1. What is the Minimum Variance Portfolio?

The Minimum Variance Portfolio is the portfolio of assets that has the lowest possible variance (risk) for a given set of assets, subject to the constraint that the weights sum to 1 (fully invested).

2. How Does the Calculator Work?

The calculator solves the optimization problem:

Where:

• \( w \) — Vector of portfolio weights
• \( \Sigma \) — Covariance matrix of asset returns

Explanation: The solution finds weights that minimize portfolio variance while being fully invested.

3. Importance of Portfolio Optimization

Details: Finding the minimum variance portfolio helps investors construct efficient portfolios that maximize returns for a given level of risk.

4. Using the Calculator

Tips: Enter the covariance matrix of asset returns as comma-separated values, with each row on a new line. The matrix must be symmetric and positive definite.

5. Frequently Asked Questions (FAQ)

Q1: Why use minimum variance portfolio?
A: It provides the lowest possible risk portfolio for a given set of assets, which is particularly useful for risk-averse investors.

Q2: What are the limitations?
A: It relies on accurate estimation of the covariance matrix and doesn't consider expected returns.

Q3: How often should the covariance matrix be updated?
A: For optimal results, update the covariance matrix regularly as market conditions change.

Q4: Can I add constraints to the optimization?
A: This basic version only includes the sum-to-one constraint. More advanced versions can include additional constraints.

Q5: What if my weights are negative?
A: Negative weights indicate short selling. If you want to prohibit short selling, you would need to add non-negativity constraints.