
An investor puts 31.00% of his investment into Cisco Systems, and the remaining 69.00% into Apple Computer. The standard deviation on Cisco Systems stock is 36.00%, while the standard deviation on Apple Computer is 29.00%. Find the standard deviation of this portfolio if the correlation between the two stocks is 0.50.

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.

An investor puts 31.00% of his investment into Cisco Systems, and the remaining 69.00% into Apple Computer. The standard deviation on Cisco Systems stock is 36.00%, while the standard deviation on Apple Computer is 29.00%. Find the standard deviation of this portfolio if the correlation between the two stocks is 0.50.

Learn how to calculate the portfolio standard deviation when investing 31% in Cisco Systems and 69% in Apple Computer, with stock standard deviations of 36% and 29%, respectively, and a correlation of 0.50. This solution uses Modern Portfolio Theory to demonstrate the calculation of portfolio risk.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation