Where:

• \( w_i \) — Weight of asset i in the portfolio
• \( \sigma_i \) — Standard deviation of returns for asset i
• \( \text{Cov}_{ij} \) — Covariance between returns of assets i and j
• \( n \) — Number of assets in the portfolio

Explanation: The formula accounts for both the individual risk of each asset (first term) and the co-movement between different assets (second term).

3. Importance of Portfolio Variance

Details: Portfolio variance helps investors understand the overall risk of their investment portfolio. Lower variance indicates more stable returns, while higher variance suggests greater volatility and potential for larger swings in portfolio value.

4. Using the Calculator

Tips: Enter weights as comma-separated values (sum should be 1), standard deviations as comma-separated values, and the covariance matrix row by row. Ensure all arrays have the same length corresponding to the number of assets.

5. Frequently Asked Questions (FAQ)

Q1: Why is covariance important in portfolio variance?
A: Covariance measures how two assets move together. Negative covariance can reduce overall portfolio risk through diversification.

Q2: How does portfolio variance differ from individual asset variance?
A: Portfolio variance considers not only individual risks but also how assets interact, which can lead to risk reduction through diversification.

Q3: What is a good portfolio variance value?
A: There's no universal "good" value - it depends on investor risk tolerance. Generally, lower variance indicates less risk.

Q4: Can portfolio variance be negative?
A: No, variance is always non-negative as it measures squared deviations from the mean.

Q5: How often should I calculate portfolio variance?
A: Regular monitoring (quarterly or annually) is recommended, especially after significant market movements or portfolio changes.