlation of 1?
3. How would increasing the weight of Cisco Systems to 50% impact the portfolio’s risk?
4. Why does diversification help in reducing portfolio risk?
5. What is the significance of standard deviation in assessing the risk of a portfolio?

Tip: A lower correlation between assets in a portfolio usually leads to a reduction in overall risk, as their movements offset each other.