1. What is the Minimum Variance Portfolio?

The Minimum Variance Portfolio is a portfolio of assets that has the lowest possible variance (risk) for a given set of assets. It's a key concept in modern portfolio theory and provides the most efficient risk-return tradeoff when assets are uncorrelated.

2. How Does the Calculator Work?

The calculator uses the Minimum Variance Portfolio formula:

Where:

• \( w_i \) — Weight of asset i in the portfolio
• \( \sigma_i^2 \) — Variance of asset i
• \( n \) — Number of assets in the portfolio

Explanation: The formula assigns higher weights to assets with lower variance (lower risk) and lower weights to assets with higher variance.

3. Importance of Portfolio Optimization

Details: Portfolio optimization helps investors minimize risk for a given level of expected return. The minimum variance portfolio represents the left-most point on the efficient frontier.

4. Using the Calculator

Tips: Enter the variance (σ²) for each asset as decimal values (e.g., 0.04 for 4% variance). You can calculate up to 4 assets. All variance values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between variance and standard deviation?
A: Variance is the square of standard deviation. Both measure risk, but variance is additive while standard deviation is not.

Q2: Does this work for correlated assets?
A: This simple formula assumes uncorrelated assets. For correlated assets, a more complex optimization using covariance is needed.

Q3: How many assets can I include?
A: The calculator handles 2-4 assets, but the formula can theoretically handle any number of assets.

Q4: What if I have expected returns data?
A: You would then use Markowitz portfolio optimization which considers both expected returns and risk.

Q5: Why would I want the minimum variance portfolio?
A: It's ideal for extremely risk-averse investors who want to minimize volatility regardless of expected return.